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• 3 Questions: How history helps us solve today's issues

3 Questions: How history helps us solve today's issues

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Science and technology are essential tools for innovation, and to reap their full potential, we also need to articulate and solve the many aspects of today’s global issues that are rooted in the political, cultural, and economic realities of the human world. With that mission in mind, MIT's School of Humanities, Arts, and Social Sciences has launched The Human Factor — an ongoing series of stories and interviews that highlight research on the human dimensions of global challenges. Contributors to this series also share ideas for cultivating the multidisciplinary collaborations needed to solve the major civilizational issues of our time.

Malick Ghachem is an attorney and a professor of history at MIT who explores questions of slavery and abolition, criminal law, and constitutional history. He is the author of  "The Old Regime and the Haitian Revolution" (Cambridge University Press, 2012), a history of the law of slavery in Saint-Domingue (Haiti) between 1685 and 1804. He teaches courses on the Age of Revolution, slavery and abolition, American criminal justice, and other topics. MIT SHASS Communications recently asked him to share his thoughts on how history can help people craft more effective public policies for today's world.  Q: Your new research focuses on economic globalization and political protest in Haiti, a country with a complex social, political, and economic history. What lessons can we learn from Haiti's history that can inform more effective public policies? A: I think the most important lesson for public policy may be that we cannot ignore the distant past — and in the case of Haiti, by "distant past" I mean only so far back as the 18th century. (With apologies to colleagues who study the yet more distant centuries of ancient and medieval history!) Public policy has a short-term memory, however, and this is especially true of economic policy, which tends to look back only so far as the early 20th century to understand, for example, how a financial crisis comes about and what it entails.

Haiti showcases the decisive present-day impact and legacies of a history that goes back more than 300 years, to the rise of the slave plantation system. My current work tells the story of a planter rebellion in the 1720s against the French Indies Company, an event that ended the era of slave-trading monopolies in Saint-Domingue (as Haiti was known under French rule) and left large-scale sugar planters in effective control of the colony.

Some of the key political and social cleavages that have characterized Haitian life ever since date back to this period. A history of Haiti that begins with the revolutionary years leading up to Haitian independence in 1804, or any period thereafter, will necessarily lack a handle on just how deeply rooted are Haiti’s current circumstances.

We can see this on any number of levels. Colonial history continues to hamper prospects for broad-based education in Haiti, as my colleague Michel DeGraff’s work on the linguistic politics of French vs. Haitian Kreyòl powerfully demonstrates. The environment is another example. Part of the resistance to accepting the reality of climate change (whether in Haiti or elsewhere) is a reluctance to acknowledge that history in this deep sense matters. Yet it is clear that deforestation in Haiti begins no later than the 17th century, when French settlers began using trees for purposes of lumber and fuel. By the time of Haiti’s independence, the lack of forest cover had already left many parts of the country vulnerable to flooding.

That historical perspective, in turn, suggests one of the difficulties that besets even the most well-intentioned relief work in Haiti today. Such work tends to focus on repairing the immediate damage caused by the latest “natural” catastrophe, whether an earthquake, a hurricane-induced flood, or an outbreak of contagious disease. These tragedies rightly call upon the generous aid of first-responders, but after the sense of emergency passes, the eyes of the world often turn elsewhere.

An understanding of how these tragedies draw on the full weight of Haitian history encourages and even demands a longer-term commitment to the problems at hand. And it suggests that effective responses to what seem like essentially medical, environmental, or legal problems must cut across conventional categories of policy analysis and understandings of responsibility. Take the case of United Nations liability for the cholera outbreak in Haiti after the 2010 earthquake.

The natural impulse of human rights lawyers in that context was to file suit against the U.N., which then spent several years digging in its heels and denying its role in the outbreak. But the U.N.’s position in Haiti is a legacy of the much deeper impact that individual nations/states — most notably, France and the United States — have had on Haitian affairs over the course of three centuries. Framing responsibility in narrowly legal or chronological terms runs head-on into this reality and limits rather than expands our sense of the potential remedies.

Q: What connections do you see between economic conditions (including globalization and monetary policy) and the ability of a people or a culture to make innovations in science, technology, and public policy?

A: Waking up hungry each morning does not leave one with great deal of energy for scientific (or any other kind of) work during the day. The resources that make possible scientific and technological innovation are the same ones that sustain the relatively high standard of daily living many of us enjoy in the United States.

Haiti’s economy has long existed in a state of colonial dependency upon one or another foreign power; today it is the United States. The country’s economy is also beset by many woes, among them an ongoing currency crisis that makes the Haitian gourde an increasingly ineffective form of money. This fact places a premium on access to U.S. dollars, which elites and companies enjoy at the expense of workers paid in the local currency.

This is a crisis of sovereignty that takes the form of a monetary crisis. The earliest such currency crisis dates back (again) to the 1720s, and it’s one dimension of my current research. One of the two key triggers of the revolt against the Indies Company was a suspicion that the Company intended to eliminate the use of local Spanish silver coins, on which most colonists depended for their livelihood. The lack of a reliable and stable currency remained a problem throughout the colonial period and continues to severely constrict the economic horizons of many Haitians today.

Q: As MIT President Reif has said, solving the great challenges of our time will require multidisciplinary problem-solving — bringing together expertise and ideas from the sciences, technology, the social sciences, arts, and humanities. Can you share why you believe it is critical for any effort to address the well-being of human populations, and the planet itself, to incorporate tools and perspectives from the field of history? Also, what challenges do you see to multi-disciplinary collaborations — and how can we overcome them?

A: President Reif’s observation is correct and important. We also need to appreciate that, even within the world of the social sciences and the humanities, there are deep and abiding differences about how best to understand and implement public policy.

Let’s take the case of development economics. There is a growing literature, associated mostly with political economy and the new institutional economics, that seeks to explain the disparities in wealth and income between more and less “developed” nations. These works tend to suggest that there is a unifying model, theory, or historical pattern that accounts for the disparities: political corruption, institutional competence, the rule of law, protection of private property, etc. These phenomena are all important, but the particular forms they take can really only be understood on a case-by-case basis.

It’s important to do the unglamorous, nitty-gritty, heavily historical work of understanding the local and the particular — which requires much more patience that even those social scientists who speak of “path dependence” tend to exhibit. I believe that this kind of sustained patience for understanding the local in historical contexts is itself a tool of public policy, a way of seeing and talking about the world, and (if wielded correctly) an instrument of power and justice.

One of the principal ways historians can contribute to problem-solving work at MIT and elsewhere is by helping to identify what the real problem is in the first place. When we can understand and articulate the roots and sources of a problem, we have a much better chance of solving it.

Interview prepared by MIT SHASS Communications Editorial team: Kathryn O'Neill, Emily Hiestand (series editor)

Share this news article on:, related links.

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• Book: "The Old Regime and the Haitian Revolution"
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• Article: "Black Histories Matter"

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A3 8 Step Practical Problem Solving – Skill Level 1: Knowledge

Brief history of modern problem solving methods.

The diagram below shows a “Time Line of Modern Problem Solving” and depicts some of the key milestones that have led to the processes used for problem solving in organisations today.

It is possible to trace the strands of the modern problem solving approaches we are familiar with in the lean movement. A five step problem solving method was originally taught in Japan as part of a course called The Fundamentals of Industrial Management by Homer Sarasohn and Charles Protzman. Deming’s modified Shewart cycle – known as the Deming Wheel was taken and developed by the Union of Japanese Scientists and Engineers (JUSE.) JUSE was key in the dissemination of problem solving processes under the guidance of Ichiro and Kaoru Ishikawa. In 1951

JUSE created the Plan-Do-Check-Act cycle which we know as PDCA. Despite Deming’s objections to the modification, this has become the dominant form of the Deming cycle today. They also invited Juran to Japan to give lectures in 1954.

Another key strand are the Training Within Industry (TWI) courses. Initially the 3J courses were taught, but in 1955, TWI Problem Solving was developed. The process outlined four basic steps of problem solving in the TWI framework to help train people, improve work methods and resolve problems in a structured way:

• 1 – Isolate the problem
• 2 – Prepare for solution
• 3 – Correct the problem
• 4 – Check and evaluate the results

In the 1960’s, various 6-step approaches were created. These can be summarised as follows:

Six Step Method

• 1- Define the problem.
• 2 – Determine the goal.
• 3 – Identify the root cause.
• 4 – Implement countermeasures.
• 5 – Check results.
• 6 – Follow up and standardise.

In the 1960’s and 70’s the concept of “kaizen” emerged in Japan. Its literal translation means “change for the better.” Different from structured problem solving and gap from standard situations, kaizen asks “How can the current standard or condition be improved upon?” Kaizen is not bound by the rules of root cause analysis thinking – it is more open ended. Processes are observed and considered for improvement.

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21 Problem Solving

Miriam Bassok, Department of Psychology, University of Washington, Seattle, WA

Laura R. Novick, Department of Psychology and Human Development, Vanderbilt University, Nashville, TN

• Published: 21 November 2012
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This chapter follows the historical development of research on problem solving. It begins with a description of two research traditions that addressed different aspects of the problem-solving process: ( 1 ) research on problem representation (the Gestalt legacy) that examined how people understand the problem at hand, and ( 2 ) research on search in a problem space (the legacy of Newell and Simon) that examined how people generate the problem's solution. It then describes some developments in the field that fueled the integration of these two lines of research: work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. Next, it presents examples of recent work on problem solving in science and mathematics that highlight the impact of visual perception and background knowledge on how people represent problems and search for problem solutions. The final section considers possible directions for future research.

People are confronted with problems on a daily basis, be it trying to extract a broken light bulb from a socket, finding a detour when the regular route is blocked, fixing dinner for unexpected guests, dealing with a medical emergency, or deciding what house to buy. Obviously, the problems people encounter differ in many ways, and their solutions require different types of knowledge and skills. Yet we have a sense that all the situations we classify as problems share a common core. Karl Duncker defined this core as follows: “A problem arises when a living creature has a goal but does not know how this goal is to be reached. Whenever one cannot go from the given situation to the desired situation simply by action [i.e., by the performance of obvious operations], then there has to be recourse to thinking” (Duncker, 1945 , p. 1). Consider the broken light bulb. The obvious operation—holding the glass part of the bulb with one's fingers while unscrewing the base from the socket—is prevented by the fact that the glass is broken. Thus, there must be “recourse to thinking” about possible ways to solve the problem. For example, one might try mounting half a potato on the broken bulb (we do not know the source of this creative solution, which is described on many “how to” Web sites).

The above definition and examples make it clear that what constitutes a problem for one person may not be a problem for another person, or for that same person at another point in time. For example, the second time one has to remove a broken light bulb from a socket, the solution likely can be retrieved from memory; there is no problem. Similarly, tying shoes may be considered a problem for 5-year-olds but not for readers of this chapter. And, of course, people may change their goal and either no longer have a problem (e.g., take the guests to a restaurant instead of fixing dinner) or attempt to solve a different problem (e.g., decide what restaurant to go to). Given the highly subjective nature of what constitutes a problem, researchers who study problem solving have often presented people with novel problems that they should be capable of solving and attempted to find regularities in the resulting problem-solving behavior. Despite the variety of possible problem situations, researchers have identified important regularities in the thinking processes by which people (a) represent , or understand, problem situations and (b) search for possible ways to get to their goal.

A problem representation is a model constructed by the solver that summarizes his or her understanding of the problem components—the initial state (e.g., a broken light bulb in a socket), the goal state (the light bulb extracted), and the set of possible operators one may apply to get from the initial state to the goal state (e.g., use pliers). According to Reitman ( 1965 ), problem components differ in the extent to which they are well defined . Some components leave little room for interpretation (e.g., the initial state in the broken light bulb example is relatively well defined), whereas other components may be ill defined and have to be defined by the solver (e.g., the possible actions one may take to extract the broken bulb). The solver's representation of the problem guides the search for a possible solution (e.g., possible attempts at extracting the light bulb). This search may, in turn, change the representation of the problem (e.g., finding that the goal cannot be achieved using pliers) and lead to a new search. Such a recursive process of representation and search continues until the problem is solved or until the solver decides to abort the goal.

Duncker ( 1945 , pp. 28–37) documented the interplay between representation and search based on his careful analysis of one person's solution to the “Radiation Problem” (later to be used extensively in research analogy, see Holyoak, Chapter 13 ). This problem requires using some rays to destroy a patient's stomach tumor without harming the patient. At sufficiently high intensity, the rays will destroy the tumor. However, at that intensity, they will also destroy the healthy tissue surrounding the tumor. At lower intensity, the rays will not harm the healthy tissue, but they also will not destroy the tumor. Duncker's analysis revealed that the solver's solution attempts were guided by three distinct problem representations. He depicted these solution attempts as an inverted search tree in which the three main branches correspond to the three general problem representations (Duncker, 1945 , p. 32). We reproduce this diagram in Figure 21.1 . The desired solution appears on the rightmost branch of the tree, within the general problem representation in which the solver aims to “lower the intensity of the rays on their way through healthy tissue.” The actual solution is to project multiple low-intensity rays at the tumor from several points around the patient “by use of lens.” The low-intensity rays will converge on the tumor, where their individual intensities will sum to a level sufficient to destroy the tumor.

A search-tree representation of one subject's solution to the radiation problem, reproduced from Duncker ( 1945 , p. 32).

Although there are inherent interactions between representation and search, some researchers focus their efforts on understanding the factors that affect how solvers represent problems, whereas others look for regularities in how they search for a solution within a particular representation. Based on their main focus of interest, researchers devise or select problems with solutions that mainly require either constructing a particular representation or finding the appropriate sequence of steps leading from the initial state to the goal state. In most cases, researchers who are interested in problem representation select problems in which one or more of the components are ill defined, whereas those who are interested in search select problems in which the components are well defined. The following examples illustrate, respectively, these two problem types.

The Bird-and-Trains problem (Posner, 1973 , pp. 150–151) is a mathematical word problem that tends to elicit two distinct problem representations (see Fig. 21.2a and b ):

Two train stations are 50 miles apart. At 2 p.m. one Saturday afternoon two trains start toward each other, one from each station. Just as the trains pull out of the stations, a bird springs into the air in front of the first train and flies ahead to the front of the second train. When the bird reaches the second train, it turns back and flies toward the first train. The bird continues to do this until the trains meet. If both trains travel at the rate of 25 miles per hour and the bird flies at 100 miles per hour, how many miles will the bird have flown before the trains meet? Fig. 21.2 Open in new tab Download slide Alternative representations of Posner's ( 1973 ) trains-and-bird problem. Adapted from Novick and Hmelo ( 1994 ).

Some solvers focus on the back-and-forth path of the bird (Fig. 21.2a ). This representation yields a problem that would be difficult for most people to solve (e.g., a series of differential equations). Other solvers focus on the paths of the trains (Fig. 21.2b ), a representation that yields a relatively easy distance-rate-time problem.

The Tower of Hanoi problem falls on the other end of the representation-search continuum. It leaves little room for differences in problem representations, and the primary work is to discover a solution path (or the best solution path) from the initial state to the goal state .

There are three pegs mounted on a base. On the leftmost peg, there are three disks of differing sizes. The disks are arranged in order of size with the largest disk on the bottom and the smallest disk on the top. The disks may be moved one at a time, but only the top disk on a peg may be moved, and at no time may a larger disk be placed on a smaller disk. The goal is to move the three-disk tower from the leftmost peg to the rightmost peg.

Figure 21.3 shows all the possible legal arrangements of disks on pegs. The arrows indicate transitions between states that result from moving a single disk, with the thicker gray arrows indicating the shortest path that connects the initial state to the goal state.

The division of labor between research on representation versus search has distinct historical antecedents and research traditions. In the next two sections, we review the main findings from these two historical traditions. Then, we describe some developments in the field that fueled the integration of these lines of research—work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. In the fifth section, we present some examples of recent work on problem solving in science and mathematics. This work highlights the role of visual perception and background knowledge in the way people represent problems and search for problem solutions. In the final section, we consider possible directions for future research.

Our review is by no means an exhaustive one. It follows the historical development of the field and highlights findings that pertain to a wide variety of problems. Research pertaining to specific types of problems (e.g., medical problems), specific processes that are involved in problem solving (e.g., analogical inferences), and developmental changes in problem solving due to learning and maturation may be found elsewhere in this volume (e.g., Holyoak, Chapter 13 ; Smith & Ward, Chapter 23 ; van Steenburgh et al., Chapter 24 ; Simonton, Chapter 25 ; Opfer & Siegler, Chapter 30 ; Hegarty & Stull, Chapter 31 ; Dunbar & Klahr, Chapter 35 ; Patel et al., Chapter 37 ; Lowenstein, Chapter 38 ; Koedinger & Roll, Chapter 40 ).

All possible problem states for the three-disk Tower of Hanoi problem. The thicker gray arrows show the optimum solution path connecting the initial state (State #1) to the goal state (State #27).

Problem Representation: The Gestalt Legacy

Research on problem representation has its origins in Gestalt psychology, an influential approach in European psychology during the first half of the 20th century. (Behaviorism was the dominant perspective in American psychology at this time.) Karl Duncker published a book on the topic in his native German in 1935, which was translated into English and published 10 years later as the monograph On Problem-Solving (Duncker, 1945 ). Max Wertheimer also published a book on the topic in 1945, titled Productive Thinking . An enlarged edition published posthumously includes previously unpublished material (Wertheimer, 1959 ). Interestingly, 1945 seems to have been a watershed year for problem solving, as mathematician George Polya's book, How to Solve It , also appeared then (a second edition was published 12 years later; Polya, 1957 ).

The Gestalt psychologists extended the organizational principles of visual perception to the domain of problem solving. They showed that various visual aspects of the problem, as well the solver's prior knowledge, affect how people understand problems and, therefore, generate problem solutions. The principles of visual perception (e.g., proximity, closure, grouping, good continuation) are directly relevant to problem solving when the physical layout of the problem, or a diagram that accompanies the problem description, elicits inferences that solvers include in their problem representations. Such effects are nicely illustrated by Maier's ( 1930 ) nine-dot problem: Nine dots are arrayed in a 3x3 grid, and the task is to connect all the dots by drawing four straight lines without lifting one's pencil from the paper. People have difficulty solving this problem because their initial representations generally include a constraint, inferred from the configuration of the dots, that the lines should not go outside the boundary of the imaginary square formed by the outer dots. With this constraint, the problem cannot be solved (but see Adams, 1979 ). Without this constraint, the problem may be solved as shown in Figure 21.4 (though the problem is still difficult for many people; see Weisberg & Alba, 1981 ).

The nine-dot problem is a classic insight problem (see van Steenburgh et al., Chapter 24 ). According to the Gestalt view (e.g., Duncker, 1945 ; Kohler, 1925 ; Maier, 1931 ; see Ohlsson, 1984 , for a review), the solution to an insight problem appears suddenly, accompanied by an “aha!” sensation, immediately following the sudden “restructuring” of one's understanding of the problem (i.e., a change in the problem representation): “The decisive points in thought-processes, the moments of sudden comprehension, of the ‘Aha!,’ of the new, are always at the same time moments in which such a sudden restructuring of the thought-material takes place” (Duncker, 1945 , p. 29). For the nine-dot problem, one view of the required restructuring is that the solver relaxes the constraint implied by the perceptual form of the problem and realizes that the lines may, in fact, extend past the boundary of the imaginary square. Later in the chapter, we present more recent accounts of insight.

The entities that appear in a problem also tend to evoke various inferences that people incorporate into their problem representations. A classic demonstration of this is the phenomenon of functional fixedness , introduced by Duncker ( 1945 ): If an object is habitually used for a certain purpose (e.g., a box serves as a container), it is difficult to see

A solution to the nine-dot problem.

that object as having properties that would enable it to be used for a dissimilar purpose. Duncker's basic experimental paradigm involved two conditions that varied in terms of whether the object that was crucial for solution was initially used for a function other than that required for solution.

Consider the candles problem—the best known of the five “practical problems” Duncker ( 1945 ) investigated. Three candles are to be mounted at eye height on a door. On the table, for use in completing this task, are some tacks and three boxes. The solution is to tack the three boxes to the door to serve as platforms for the candles. In the control condition, the three boxes were presented to subjects empty. In the functional-fixedness condition, they were filled with candles, tacks, and matches. Thus, in the latter condition, the boxes initially served the function of container, whereas the solution requires that they serve the function of platform. The results showed that 100% of the subjects who received empty boxes solved the candles problem, compared with only 43% of subjects who received filled boxes. Every one of the five problems in this study showed a difference favoring the control condition over the functional-fixedness condition, with average solution rates across the five problems of 97% and 58%, respectively.

The function of the objects in a problem can be also “fixed” by their most recent use. For example, Birch and Rabinowitz ( 1951 ) had subjects perform two consecutive tasks. In the first task, people had to use either a switch or a relay to form an electric circuit. After completing this task, both groups of subjects were asked to solve Maier's ( 1931 ) two-ropes problem. The solution to this problem requires tying an object to one of the ropes and making the rope swing as a pendulum. Subjects could create the pendulum using either the object from the electric-circuit task or the other object. Birch and Rabinowitz found that subjects avoided using the same object for two unrelated functions. That is, those who used the switch in the first task made the pendulum using the relay, and vice versa. The explanations subjects subsequently gave for their object choices revealed that they were unaware of the functional-fixedness constraint they imposed on themselves.

In addition to investigating people's solutions to such practical problems as irradiating a tumor, mounting candles on the wall, or tying ropes, the Gestalt psychologists examined how people understand and solve mathematical problems that require domain-specific knowledge. For example, Wertheimer ( 1959 ) observed individual differences in students' learning and subsequent application of the formula for finding the area of a parallelogram (see Fig. 21.5a ). Some students understood the logic underlying the learned formula (i.e., the fact that a parallelogram can be transformed into a rectangle by cutting off a triangle from one side and pasting it onto the other side) and exhibited “productive thinking”—using the same logic to find the area of the quadrilateral in Figure 21.5b and the irregularly shaped geometric figure in Figure 21.5c . Other students memorized the formula and exhibited “reproductive thinking”—reproducing the learned solution only to novel parallelograms that were highly similar to the original one.

The psychological study of human problem solving faded into the background after the demise of the Gestalt tradition (during World War II), and problem solving was investigated only sporadically until Allen Newell and Herbert Simon's ( 1972 ) landmark book Human Problem Solving sparked a flurry of research on this topic. Newell and Simon adopted and refined Duncker's ( 1945 ) methodology of collecting and analyzing the think-aloud protocols that accompany problem solutions and extended Duncker's conceptualization of a problem solution as a search tree. However, their initial work did not aim to extend the Gestalt findings

Finding the area of ( a ) a parallelogram, ( b ) a quadrilateral, and ( c ) an irregularly shaped geometric figure. The solid lines indicate the geometric figures whose areas are desired. The dashed lines show how to convert the given figures into rectangles (i.e., they show solutions with understanding).

pertaining to problem representation. Instead, as we explain in the next section, their objective was to identify the general-purpose strategies people use in searching for a problem solution.

Search in a Problem Space: The Legacy of Newell and Simon

Newell and Simon ( 1972 ) wrote a magnum opus detailing their theory of problem solving and the supporting research they conducted with various collaborators. This theory was grounded in the information-processing approach to cognitive psychology and guided by an analogy between human and artificial intelligence (i.e., both people and computers being “Physical Symbol Systems,” Newell & Simon, 1976 ; see Doumas & Hummel, Chapter 5 ). They conceptualized problem solving as a process of search through a problem space for a path that connects the initial state to the goal state—a metaphor that alludes to the visual or spatial nature of problem solving (Simon, 1990 ). The term problem space refers to the solver's representation of the task as presented (Simon, 1978 ). It consists of ( 1 ) a set of knowledge states (the initial state, the goal state, and all possible intermediate states), ( 2 ) a set of operators that allow movement from one knowledge state to another, ( 3 ) a set of constraints, and ( 4 ) local information about the path one is taking through the space (e.g., the current knowledge state and how one got there).

We illustrate the components of a problem space for the three-disk Tower of Hanoi problem, as depicted in Figure 21.3 . The initial state appears at the top (State #1) and the goal state at the bottom right (State #27). The remaining knowledge states in the figure are possible intermediate states. The current knowledge state is the one at which the solver is located at any given point in the solution process. For example, the current state for a solver who has made three moves along the optimum solution path would be State #9. The solver presumably would know that he or she arrived at this state from State #5. This knowledge allows the solver to recognize a move that involves backtracking. The three operators in this problem are moving each of the three disks from one peg to another. These operators are subject to the constraint that a larger disk may not be placed on a smaller disk.

Newell and Simon ( 1972 ), as well as other contemporaneous researchers (e.g., Atwood & Polson, 1976 ; Greeno, 1974 ; Thomas, 1974 ), examined how people traverse the spaces of various well-defined problems (e.g., the Tower of Hanoi, Hobbits and Orcs). They discovered that solvers' search is guided by a number of shortcut strategies, or heuristics , which are likely to get the solver to the goal state without an extensive amount of search. Heuristics are often contrasted with algorithms —methods that are guaranteed to yield the correct solution. For example, one could try every possible move in the three-disk Tower of Hanoi problem and, eventually, find the correct solution. Although such an exhaustive search is a valid algorithm for this problem, for many problems its application is very time consuming and impractical (e.g., consider the game of chess).

In their attempts to identify people's search heuristics, Newell and Simon ( 1972 ) relied on two primary methodologies: think-aloud protocols and computer simulations. Their use of think-aloud protocols brought a high degree of scientific rigor to the methodology used by Duncker ( 1945 ; see Ericsson & Simon, 1980 ). Solvers were required to say out loud everything they were thinking as they solved the problem, that is, everything that went through their verbal working memory. Subjects' verbalizations—their think-aloud protocols—were tape-recorded and then transcribed verbatim for analysis. This method is extremely time consuming (e.g., a transcript of one person's solution to the cryptarithmetic problem DONALD + GERALD = ROBERT, with D = 5, generated a 17-page transcript), but it provides a detailed record of the solver's ongoing solution process.

An important caveat to keep in mind while interpreting a subject's verbalizations is that “a protocol is relatively reliable only for what it positively contains, but not for that which it omits” (Duncker, 1945 , p. 11). Ericsson and Simon ( 1980 ) provided an in-depth discussion of the conditions under which this method is valid (but see Russo, Johnson, & Stephens, 1989 , for an alternative perspective). To test their interpretation of a subject's problem solution, inferred from the subject's verbal protocol, Newell and Simon ( 1972 ) created a computer simulation program and examined whether it solved the problem the same way the subject did. To the extent that the computer simulation provided a close approximation of the solver's step-by-step solution process, it lent credence to the researcher's interpretation of the verbal protocol.

Newell and Simon's ( 1972 ) most famous simulation was the General Problem Solver or GPS (Ernst & Newell, 1969 ). GPS successfully modeled human solutions to problems as different as the Tower of Hanoi and the construction of logic proofs using a single general-purpose heuristic: means-ends analysis . This heuristic captures people's tendency to devise a solution plan by setting subgoals that could help them achieve their final goal. It consists of the following steps: ( 1 ) Identify a difference between the current state and the goal (or subgoal ) state; ( 2 ) Find an operator that will remove (or reduce) the difference; (3a) If the operator can be directly applied, do so, or (3b) If the operator cannot be directly applied, set a subgoal to remove the obstacle that is preventing execution of the desired operator; ( 4 ) Repeat steps 1–3 until the problem is solved. Next, we illustrate the implementation of this heuristic for the Tower of Hanoi problem, using the problem space in Figure 21.3 .

As can be seen in Figure 21.3 , a key difference between the initial state and the goal state is that the large disk is on the wrong peg (step 1). To remove this difference (step 2), one needs to apply the operator “move-large-disk.” However, this operator cannot be applied because of the presence of the medium and small disks on top of the large disk. Therefore, the solver may set a subgoal to move that two-disk tower to the middle peg (step 3b), leaving the rightmost peg free for the large disk. A key difference between the initial state and this new subgoal state is that the medium disk is on the wrong peg. Because application of the move-medium-disk operator is blocked, the solver sets another subgoal to move the small disk to the right peg. This subgoal can be satisfied immediately by applying the move-small-disk operator (step 3a), generating State #3. The solver then returns to the previous subgoal—moving the tower consisting of the small and medium disks to the middle peg. The differences between the current state (#3) and the subgoal state (#9) can be removed by first applying the move-medium-disk operator (yielding State #5) and then the move-small-disk operator (yielding State #9). Finally, the move-large-disk operator is no longer blocked. Hence, the solver moves the large disk to the right peg, yielding State #11.

Notice that the subgoals are stacked up in the order in which they are generated, so that they pop up in the order of last in first out. Given the first subgoal in our example, repeated application of the means-ends analysis heuristic will yield the shortest-path solution, indicated by the large gray arrows. In general, subgoals provide direction to the search and allow solvers to plan several moves ahead. By assessing progress toward a required subgoal rather than the final goal, solvers may be able to make moves that otherwise seem unwise. To take a concrete example, consider the transition from State #1 to State #3 in Figure 21.3 . Comparing the initial state to the goal state, this move seems unwise because it places the small disk on the bottom of the right peg, whereas it ultimately needs to be at the top of the tower on that peg. But comparing the initial state to the solver-generated subgoal state of having the medium disk on the middle peg, this is exactly where the small disk needs to go.

Means-ends analysis and various other heuristics (e.g., the hill-climbing heuristic that exploits the similarity, or distance, between the state generated by the next operator and the goal state; working backward from the goal state to the initial state) are flexible strategies that people often use to successfully solve a large variety of problems. However, the generality of these heuristics comes at a cost: They are relatively weak and fallible (e.g., in the means-ends solution to the problem of fixing a hole in a bucket, “Dear Liza” leads “Dear Henry” in a loop that ends back at the initial state; the lyrics of this famous song can be readily found on the Web). Hence, although people use general-purpose heuristics when they encounter novel problems, they replace them as soon as they acquire experience with and sufficient knowledge about the particular problem space (e.g., Anzai & Simon, 1979 ).

Despite the fruitfulness of this research agenda, it soon became evident that a fundamental weakness was that it minimized the importance of people's background knowledge. Of course, Newell and Simon ( 1972 ) were aware that problem solutions require relevant knowledge (e.g., the rules of logical proofs, or rules for stacking disks). Hence, in programming GPS, they supplemented every problem they modeled with the necessary background knowledge. This practice highlighted the generality and flexibility of means-ends analysis but failed to capture how people's background knowledge affects their solutions. As we discussed in the previous section, domain knowledge is likely to affect how people represent problems and, therefore, how they generate problem solutions. Moreover, as people gain experience solving problems in a particular knowledge domain (e.g., math, physics), they change their representations of these problems (e.g., Chi, Feltovich, & Glaser, 1981 ; Haverty, Koedinger, Klahr, & Alibali, 2000 ; Schoenfeld & Herrmann, 1982 ) and learn domain-specific heuristics (e.g., Polya, 1957 ; Schoenfeld, 1979 ) that trump the general-purpose strategies.

It is perhaps inevitable that the two traditions in problem-solving research—one emphasizing representation and the other emphasizing search strategies—would eventually come together. In the next section we review developments that led to this integration.

The Two Legacies Converge

Because Newell and Simon ( 1972 ) aimed to discover the strategies people use in searching for a solution, they investigated problems that minimized the impact of factors that tend to evoke differences in problem representations, of the sort documented by the Gestalt psychologists. In subsequent work, however, Simon and his collaborators showed that such factors are highly relevant to people's solutions of well-defined problems, and Simon ( 1986 ) incorporated these findings into the theoretical framework that views problem solving as search in a problem space.

In this section, we first describe illustrative examples of this work. We then describe research on insight solutions that incorporates ideas from the two legacies described in the previous sections.

Relevance of the Gestalt Ideas to the Solution of Search Problems

In this subsection we describe two lines of research by Simon and his colleagues, and by other researchers, that document the importance of perception and of background knowledge to the way people search for a problem solution. The first line of research used variants of relatively well-defined riddle problems that had the same structure (i.e., “problem isomorphs”) and, therefore, supposedly the same problem space. It documented that people's search depended on various perceptual and conceptual inferences they tended to draw from a specific instantiation of the problem's structure. The second line of research documented that people's search strategies crucially depend on their domain knowledge and on their prior experience with related problems.

Problem Isomorphs

Hayes and Simon ( 1977 ) used two variants of the Tower of Hanoi problem that, instead of disks and pegs, involved monsters and globes that differed in size (small, medium, and large). In both variants, the initial state had the small monster holding the large globe, the medium-sized monster holding the small globe, and the large monster holding the medium-sized globe. Moreover, in both variants the goal was for each monster to hold a globe proportionate to its own size. The only difference between the problems concerned the description of the operators. In one variant (“transfer”), subjects were told that the monsters could transfer the globes from one to another as long as they followed a set of rules, adapted from the rules in the original Tower of Hanoi problem (e.g., only one globe may be transferred at a time). In the other variant (“change”), subjects were told that the monsters could shrink and expand themselves according to a set of rules, which corresponded to the rules in the transfer version of the problem (e.g., only one monster may change its size at a time). Despite the isomorphism of the two variants, subjects conducted their search in two qualitatively different problem spaces, which led to solution times for the change variant being almost twice as long as those for the transfer variant. This difference arose because subjects could more readily envision and track an object that was changing its location with every move than one that was changing its size.

Recent work by Patsenko and Altmann ( 2010 ) found that, even in the standard Tower of Hanoi problem, people's solutions involve object-bound routines that depend on perception and selective attention. The subjects in their study solved various Tower of Hanoi problems on a computer. During the solution of a particular “critical” problem, the computer screen changed at various points without subjects' awareness (e.g., a disk was added, such that a subject who started with a five-disc tower ended with a six-disc tower). Patsenko and Altmann found that subjects' moves were guided by the configurations of the objects on the screen rather than by solution plans they had stored in memory (e.g., the next subgoal).

The Gestalt psychologists highlighted the role of perceptual factors in the formation of problem representations (e.g., Maier's, 1930 , nine-dot problem) but were generally silent about the corresponding implications for how the problem was solved (although they did note effects on solution accuracy). An important contribution of the work on people's solutions of the Tower of Hanoi problem and its variants was to show the relevance of perceptual factors to the application of various operators during search for a problem solution—that is, to the how of problem solving. In the next section, we describe recent work that documents the involvement of perceptual factors in how people understand and use equations and diagrams in the context of solving math and science problems.

Kotovsky, Hayes, and Simon ( 1985 ) further investigated factors that affect people's representation and search in isomorphs of the Tower of Hanoi problem. In one of their isomorphs, three disks were stacked on top of each other to form an inverted pyramid, with the smallest disc on the bottom and the largest on top. Subjects' solutions of the inverted pyramid version were similar to their solutions of the standard version that has the largest disc on the bottom and the smallest on top. However, the two versions were solved very differently when subjects were told that the discs represent acrobats. Subjects readily solved the version in which they had to place a small acrobat on the shoulders of a large one, but they refrained from letting a large acrobat stand on the shoulders of a small one. In other words, object-based inferences that draw on people's semantic knowledge affected the solution of search problems, much as they affect the solution of the ill-defined problems investigated by the Gestalt psychologists (e.g., Duncker's, 1945 , candles problem). In the next section, we describe more recent work that shows similar effects in people's solutions to mathematical word problems.

The work on differences in the representation and solution of problem isomorphs is highly relevant to research on analogical problem solving (or analogical transfer), which examines when and how people realize that two problems that differ in their cover stories have a similar structure (or a similar problem space) and, therefore, can be solved in a similar way. This research shows that minor differences between example problems, such as the use of X-rays versus ultrasound waves to fuse a broken filament of a light bulb, can elicit different problem representations that significantly affect the likelihood of subsequent transfer to novel problem analogs (Holyoak & Koh, 1987 ). Analogical transfer has played a central role in research on human problem solving, in part because it can shed light on people's understanding of a given problem and its solution and in part because it is believed to provide a window onto understanding and investigating creativity (see Smith & Ward, Chapter 23 ). We briefly mention some findings from the analogy literature in the next subsection on expertise, but we do not discuss analogical transfer in detail because this topic is covered elsewhere in this volume (Holyoak, Chapter 13 ).

Expertise and Its Development

In another line of research, Simon and his colleagues examined how people solve ecologically valid problems from various rule-governed and knowledge-rich domains. They found that people's level of expertise in such domains, be it in chess (Chase & Simon, 1973 ; Gobet & Simon, 1996 ), mathematics (Hinsley, Hayes, & Simon, 1977 ; Paige & Simon, 1966 ), or physics (Larkin, McDermott, Simon, & Simon, 1980 ; Simon & Simon, 1978 ), plays a crucial role in how they represent problems and search for solutions. This work, and the work of numerous other researchers, led to the discovery (and rediscovery, see Duncker, 1945 ) of important differences between experts and novices, and between “good” and “poor” students.

One difference between experts and novices pertains to pattern recognition. Experts' attention is quickly captured by familiar configurations within a problem situation (e.g., a familiar configuration of pieces in a chess game). In contrast, novices' attention is focused on isolated components of the problem (e.g., individual chess pieces). This difference, which has been found in numerous domains, indicates that experts have stored in memory many meaningful groups (chunks) of information: for example, chess (Chase & Simon, 1973 ), circuit diagrams (Egan & Schwartz, 1979 ), computer programs (McKeithen, Reitman, Rueter, & Hirtle, 1981 ), medicine (Coughlin & Patel, 1987 ; Myles-Worsley, Johnston, & Simons, 1988 ), basketball and field hockey (Allard & Starkes, 1991 ), and figure skating (Deakin & Allard, 1991 ).

The perceptual configurations that domain experts readily recognize are associated with stored solution plans and/or compiled procedures (Anderson, 1982 ). As a result, experts' solutions are much faster than, and often qualitatively different from, the piecemeal solutions that novice solvers tend to construct (e.g., Larkin et al., 1980 ). In effect, experts often see the solutions that novices have yet to compute (e.g., Chase & Simon, 1973 ; Novick & Sherman, 2003 , 2008 ). These findings have led to the design of various successful instructional interventions (e.g., Catrambone, 1998 ; Kellman et al., 2008 ). For example, Catrambone ( 1998 ) perceptually isolated the subgoals of a statistics problem. This perceptual chunking of meaningful components of the problem prompted novice students to self-explain the meaning of the chunks, leading to a conceptual understanding of the learned solution. In the next section, we describe some recent work that shows the beneficial effects of perceptual pattern recognition on the solution of familiar mathematics problems, as well as the potentially detrimental effects of familiar perceptual chunks to understanding and reasoning with diagrams depicting evolutionary relationships among taxa.

Another difference between experts and novices pertains to their understanding of the solution-relevant problem structure. Experts' knowledge is highly organized around domain principles, and their problem representations tend to reflect this principled understanding. In particular, they can extract the solution-relevant structure of the problems they encounter (e.g., meaningful causal relations among the objects in the problem; see Cheng & Buehner, Chapter 12 ). In contrast, novices' representations tend to be bound to surface features of the problems that may be irrelevant to solution (e.g., the particular objects in a problem). For example, Chi, Feltovich, and Glaser ( 1981 ) examined how students with different levels of physics expertise group mechanics word problems. They found that advanced graduate students grouped the problems based on the physics principles relevant to the problems' solutions (e.g., conservation of energy, Newton's second law). In contrast, undergraduates who had successfully completed an introductory course in mechanics grouped the problems based on the specific objects involved (e.g., pulley problems, inclined plane problems). Other researchers have found similar results in the domains of biology, chemistry, computer programming, and math (Adelson, 1981 ; Kindfield, 1993 / 1994 ; Kozma & Russell, 1997 ; McKeithen et al., 1981 ; Silver, 1979 , 1981 ; Weiser & Shertz, 1983 ).

The level of domain expertise and the corresponding representational differences are, of course, a matter of degree. With increasing expertise, there is a gradual change in people's focus of attention from aspects that are not relevant to solution to those that are (e.g., Deakin & Allard, 1991 ; Hardiman, Dufresne, & Mestre, 1989 ; McKeithen et al., 1981 ; Myles-Worsley et al., 1988 ; Schoenfeld & Herrmann, 1982 ; Silver, 1981 ). Interestingly, Chi, Bassok, Lewis, Reimann, and Glaser ( 1989 ) found similar differences in focus on structural versus surface features among a group of novices who studied worked-out examples of mechanics problems. These differences, which echo Wertheimer's ( 1959 ) observations of individual differences in students' learning about the area of parallelograms, suggest that individual differences in people's interests and natural abilities may affect whether, or how quickly, they acquire domain expertise.

An important benefit of experts' ability to focus their attention on solution-relevant aspects of problems is that they are more likely than novices to recognize analogous problems that involve different objects and cover stories (e.g., Chi et al., 1989 ; Novick, 1988 ; Novick & Holyoak, 1991 ; Wertheimer, 1959 ) or that come from other knowledge domains (e.g., Bassok & Holyoak, 1989 ; Dunbar, 2001 ; Goldstone & Sakamoto, 2003 ). For example, Bassok and Holyoak ( 1989 ) found that, after learning to solve arithmetic-progression problems in algebra, subjects spontaneously applied these algebraic solutions to analogous physics problems that dealt with constantly accelerated motion. Note, however, that experts and good students do not simply ignore the surface features of problems. Rather, as was the case in the problem isomorphs we described earlier (Kotovsky et al., 1985 ), they tend to use such features to infer what the problem's structure could be (e.g., Alibali, Bassok, Solomon, Syc, & Goldin-Meadow, 1999 ; Blessing & Ross, 1996 ). For example, Hinsley et al. ( 1977 ) found that, after reading no more than the first few words of an algebra word problem, expert solvers classified the problem into a likely problem category (e.g., a work problem, a distance problem) and could predict what questions they might be asked and the equations they likely would need to use.

Surface-based problem categorization has a heuristic value (Medin & Ross, 1989 ): It does not ensure a correct categorization (Blessing & Ross, 1996 ), but it does allow solvers to retrieve potentially appropriate solutions from memory and to use them, possibly with some adaptation, to solve a variety of novel problems. Indeed, although experts exploit surface-structure correlations to save cognitive effort, they have the capability to realize that a particular surface cue is misleading (Hegarty, Mayer, & Green, 1992 ; Lewis & Mayer, 1987 ; Martin & Bassok, 2005 ; Novick 1988 , 1995 ; Novick & Holyoak, 1991 ). It is not surprising, therefore, that experts may revert to novice-like heuristic methods when solving problems under pressure (e.g., Beilock, 2008 ) or in subdomains in which they have general but not specific expertise (e.g., Patel, Groen, & Arocha, 1990 ).

Relevance of Search to Insight Solutions

We introduced the notion of insight in our discussion of the nine-dot problem in the section on the Gestalt tradition. The Gestalt view (e.g., Duncker, 1945 ; Maier, 1931 ; see Ohlsson, 1984 , for a review) was that insight problem solving is characterized by an initial work period during which no progress toward solution is made (i.e., an impasse), a sudden restructuring of one's problem representation to a more suitable form, followed immediately by the sudden appearance of the solution. Thus, solving problems by insight was believed to be all about representation, with essentially no role for a step-by-step solution process (i.e., search). Subsequent and contemporary researchers have generally concurred with the Gestalt view that getting the right representation is crucial. However, research has shown that insight solutions do not necessarily arise suddenly or full blown after restructuring (e.g., Weisberg & Alba, 1981 ); and even when they do, the underlying solution process (in this case outside of awareness) may reflect incremental progress toward the goal (Bowden & Jung-Beeman, 2003 ; Durso, Rea, & Dayton, 1994 ; Novick & Sherman, 2003 ).

“Demystifying insight,” to borrow a phrase from Bowden, Jung-Beeman, Fleck, and Kounios ( 2005 ), requires explaining ( 1 ) why solvers initially reach an impasse in solving a problem for which they have the necessary knowledge to generate the solution, ( 2 ) how the restructuring occurred, and ( 3 ) how it led to the solution. A detailed discussion of these topics appears elsewhere in this volume (van Steenburgh et al., Chapter 24 ). Here, we describe briefly three recent theories that have attempted to account for various aspects of these phenomena: Knoblich, Ohlsson, Haider, and Rhenius's ( 1999 ) representational change theory, MacGregor, Ormerod, and Chronicle's ( 2001 ) progress monitoring theory, and Bowden et al.'s ( 2005 ) neurological model. We then propose the need for an integrated approach to demystifying insight that considers both representation and search.

According to Knoblich et al.'s ( 1999 ) representational change theory, problems that are solved with insight are highly likely to evoke initial representations in which solvers place inappropriate constraints on their solution attempts, leading to an impasse. An impasse can be resolved by revising one's representation of the problem. Knoblich and his colleagues tested this theory using Roman numeral matchstick arithmetic problems in which solvers must move one stick to a new location to change a false numerical statement (e.g., I = II + II ) into a statement that is true. According to representational change theory, re-representation may occur through either constraint relaxation or chunk decomposition. (The solution to the example problem is to change II + to III – , which requires both methods of re-representation, yielding I = III – II ). Good support for this theory has been found based on measures of solution rate, solution time, and eye fixation (Knoblich et al., 1999 ; Knoblich, Ohlsson, & Raney, 2001 ; Öllinger, Jones, & Knoblich, 2008 ).

Progress monitoring theory (MacGregor et al., 2001 ) was proposed to account for subjects' difficulty in solving the nine-dot problem, which has traditionally been classified as an insight problem. According to this theory, solvers use the hill-climbing search heuristic to solve this problem, just as they do for traditional search problems (e.g., Hobbits and Orcs). In particular, solvers are hypothesized to monitor their progress toward solution using a criterion generated from the problem's current state. If solvers reach criterion failure, they seek alternative solutions by trying to relax one or more problem constraints. MacGregor et al. found support for this theory using several variants of the nine-dot problem (also see Ormerod, MacGregor, & Chronicle, 2002 ). Jones ( 2003 ) suggested that progress monitoring theory provides an account of the solution process up to the point an impasse is reached and representational change is sought, at which point representational change theory picks up and explains how insight may be achieved. Hence, it appears that a complete account of insight may require an integration of concepts from the Gestalt (representation) and Newell and Simon's (search) legacies.

Bowden et al.'s ( 2005 ) neurological model emphasizes the overlap between problem solving and language comprehension, and it hinges on differential processing in the right and left hemispheres. They proposed that an impasse is reached because initial processing of the problem produces strong activation of information irrelevant to solution in the left hemisphere. At the same time, weak semantic activation of alternative semantic interpretations, critical for solution, occurs in the right hemisphere. Insight arises when the weakly activated concepts reinforce each other, eventually rising above the threshold required for conscious awareness. Several studies of problem solving using compound remote associates problems, involving both behavioral and neuroimaging data, have found support for this model (Bowden & Jung-Beeman, 1998 , 2003 ; Jung-Beeman & Bowden, 2000 ; Jung-Beeman et al., 2004 ; also see Moss, Kotovsky, & Cagan, 2011 ).

Note that these three views of insight have received support using three quite distinct types of problems (Roman numeral matchstick arithmetic problems, the nine-dot problem, and compound remote associates problems, respectively). It remains to be established, therefore, whether these accounts can be generalized across problems. Kershaw and Ohlsson ( 2004 ) argued that insight problems are difficult because the key behavior required for solution may be hindered by perceptual factors (the Gestalt view), background knowledge (so expertise may be important; e.g., see Novick & Sherman, 2003 , 2008 ), and/or process factors (e.g., those affecting search). From this perspective, solving visual problems (e.g., the nine-dot problem) with insight may call upon more general visual processes, whereas solving verbal problems (e.g., anagrams, compound remote associates) with insight may call upon general verbal/semantic processes.

The work we reviewed in this section shows the relevance of problem representation (the Gestalt legacy) to the way people search the problem space (the legacy of Newell and Simon), and the relevance of search to the solution of insight problems that require a representational change. In addition to this inevitable integration of the two legacies, the work we described here underscores the fact that problem solving crucially depends on perceptual factors and on the solvers' background knowledge. In the next section, we describe some recent work that shows the involvement of these factors in the solution of problems in math and science.

Effects of Perception and Knowledge in Problem Solving in Academic Disciplines

Although the use of puzzle problems continues in research on problem solving, especially in investigations of insight, many contemporary researchers tackle problem solving in knowledge-rich domains, often in academic disciplines (e.g., mathematics, biology, physics, chemistry, meteorology). In this section, we provide a sampling of this research that highlights the importance of visual perception and background knowledge for successful problem solving.

The Role of Visual Perception

We stated at the outset that a problem representation (e.g., the problem space) is a model of the problem constructed by solvers to summarize their understanding of the problem's essential nature. This informal definition refers to the internal representations people construct and hold in working memory. Of course, people may also construct various external representations (Markman, 1999 ) and even manipulate those representations to aid in solution (see Hegarty & Stull, Chapter 31 ). For example, solvers often use paper and pencil to write notes or draw diagrams, especially when solving problems from formal domains (e.g., Cox, 1999 ; Kindfield, 1993 / 1994 ; S. Schwartz, 1971 ). In problems that provide solvers with external representation, such as the Tower of Hanoi problem, people's planning and memory of the current state is guided by the actual configurations of disks on pegs (Garber & Goldin-Meadow, 2002 ) or by the displays they see on a computer screen (Chen & Holyoak, 2010 ; Patsenko & Altmann, 2010 ).

In STEM (science, technology, engineering, and mathematics) disciplines, it is common for problems to be accompanied by diagrams or other external representations (e.g., equations) to be used in determining the solution. Larkin and Simon ( 1987 ) examined whether isomorphic sentential and diagrammatic representations are interchangeable in terms of facilitating solution. They argued that although the two formats may be equivalent in the sense that all of the information in each format can be inferred from the other format (informational equivalence), the ease or speed of making inferences from the two formats might differ (lack of computational equivalence). Based on their analysis of several problems in physics and math, Larkin and Simon further argued for the general superiority of diagrammatic representations (but see Mayer & Gallini, 1990 , for constraints on this general conclusion).

Novick and Hurley ( 2001 , p. 221) succinctly summarized the reasons for the general superiority of diagrams (especially abstract or schematic diagrams) over verbal representations: They “(a) simplify complex situations by discarding unnecessary details (e.g., Lynch, 1990 ; Winn, 1989 ), (b) make abstract concepts more concrete by mapping them onto spatial layouts with familiar interpretational conventions (e.g., Winn, 1989 ), and (c) substitute easier perceptual inferences for more computationally intensive search processes and sentential deductive inferences (Barwise & Etchemendy, 1991 ; Larkin & Simon, 1987 ).” Despite these benefits of diagrammatic representations, there is an important caveat, noted by Larkin and Simon ( 1987 , p. 99) at the very end of their paper: “Although every diagram supports some easy perceptual inferences, nothing ensures that these inferences must be useful in the problem-solving process.” We will see evidence of this in several of the studies reviewed in this section.

Next we describe recent work on perceptual factors that are involved in people's use of two types of external representations that are provided as part of the problem in two STEM disciplines: equations in algebra and diagrams in evolutionary biology. Although we focus here on effects of perceptual factors per se, it is important to note that such factors only influence performance when subjects have background knowledge that supports differential interpretation of the alternative diagrammatic depictions presented (Hegarty, Canham, & Fabricant, 2010 ).

In the previous section, we described the work of Patsenko and Altmann ( 2010 ) that shows direct involvement of visual attention and perception in the sequential application of move operators during the solution of the Tower of Hanoi problem. A related body of work documents similar effects in tasks that require the interpretation and use of mathematical equations (Goldstone, Landy, & Son, 2010 ; Landy & Goldstone, 2007a , b). For example, Landy and Goldstone ( 2007b ) varied the spatial proximity of arguments to the addition (+) and multiplication (*) operators in algebraic equations, such that the spatial layout of the equation was either consistent or inconsistent with the order-of-operations rule that multiplication precedes addition. In consistent equations , the space was narrower around multiplication than around addition (e.g., g*m + r*w = m*g + w*r ), whereas in inconsistent equations this relative spacing was reversed (e.g., s * n+e * c = n * s+c * e ). Subjects' judgments of the validity of such equations (i.e., whether the expressions on the two sides of the equal sign are equivalent) were significantly faster and more accurate for consistent than inconsistent equations.

In discussing these findings and related work with other external representations, Goldstone et al. ( 2010 ) proposed that experience with solving domain-specific problems leads people to “rig up” their perceptual system such that it allows them to look at the problem in a way that is consistent with the correct rules. Similar logic guides the Perceptual Learning Modules developed by Kellman and his collaborators to help students interpret and use algebraic equations and graphs (Kellman et al., 2008 ; Kellman, Massey, & Son, 2009 ). These authors argued and showed that, consistent with the previously reviewed work on expertise, perceptual training with particular external representations supports the development of perceptual fluency. This fluency, in turn, supports students' subsequent use of these external representations for problem solving.

This research suggests that extensive experience with particular equations or graphs may lead to perceptual fluency that could replace the more mindful application of domain-specific rules. Fisher, Borchert, and Bassok ( 2011 ) reported results from algebraic-modeling tasks that are consistent with this hypothesis. For example, college students were asked to represent verbal statements with algebraic equations, a task that typically elicits systematic errors (e.g., Clement, Lochhead, & Monk, 1981 ). Fisher et al. found that such errors were very common when subjects were asked to construct “standard form” equations ( y = ax ), which support fluent left-to-right translation of words to equations, but were relatively rare when subjects were asked to construct nonstandard division-format equations (x = y/a) that do not afford such translation fluency.

In part because of the left-to-right order in which people process equations, which mirrors the linear order in which they process text, equations have traditionally been viewed as sentential representations. However, Landy and Goldstone ( 2007a ) have proposed that equations also share some properties with diagrammatic displays and that, in fact, in some ways they are processed like diagrams. That is, spatial information is used to represent and to support inferences about syntactic structure. This hypothesis received support from Landy and Goldstone's ( 2007b ) results, described earlier, in which subjects' judgments of the validity of equations were affected by the Gestalt principle of grouping: Subjects did better when the grouping was consistent rather than inconsistent with the underlying structure of the problem (order of operations). Moreover, Landy and Goldstone ( 2007a ) found that when subjects wrote their own equations they grouped numbers and operators (+, *, =) in a way that reflected the hierarchical structure imposed by the order-of-operations rule.

In a recent line of research, Novick and Catley ( 2007 ; Novick, Catley, & Funk, 2010 ; Novick, Shade, & Catley, 2011 ) have examined effects of the spatial layout of diagrams depicting the evolutionary history of a set of taxa on people's ability to reason about patterns of relationship among those taxa. We consider here their work that investigates the role of another Gestalt perceptual principle—good continuation—in guiding students' reasoning. According to this principle, a continuous line is perceived as a single entity (Kellman, 2000 ). Consider the diagrams shown in Figure 21.6 . Each is a cladogram, a diagram that depicts nested sets of taxa that are related in terms of levels of most recent common ancestry. For example, chimpanzees and starfish are more closely related to each other than either is to spiders. The supporting evidence for their close relationship is their most recent common ancestor, which evolved the novel character of having radial cleavage. Spiders do not share this ancestor and thus do not have this character.

Cladograms are typically drawn in two isomorphic formats, which Novick and Catley ( 2007 ) referred to as trees and ladders. Although these formats are informationally equivalent (Larkin & Simon, 1987 ), Novick and Catley's ( 2007 ) research shows that they are not computationally equivalent (Larkin & Simon, 1987 ). Imagine that you are given evolutionary relationships in the ladder format, such as in Figure 21.6a (but without the four characters—hydrostatic skeleton, bilateral symmetry, radial cleavage, and trocophore larvae—and associated short lines indicating their locations on the cladogram), and your task is to translate that diagram to the tree format. A correct translation is shown in Figure 21.6b . Novick and Catley ( 2007 ) found that college students were much more likely to get such problems correct when the presented cladogram was in the nested circles (e.g., Figure 21.6d ) rather than the ladder format. Because the Gestalt principle of good continuation makes the long slanted line at the base of the ladder appear to represent a single hierarchical level, a common translation error for the ladder to tree problems was to draw a diagram such as that shown in Figure 21.6c .

The difficulty that good continuation presents for interpreting relationships depicted in the ladder format extends to answering reasoning questions as well. Novick and Catley (unpublished data) asked comparable questions about relationships depicted in the ladder and tree formats. For example, using the cladograms depicted in Figures 21.6a and 21.6b , consider the following questions: (a) Which taxon—jellyfish or earthworm—is the closest evolutionary relation to starfish, and what evidence supports your answer? (b) Do the bracketed taxa comprise a clade (a set of taxa consisting of the most recent common ancestor and all of its descendants), and what evidence supports your answer? For both such questions, students had higher accuracy and evidence quality composite scores when the relationships were depicted in the tree than the ladder format.

Four cladograms depicting evolutionary relationships among six animal taxa. Cladogram ( a ) is in the ladder format, cladograms ( b ) and ( c ) are in the tree format, and cladogram ( d ) is in the nested circles format. Cladograms ( a ), ( b ), and ( d ) are isomorphic.

If the difficulty in extracting the hierarchical structure of the ladder format is due to good continuation (which leads problem solvers to interpret continuous lines that depict multiple hierarchical levels as depicting only a single level), then a manipulation that breaks good continuation at the points where a new hierarchical level occurs should improve understanding. Novick et al. ( 2010 ) tested this hypothesis using a translation task by manipulating whether characters that are the markers for the most recent common ancestor of each nested set of taxa were included on the ladders. Figure 21.6a shows a ladder with such characters. As predicted, translation accuracy increased dramatically simply by adding these characters to the ladders, despite the additional information subjects had to account for in their translations.

The Role of Background Knowledge

As we mentioned earlier, the specific entities in the problems people encounter evoke inferences that affect how people represent these problems (e.g., the candle problem; Duncker, 1945 ) and how they apply the operators in searching for the solution (e.g., the disks vs. acrobats versions of the Tower of Hanoi problem; Kotovsky et al., 1985 ). Such object-based inferences draw on people's knowledge about the properties of the objects (e.g., a box is a container, an acrobat is a person who can be hurt). Here, we describe the work of Bassok and her colleagues, who found that similar inferences affect how people select mathematical procedures to solve problems in various formal domains. This work shows that the objects in the texts of mathematical word problems affect how people represent the problem situation (i.e., the situation model they construct; Kintsch & Greeno, 1985 ) and, in turn, lead them to select mathematical models that have a corresponding structure. To illustrate, a word problem that describes constant change in the rate at which ice is melting off a glacier evokes a model of continuous change, whereas a word problem that describes constant change in the rate at which ice is delivered to a restaurant evokes a model of discrete change. These distinct situation models lead subjects to select corresponding visual representations (e.g., Bassok & Olseth, 1995 ) and solutions methods, such as calculating the average change over time versus adding the consecutive changes (e.g., Alibali et al., 1999 ).

In a similar manner, people draw on their general knowledge to infer how the objects in a given problem are related to each other and construct mathematical solutions that correspond to these inferred object relations. For example, a word problem that involves doctors from two hospitals elicits a situation model in which the two sets of doctors play symmetric roles (e.g., work with each other), whereas a mathematically isomorphic problem that involves mechanics and cars elicits a situation model in which the sets play asymmetric roles (e.g., mechanics fix cars). The mathematical solutions people construct to such problems reflect this difference in symmetry (Bassok, Wu, & Olseth, 1995 ). In general, people tend to add objects that belong to the same taxonomic category (e.g., doctors + doctors) but divide functionally related objects (e.g., cars ÷ mechanics). People establish this correspondence by a process of analogical alignment between semantic and arithmetic relations, which Bassok and her colleagues refer to as “semantic alignment” (Bassok, Chase, & Martin, 1998 ; Doumas, Bassok, Guthormsen, & Hummel, 2006 ; Fisher, Bassok, & Osterhout, 2010 ).

Semantic alignment occurs very early in the solution process and can prime arithmetic facts that are potentially relevant to the problem solution (Bassok, Pedigo, & Oskarsson, 2008 ). Although such alignments can lead to erroneous solutions, they have a high heuristic value because, in most textbook problems, object relations indeed correspond to analogous mathematical relations (Bassok et al., 1998 ). Interestingly, unlike in the case of reliance on specific surface-structure correlations (e.g., the keyword “more” typically appears in word problems that require addition; Lewis & Mayer, 1987 ), people are more likely to exploit semantic alignment when they have more, rather than less modeling experience. For example, Martin and Bassok ( 2005 ) found very strong semantic-alignment effects when subjects solved simple division word problems, but not when they constructed algebraic equations to represent the relational statements that appeared in the problems. Of course, these subjects had significantly more experience with solving numerical word problems than with constructing algebraic models of relational statements. In a subsequent study, Fisher and Bassok ( 2009 ) found semantic-alignment effects for subjects who constructed correct algebraic models, but not for those who committed modeling errors.

Conclusions and Future Directions

In this chapter, we examined two broad components of the problem-solving process: representation (the Gestalt legacy) and search (the legacy of Newell and Simon). Although many researchers choose to focus their investigation on one or the other of these components, both Duncker ( 1945 ) and Simon ( 1986 ) underscored the necessity to investigate their interaction, as the representation one constructs for a problem determines (or at least constrains) how one goes about trying to generate a solution, and searching the problem space may lead to a change in problem representation. Indeed, Duncker's ( 1945 ) initial account of one subject's solution to the radiation problem was followed up by extensive and experimentally sophisticated work by Simon and his colleagues and by other researchers, documenting the involvement of visual perception and background knowledge in how people represent problems and search for problem solutions.

The relevance of perception and background knowledge to problem solving illustrates the fact that, when people attempt to find or devise ways to reach their goals, they draw on a variety of cognitive resources and engage in a host of cognitive activities. According to Duncker ( 1945 ), such goal-directed activities may include (a) placing objects into categories and making inferences based on category membership, (b) making inductive inferences from multiple instances, (c) reasoning by analogy, (d) identifying the causes of events, (e) deducing logical implications of given information, (f) making legal judgments, and (g) diagnosing medical conditions from historical and laboratory data. As this list suggests, many of the chapters in the present volume describe research that is highly relevant to the understanding of problem-solving behavior. We believe that important advancements in problem-solving research would emerge by integrating it with research in other areas of thinking and reasoning, and that research in these other areas could be similarly advanced by incorporating the insights gained from research on what has more traditionally been identified as problem solving.

As we have described in this chapter, many of the important findings in the field have been established by a careful investigation of various riddle problems. Although there are good methodological reasons for using such problems, many researchers choose to investigate problem solving using ecologically valid educational materials. This choice, which is increasingly common in contemporary research, provides researchers with the opportunity to apply their basic understanding of problem solving to benefit the design of instruction and, at the same time, allows them to gain a better understanding of the processes by which domain knowledge and educational conventions affect the solution process. We believe that the trend of conducting educationally relevant research is likely to continue, and we expect a significant expansion of research on people's understanding and use of dynamic and technologically rich external representations (e.g., Kellman et al., 2008 ; Mayer, Griffith, Jurkowitz, & Rothman, 2008 ; Richland & McDonough, 2010 ; Son & Goldstone, 2009 ). Such investigations are likely to yield both practical and theoretical payoffs.

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Supplement to Critical Thinking

This supplement elaborates on the history of the articulation, promotion and adoption of critical thinking as an educational goal.

John Dewey (1910: 74, 82) introduced the term ‘critical thinking’ as the name of an educational goal, which he identified with a scientific attitude of mind. More commonly, he called the goal ‘reflective thought’, ‘reflective thinking’, ‘reflection’, or just ‘thought’ or ‘thinking’. He describes his book as written for two purposes. The first was to help people to appreciate the kinship of children’s native curiosity, fertile imagination and love of experimental inquiry to the scientific attitude. The second was to help people to consider how recognizing this kinship in educational practice “would make for individual happiness and the reduction of social waste” (iii). He notes that the ideas in the book obtained concreteness in the Laboratory School in Chicago.

Dewey’s ideas were put into practice by some of the schools that participated in the Eight-Year Study in the 1930s sponsored by the Progressive Education Association in the United States. For this study, 300 colleges agreed to consider for admission graduates of 30 selected secondary schools or school systems from around the country who experimented with the content and methods of teaching, even if the graduates had not completed the then-prescribed secondary school curriculum. One purpose of the study was to discover through exploration and experimentation how secondary schools in the United States could serve youth more effectively (Aikin 1942). Each experimental school was free to change the curriculum as it saw fit, but the schools agreed that teaching methods and the life of the school should conform to the idea (previously advocated by Dewey) that people develop through doing things that are meaningful to them, and that the main purpose of the secondary school was to lead young people to understand, appreciate and live the democratic way of life characteristic of the United States (Aikin 1942: 17–18). In particular, school officials believed that young people in a democracy should develop the habit of reflective thinking and skill in solving problems (Aikin 1942: 81). Students’ work in the classroom thus consisted more often of a problem to be solved than a lesson to be learned. Especially in mathematics and science, the schools made a point of giving students experience in clear, logical thinking as they solved problems. The report of one experimental school, the University School of Ohio State University, articulated this goal of improving students’ thinking:

Critical or reflective thinking originates with the sensing of a problem. It is a quality of thought operating in an effort to solve the problem and to reach a tentative conclusion which is supported by all available data. It is really a process of problem solving requiring the use of creative insight, intellectual honesty, and sound judgment. It is the basis of the method of scientific inquiry. The success of democracy depends to a large extent on the disposition and ability of citizens to think critically and reflectively about the problems which must of necessity confront them, and to improve the quality of their thinking is one of the major goals of education. (Commission on the Relation of School and College of the Progressive Education Association 1943: 745–746)

The Eight-Year Study had an evaluation staff, which developed, in consultation with the schools, tests to measure aspects of student progress that fell outside the focus of the traditional curriculum. The evaluation staff classified many of the schools’ stated objectives under the generic heading “clear thinking” or “critical thinking” (Smith, Tyler, & Evaluation Staff 1942: 35–36). To develop tests of achievement of this broad goal, they distinguished five overlapping aspects of it: ability to interpret data, abilities associated with an understanding of the nature of proof, and the abilities to apply principles of science, of social studies and of logical reasoning. The Eight-Year Study also had a college staff, directed by a committee of college administrators, whose task was to determine how well the experimental schools had prepared their graduates for college. The college staff compared the performance of 1,475 college students from the experimental schools with an equal number of graduates from conventional schools, matched in pairs by sex, age, race, scholastic aptitude scores, home and community background, interests, and probable future. They concluded that, on 18 measures of student success, the graduates of the experimental schools did a somewhat better job than the comparison group. The graduates from the six most traditional of the experimental schools showed no large or consistent differences. The graduates from the six most experimental schools, on the other hand, had much greater differences in their favour. The graduates of the two most experimental schools, the college staff reported:

… surpassed their comparison groups by wide margins in academic achievement, intellectual curiosity, scientific approach to problems, and interest in contemporary affairs. The differences in their favor were even greater in general resourcefulness, in enjoyment of reading, [in] participation in the arts, in winning non-academic honors, and in all aspects of college life except possibly participation in sports and social activities. (Aikin 1942: 114)

One of these schools was a private school with students from privileged families and the other the experimental section of a public school with students from non-privileged families. The college staff reported that the graduates of the two schools were indistinguishable from each other in terms of college success.

In 1933 Dewey issued an extensively rewritten edition of his How We Think (Dewey 1910), with the sub-title “A restatement of the relation of reflective thinking to the educative process”. Although the restatement retains the basic structure and content of the original book, Dewey made a number of changes. He rewrote and simplified his logical analysis of the process of reflection, made his ideas clearer and more definite, replaced the terms ‘induction’ and ‘deduction’ by the phrases ‘control of data and evidence’ and ‘control of reasoning and concepts’, added more illustrations, rearranged chapters, and revised the parts on teaching to reflect changes in schools since 1910. In particular, he objected to one-sided practices of some “experimental” and “progressive” schools that allowed children freedom but gave them no guidance, citing as objectionable practices novelty and variety for their own sake, experiences and activities with real materials but of no educational significance, treating random and disconnected activity as if it were an experiment, failure to summarize net accomplishment at the end of an inquiry, non-educative projects, and treatment of the teacher as a negligible factor rather than as “the intellectual leader of a social group” (Dewey 1933: 273). Without explaining his reasons, Dewey eliminated the previous edition’s uses of the words ‘critical’ and ‘uncritical’, thus settling firmly on ‘reflection’ or ‘reflective thinking’ as the preferred term for his subject-matter. In the revised edition, the word ‘critical’ occurs only once, where Dewey writes that “a person may not be sufficiently critical about the ideas that occur to him” (1933: 16, italics in original); being critical is thus a component of reflection, not the whole of it. In contrast, the Eight-Year Study by the Progressive Education Association treated ‘critical thinking’ and ‘reflective thinking’ as synonyms.

In the same period, Dewey collaborated on a history of the Laboratory School in Chicago with two former teachers from the school (Mayhew & Edwards 1936). The history describes the school’s curriculum and organization, activities aimed at developing skills, parents’ involvement, and the habits of mind that the children acquired. A concluding chapter evaluates the school’s achievements, counting as a success its staging of the curriculum to correspond to the natural development of the growing child. In two appendices, the authors describe the evolution of Dewey’s principles of education and Dewey himself describes the theory of the Chicago experiment (Dewey 1936).

Glaser (1941) reports in his doctoral dissertation the method and results of an experiment in the development of critical thinking conducted in the fall of 1938. He defines critical thinking as Dewey defined reflective thinking:

Critical thinking calls for a persistent effort to examine any belief or supposed form of knowledge in the light of the evidence that supports it and the further conclusions to which it tends. (Glaser 1941: 6; cf. Dewey 1910: 6; Dewey 1933: 9)

In the experiment, eight lesson units directed at improving critical thinking abilities were taught to four grade 12 high school classes, with pre-test and post-test of the students using the Otis Quick-Scoring Mental Ability Test and the Watson-Glaser Tests of Critical Thinking (developed in collaboration with Glaser’s dissertation sponsor, Goodwin Watson). The average gain in scores on these tests was greater to a statistically significant degree among the students who received the lessons in critical thinking than among the students in a control group of four grade 12 high school classes taking the usual curriculum in English. Glaser concludes:

The aspect of critical thinking which appears most susceptible to general improvement is the attitude of being disposed to consider in a thoughtful way the problems and subjects that come within the range of one’s experience. An attitude of wanting evidence for beliefs is more subject to general transfer. Development of skill in applying the methods of logical inquiry and reasoning, however, appears to be specifically related to, and in fact limited by, the acquisition of pertinent knowledge and facts concerning the problem or subject matter toward which the thinking is to be directed. (Glaser 1941: 175)

Retest scores and observable behaviour indicated that students in the intervention group retained their growth in ability to think critically for at least six months after the special instruction.

In 1948 a group of U.S. college examiners decided to develop taxonomies of educational objectives with a common vocabulary that they could use for communicating with each other about test items. The first of these taxonomies, for the cognitive domain, appeared in 1956 (Bloom et al. 1956), and included critical thinking objectives. It has become known as Bloom’s taxonomy. A second taxonomy, for the affective domain (Krathwohl, Bloom, & Masia 1964), and a third taxonomy, for the psychomotor domain (Simpson 1966–67), appeared later. Each of the taxonomies is hierarchical, with achievement of a higher educational objective alleged to require achievement of corresponding lower educational objectives.

Bloom’s taxonomy has six major categories. From lowest to highest, they are knowledge, comprehension, application, analysis, synthesis, and evaluation. Within each category, there are sub-categories, also arranged hierarchically from the educationally prior to the educationally posterior. The lowest category, though called ‘knowledge’, is confined to objectives of remembering information and being able to recall or recognize it, without much transformation beyond organizing it (Bloom et al. 1956: 28–29). The five higher categories are collectively termed “intellectual abilities and skills” (Bloom et al. 1956: 204). The term is simply another name for critical thinking abilities and skills:

Although information or knowledge is recognized as an important outcome of education, very few teachers would be satisfied to regard this as the primary or the sole outcome of instruction. What is needed is some evidence that the students can do something with their knowledge, that is, that they can apply the information to new situations and problems. It is also expected that students will acquire generalized techniques for dealing with new problems and new materials. Thus, it is expected that when the student encounters a new problem or situation, he will select an appropriate technique for attacking it and will bring to bear the necessary information, both facts and principles. This has been labeled “critical thinking” by some, “reflective thinking” by Dewey and others, and “problem solving” by still others. In the taxonomy, we have used the term “intellectual abilities and skills”. (Bloom et al. 1956: 38)

Comprehension and application objectives, as their names imply, involve understanding and applying information. Critical thinking abilities and skills show up in the three highest categories of analysis, synthesis and evaluation. The condensed version of Bloom’s taxonomy (Bloom et al. 1956: 201–207) gives the following examples of objectives at these levels:

• analysis objectives : ability to recognize unstated assumptions, ability to check the consistency of hypotheses with given information and assumptions, ability to recognize the general techniques used in advertising, propaganda and other persuasive materials
• synthesis objectives : organizing ideas and statements in writing, ability to propose ways of testing a hypothesis, ability to formulate and modify hypotheses
• evaluation objectives : ability to indicate logical fallacies, comparison of major theories about particular cultures

The analysis, synthesis and evaluation objectives in Bloom’s taxonomy collectively came to be called the “higher-order thinking skills” (Tankersley 2005: chap. 5). Although the analysis-synthesis-evaluation sequence mimics phases in Dewey’s (1933) logical analysis of the reflective thinking process, it has not generally been adopted as a model of a critical thinking process. While commending the inspirational value of its ratio of five categories of thinking objectives to one category of recall objectives, Ennis (1981b) points out that the categories lack criteria applicable across topics and domains. For example, analysis in chemistry is so different from analysis in literature that there is not much point in teaching analysis as a general type of thinking. Further, the postulated hierarchy seems questionable at the higher levels of Bloom’s taxonomy. For example, ability to indicate logical fallacies hardly seems more complex than the ability to organize statements and ideas in writing.

A revised version of Bloom’s taxonomy (Anderson et al. 2001) distinguishes the intended cognitive process in an educational objective (such as being able to recall, to compare or to check) from the objective’s informational content (“knowledge”), which may be factual, conceptual, procedural, or metacognitive. The result is a so-called “Taxonomy Table” with four rows for the kinds of informational content and six columns for the six main types of cognitive process. The authors name the types of cognitive process by verbs, to indicate their status as mental activities. They change the name of the ‘comprehension’ category to ‘understand’ and of the ‘synthesis’ category to ’create’, and switch the order of synthesis and evaluation. The result is a list of six main types of cognitive process aimed at by teachers: remember, understand, apply, analyze, evaluate, and create. The authors retain the idea of a hierarchy of increasing complexity, but acknowledge some overlap, for example between understanding and applying. And they retain the idea that critical thinking and problem solving cut across the more complex cognitive processes. The terms ‘critical thinking’ and ‘problem solving’, they write:

are widely used and tend to become touchstones of curriculum emphasis. Both generally include a variety of activities that might be classified in disparate cells of the Taxonomy Table. That is, in any given instance, objectives that involve problem solving and critical thinking most likely call for cognitive processes in several categories on the process dimension. For example, to think critically about an issue probably involves some Conceptual knowledge to Analyze the issue. Then, one can Evaluate different perspectives in terms of the criteria and, perhaps, Create a novel, yet defensible perspective on this issue. (Anderson et al. 2001: 269–270; italics in original)

In the revised taxonomy, only a few sub-categories, such as inferring, have enough commonality to be treated as a distinct critical thinking ability that could be taught and assessed as a general ability.

A landmark contribution to philosophical scholarship on the concept of critical thinking was a 1962 article in the Harvard Educational Review by Robert H. Ennis, with the title “A concept of critical thinking: A proposed basis for research in the teaching and evaluation of critical thinking ability” (Ennis 1962). Ennis took as his starting-point a conception of critical thinking put forward by B. Othanel Smith:

We shall consider thinking in terms of the operations involved in the examination of statements which we, or others, may believe. A speaker declares, for example, that “Freedom means that the decisions in America’s productive effort are made not in the minds of a bureaucracy but in the free market”. Now if we set about to find out what this statement means and to determine whether to accept or reject it, we would be engaged in thinking which, for lack of a better term, we shall call critical thinking. If one wishes to say that this is only a form of problem-solving in which the purpose is to decide whether or not what is said is dependable, we shall not object. But for our purposes we choose to call it critical thinking. (Smith 1953: 130)

Adding a normative component to this conception, Ennis defined critical thinking as “the correct assessing of statements” (Ennis 1962: 83). On the basis of this definition, he distinguished 12 “aspects” of critical thinking corresponding to types or aspects of statements, such as judging whether an observation statement is reliable and grasping the meaning of a statement. He noted that he did not include judging value statements. Cutting across the 12 aspects, he distinguished three dimensions of critical thinking: logical (judging relationships between meanings of words and statements), criterial (knowledge of the criteria for judging statements), and pragmatic (the impression of the background purpose). For each aspect, Ennis described the applicable dimensions, including criteria. He proposed the resulting construct as a basis for developing specifications for critical thinking tests and for research on instructional methods and levels.

In the 1970s and 1980s there was an upsurge of attention to the development of thinking skills. The annual International Conference on Critical Thinking and Educational Reform has attracted since its start in 1980 tens of thousands of educators from all levels. In 1983 the College Entrance Examination Board proclaimed reasoning as one of six basic academic competencies needed by college students (College Board 1983). Departments of education in the United States and around the world began to include thinking objectives in their curriculum guidelines for school subjects. For example, Ontario’s social sciences and humanities curriculum guideline for secondary schools requires “the use of critical and creative thinking skills and/or processes” as a goal of instruction and assessment in each subject and course (Ontario Ministry of Education 2013: 30). The document describes critical thinking as follows:

Critical thinking is the process of thinking about ideas or situations in order to understand them fully, identify their implications, make a judgement, and/or guide decision making. Critical thinking includes skills such as questioning, predicting, analysing, synthesizing, examining opinions, identifying values and issues, detecting bias, and distinguishing between alternatives. Students who are taught these skills become critical thinkers who can move beyond superficial conclusions to a deeper understanding of the issues they are examining. They are able to engage in an inquiry process in which they explore complex and multifaceted issues, and questions for which there may be no clear-cut answers (Ontario Ministry of Education 2013: 46).

Sweden makes schools responsible for ensuring that each pupil who completes compulsory school “can make use of critical thinking and independently formulate standpoints based on knowledge and ethical considerations” (Skolverket 2018: 12). Subject syllabi incorporate this requirement, and items testing critical thinking skills appear on national tests that are a required step toward university admission. For example, the core content of biology, physics and chemistry in years 7-9 includes critical examination of sources of information and arguments encountered by pupils in different sources and social discussions related to these sciences, in both digital and other media. (Skolverket 2018: 170, 181, 192). Correspondingly, in year 9 the national tests require using knowledge of biology, physics or chemistry “to investigate information, communicate and come to a decision on issues concerning health, energy, technology, the environment, use of natural resources and ecological sustainability” (see the message from the School Board ). Other jurisdictions similarly embed critical thinking objectives in curriculum guidelines.

At the college level, a new wave of introductory logic textbooks, pioneered by Kahane (1971), applied the tools of logic to contemporary social and political issues. Popular contemporary textbooks of this sort include those by Bailin and Battersby (2016b), Boardman, Cavender and Kahane (2018), Browne and Keeley (2018), Groarke and Tindale (2012), and Moore and Parker (2020). In their wake, colleges and universities in North America transformed their introductory logic course into a general education service course with a title like ‘critical thinking’ or ‘reasoning’. In 1980, the trustees of California’s state university and colleges approved as a general education requirement a course in critical thinking, described as follows:

Instruction in critical thinking is to be designed to achieve an understanding of the relationship of language to logic, which should lead to the ability to analyze, criticize, and advocate ideas, to reason inductively and deductively, and to reach factual or judgmental conclusions based on sound inferences drawn from unambiguous statements of knowledge or belief. The minimal competence to be expected at the successful conclusion of instruction in critical thinking should be the ability to distinguish fact from judgment, belief from knowledge, and skills in elementary inductive and deductive processes, including an understanding of the formal and informal fallacies of language and thought. (Dumke 1980)

Since December 1983, the Association for Informal Logic and Critical Thinking has sponsored sessions at the three annual divisional meetings of the American Philosophical Association. In December 1987, the Committee on Pre-College Philosophy of the American Philosophical Association invited Peter Facione to make a systematic inquiry into the current state of critical thinking and critical thinking assessment. Facione assembled a group of 46 other academic philosophers and psychologists to participate in a multi-round Delphi process, whose product was entitled Critical Thinking: A Statement of Expert Consensus for Purposes of Educational Assessment and Instruction (Facione 1990a). The statement listed abilities and dispositions that should be the goals of a lower-level undergraduate course in critical thinking. Researchers in nine European countries determined which of these skills and dispositions employers expect of university graduates (Dominguez 2018 a), compared those expectations to critical thinking educational practices in post-secondary educational institutions (Dominguez 2018b), developed a course on critical thinking education for university teachers (Dominguez 2018c) and proposed in response to identified gaps between expectations and practices an “educational protocol” that post-secondary educational institutions in Europe could use to develop critical thinking (Elen et al. 2019).

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What Is the Problem? Understanding the History of Ideas

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“What is the problem?” If you ever were a student of Joseph Agassi, you remember this question fondly. Agassi expanded and refined Popper’s characterization of a “critical tradition,” in his philosophical writings, historical studies, and as a teacher. His challenge to his students was both to understand the growth of knowledge in past traditions, and to then take on the task of advancing one—in no matter what field. And “What is the problem?” was always the first question to begin understanding the development of ideas and traditions.

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Agassi, Joseph. 1964. The nature of scientific problems and their roots in metaphysics. In The critical approach to science and philosophy: Essays in honor of Karl Popper , ed. Mario Bunge, 189–211. New York: Free Press. Reprinted in Agassi 1975.

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Berkson, William, and Wettersten, John. 1984. Learning from error: Karl Popper’s psychology of learning. (Open Court).

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Berkson, W. (2017). What Is the Problem? Understanding the History of Ideas. In: Bar-Am, N., Gattei, S. (eds) Encouraging Openness. Boston Studies in the Philosophy and History of Science, vol 325. Springer, Cham. https://doi.org/10.1007/978-3-319-57669-5_16

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Defining Authenticity in Historical Problem Solving

At Sammamish High School, we've identified seven key elements of problem-based learning, an approach that drives our comprehensive curriculum. I teach tenth grade history, which puts me in a unique position to describe the key element of authentic problems.

What is an authentic problem in world history? My colleagues and I grappled with this question when we set about to design a problem-based learning (PBL) class for AP World History. We looked enviously at some of our peer disciplines such as biology which we imagined having clear problems for students to work on (they didn't, but that is another blog post).

We consulted a number of sources in research. What did the College Board say? What do the state standards say? We reached out to Walter Parker, the social studies methods instructor at the University of Washington School of Education, to help us clarify our thinking.

We arrived at two ways to think about authentic problems. One I will call the work of historians in the field, and the other was the work of historical actors at the time. We quickly felt a healthy tension between these two ideas.

Living the Decisions

The work of historians involves creating and debating the frameworks for the historical narratives our students use to interpret history. One problem that historians debate is the question of periodization, or how history should be divided chronologically in order to better understand it. We know these chunks of time -- or eras -- by the more familiar labels given them by historians: classical, medieval and modern, to name a few. These debates are highly charged because they are so important in defining what students entering the field should study. For example, should World War I be considered a turning point in world history, or is World War I really a European civil war whose significance as a global turning point diminishes with passing of each decade?

It was exciting to consider that our students would engage in such high-level and rigorous academic thinking. We could think of many meaty questions for them to explore and discuss: What was the legacy of Mongol rule? Is the modern era a time of progress? Even the question, "Is there really such a thing as world history?" However, we wondered, was it realistic to ask students to do the work of historians? Could we prepare them well enough to have these highly abstract but critical conversations? College professors spend years steeping themselves exclusively in their discipline, while our students devote one seventh of their class time to world history. My colleague and I had both engaged students in such debates during our practice, but not in an integrated systematic way.

Our approach to authentic problems came from a different perspective: that of the historical actor and decision-makers. By giving students roles based around a historical problem we could ask them, "What would you do, and why?" This, of course, is nothing new. Teachers have been creating simulations and role-plays to engage their students for generations. We wanted to build a unit or "challenge cycle" around these activities.

Ultimately, we decided that it would be difficult for students to do the work of historians if they had not done the work of historical actors. By "living" the decisions through problem-based simulations, our students would collectively be better prepared to engage in the larger questions that are debated in the discipline of history.

Challenge Cycles

What did this look like in World History? We created challenge cycles based on each of the eras into which the course was divided. Our first attempt at building a PBL challenge cycle took place when we studied the Early Modern Era (1450-1750) and focused on the theme of diplomacy. Students were assigned to empire teams based on their interests, and they played the role of foreign policy advisors. Their mission: to determine how diplomacy could help their empire maintain and expand power. The simulation component culminated in a round of treaty negotiations between empires. We found that while students were energized and came to know their roles deeply, they were not directly engaging in the conversations and debates that historians have.

After we piloted our first PBL units, we built in a day for a debrief discussion explicitly linking the challenge cycle with the authentic questions that historians address. This debrief day also allowed students to drop their simulation roles, which frequently put them in competitive or modestly adversarial relationships with one another. They were free to argue against the position their historical figure would have taken. For example, during our diplomacy challenge debrief, the Ottoman Empire could argue the position of their Spanish archrivals. We also broke down our challenge cycle into components that allowed students to deepen their understanding of their historical actors in relation to others. In our diplomacy challenge, this meant building in a diplomatic reception in which our student diplomats had to toast an empire with which they wanted to engage in trade.

Diplomats and Historians

What kind of comments have we heard from students? Their response has become more positive as we have refined our pilot units. Here is a brief sample from a survey we took on our diplomacy challenge unit:

• "We all were sort of competing, which made us try harder."
• "The reception was super neat."
• "I really enjoyed knowing about my empire, therefore I wanted to learn more about that empire and master it . . . I liked the process: 1st power point, to get to know the empire. 2nd Toast. This process helped me understand the empires. ."
• "Elaborate more on what actually happened instead of the Socratic seminar [debrief] because I would've liked to know more concrete details."
• "Remove the reception (I think this could have been a two-week project)."

After a year of designing and testing the curriculum, we have come to understand that some problems and their components feel more authentic than others. Representatives of the early modern empires were rarely gathered together at one reception, and diplomacy is obviously conducted over a longer period of time with changing players. However, the toasts our student diplomats made at that diplomatic reception would not have been out of place at a White House state dinner (although our students' were briefer), and the skills they used in trying to woo a trading partner were just as real.

As we continue to refine this course of study, the healthy tension between the work of the historian and the work of the actor remains, as does the desire to create a curriculum where students can meaningfully engage in both.

Editor's Note: Visit " Case Study: Reinventing a Public High School with Problem-Based Learning " to stay updated on Edutopia's coverage of Sammamish High School.

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Building New Course Structures

6 Teaching Undergraduate History: A Problem-Based Approach

Robert K. Poch and Eskender Yousuf

problem solving, historical thinking skills, learning assessment

Introduction

Among the challenges that faculty encounter is facilitating active engagement with their discipline within classrooms of diverse undergraduate students (Calder, 2006; Rendon, 2009). We face this challenge regularly when teaching history. Within a mostly lecture-based format, it is easy to deny students opportunities to engage the discipline as historians.

While we concentrate primarily on the discipline of history, this approach can be applied within other disciplines where the aim is to provide diverse undergraduate students with the opportunity to “do” the work of those disciplines and find personal connection within them.  Historians discover and use primary source documents, confront vexing contextual and interpretational problems, experience the diverse perspectives of peers, and so too can students. For many faculty, the temptation in undergraduate survey courses is to place full emphasis on content coverage and to ignore or minimize development of discipline-based skills (Calder, 2006; Sipress and Voelker, 2009). This produces poor results if our instructional goals include providing a more genuine experience with our discipline, developing analytic skills, and engaging students meaningfully (Weimer 2002). When students are passive recipients of disciplinary information with no apparent connection to themselves, they withdraw intellectually and emotionally (Freire 1970; Langer 1997).

However, it is possible for highly diverse students to experience the dynamic nature of disciplines such as history by “doing” – that is, by actively developing the skills and engaging the processes and problems involved in being a practitioner of the discipline (Sipress and Voelker, 2009; Weimer, 2002). This can happen in large and small classes and also in survey courses. We want students to encounter history as historians. We also want them to experience the excitement of historical discovery and personal meaning-making that first drew us into the work. In doing so, students also learn and retain substantive course content.

We focus below on a “problem-based” approach to teaching and learning history where students are active disciplinary practitioners engaged in addressing problem topics of relevance and connection to their diverse lives. In doing so, the following questions are addressed:

• What are some of the core elements of historical inquiry? What do skilled historians actually do?
• What actions encourage students from different cultural and disciplinary backgrounds to engage the core elements of historical inquiry as practitioners?
• How can course pedagogy, assignments, and assessments become consistent with what skilled historians do and foster student engagement?
• How can the results of these efforts be assessed? What are some of the assessment results from using a problem-based approach to learning history?

While we concentrate primarily on the discipline of history, this approach can be applied within other disciplines where the aim is to provide diverse undergraduate students with the opportunity to “do” the work of those disciplines and find personal connection within them (Gurung, Chick, and Haynie, 2009).

Identifying and Using Core Elements of Historical Inquiry

In creating learning environments where students become historians, it is necessary to consider what it is that historians do and what skills are necessary to be practitioners of the discipline. In a macro sense, many historians describe their work as problem solving guided by active questioning (Elton, 1967; Fischer, 1970; Marius and Page, 2005; Nevins, 1963). That is, questions are posed; sources and facts are collected, critically read, contextualized, and organized; and, an interpretation of the past is formed while recognizing that the complexities of history defy easy explanations (Ayers, 2006; Commager, 1965; Wineburg, 1991, 1999). Whenever possible, historians utilize primary sources to form their own interpretations rather than relying mostly on the interpretations of other historians.

Historians are regularly challenged to analyze, contextualize, and interpret the past from incomplete disparate sources. Such actions require a series of more discrete skills including the critical evaluation, interpretation, and communication of evidence; the detection of bias; and careful consideration of historical causation (Ayers, 2005; Barzun and Graff, 1977; Bloch, 1953; Carr, 1961; Commager, 1965; Elton, 1967; Evans, 1999; Fischer, 1970; Lerner, 1997; Nevins, 1963; Wood, 2008). These skills are expressed concisely as the “5Cs” of historical thinking: “change over time, causality, context, complexity, and contingency” (Andrews and Burke, 2007, 1).

Through using the 5Cs, students become increasingly aware of how much can change over time – such as political systems, landscapes, and social values – while, simultaneously, acknowledging retention of strong elements of the past such as holidays and the rituals surrounding them. Further, once developed through classroom engagement with historical sources, the elements of causality, context, complexity, and contingency enable students to identify and appreciate the incomplete nature of historical records and the intricate, simultaneous, and broad scale human interactions and competing interests in history (Ayers, 2006; Nevins, 1963; Wood, 2008). The awareness of complexity causes professional historians and students to probe more deeply into explanations of causality and to reject simplistic reasoning.

To have students engage history problems in a manner that is relevant and meaningful, it is necessary to also think carefully about how to invite students and their interests into the process of historical inquiry. While engineering, mathematics, physics and accounting are experienced as real, relevant, and practical, history is not experienced that way. Students often encounter it as an abstruse, fact-laden, memorization-based, irrelevant, impersonal discipline. We must, therefore, address how to engage students in being practitioners of historical inquiry and interpretation. These are some of the key components of the real work of historians and the historical reasoning used to create interpretations of the past. In working with undergraduate students – some of whom just graduated from high school – the 5Cs are a useful, understandable, and easy to remember toolset for engaging historical inquiry. With these parts of the work of historians and historical thinking in mind, it is possible to design classroom experiences that bring students into the dynamic nature of this work and its associated challenges. Students can then experience the discipline of history more fully and also learn how to create their own historical meaning from available sources (Sipress and Voelker, 2009). These components of historical thinking help to form the “history problems” that we utilize in our U.S. history classroom and which we describe further below.

However, to have students engage history problems in a manner that is relevant and meaningful, it is necessary to also think carefully about how to invite students and their interests into the process of historical inquiry. While engineering, mathematics, physics and accounting are experienced as real, relevant, and practical, history is not experienced that way. Students often encounter it as an abstruse, fact-laden, memorization-based, irrelevant, impersonal discipline. We must, therefore, address how to engage students in being practitioners of historical inquiry and interpretation.

Engaging Students in Core Elements of Historical Inquiry as Practitioners

The invitation to participate in our class, “America’s Past and Present: Multicultural Perspectives,” is underscored by bringing students into direct interaction with historical thinking skills, primary source materials that are reflective of multiple cultures on the American landscape, and with complex historical issues and problems that invite students to interpret history with their own voices rather than having a textbook or the instructor be the sole interpretive voices. We want students to gain more elegant and inclusive views of history that expose the complex dynamics between people over time and which stimulate curiosity about how life was experienced and interpreted by different diverse populations. This is enabled in part by the diversity of our students. The multiple complexities of persons in the past are reflected in our students. As observed by Lee, Poch, Shaw, and Williams (2012),

“…we have observed our institution’s student population become increasingly diverse in terms of racial and ethnic demographics. Historically, generalized categories of racial and ethnic identity have become more diffuse and complex. We are also more mindful of the often less visible forms of difference that are present in any learning environment, such as socioeconomic status, sexual orientation, religion, disability, and many others”

As students engage each other in class and discover how their classmates form different historical interpretations based in part on their different lived experiences, it stimulates and reinforces an understanding of the different perspectives and lived experiences of persons throughout history.

To better ensure the relevance of the history problems to diverse student interests, students are asked on the first day of the course what part of U.S. history between the Civil War and present time is of greatest interest to them. While some students do not know how to answer such a question at first, many others have some notion of their interests. Examples of these student responses from spring semester 2015 are as follows:

• World War II
• U.S. Civil Rights movements (including the role of youth in such movements)
• Vietnam War
• The Great Depression
• 9/11 and its effect on the world
• Other countries and perceptions of the U.S.
• Native Americans and Tribes
• Civil War & differing economies

When we, as instructors, are responsive to such interests, students more fully engage with the topics and are willing to invest the energy to do the challenging work of historical meaning-making using disciplinary thinking skills. These interests are invaluable in making the course ours – that is, a shared experience of historical investigation that reflects mutual interests rather than those of the instructor alone. It is a powerful opportunity to communicate to students at the beginning of the course that the instructors are engaged co-investigators of historical topics that the students suggest and that student interests are of great value. We use student historical interests to create substantive class discussion questions, short reading and writing assignments, and further engagement with historical thinking skills through lengthier history problems that come later in the semester. While assembling sources related to the interests, we spend the first three to four weeks of the course introducing and practicing the 5Cs of historical thinking. Initial reading and writing assignments selected before the course starts enable students to begin the process of understanding, recognizing, and using context, causality, complexity, change and continuity over time, and contingency. These historical thinking skills are then used to explore more deeply and intentionally the historical topics that students suggest. In doing so, student interests become integrated and useful parts of the course experience.

Students also tell us that they want to explore historical themes and issues that are not commonly approached in historical texts or rooted in fact memorization. For example, one student expressed in a topical interest survey that she wanted “…to learn the truth about history. The real original text. I want to find it and research it. Interest in causality and what caused all the events in history to happen? WHYYY! The reason things went down the way they did!” Students express that they want to explore the meaning and use of racism, the rise of feminism, and the perspectives of other nations whose histories intersect with those of the United States. They want to do so in a way that engages history through interesting questions full of encounters with ordinary people who experienced the past in powerful but mostly unknown ways. When we, as instructors, are responsive to such interests, students more fully engage with the topics and are willing to invest the energy to do the challenging work of historical meaning-making using disciplinary thinking skills.

Making Pedagogy, Assignments, and Assessments Consistent with what Historians Actually Do

Engaging students as historians takes careful thought and planning. Core elements of course design are important parts of this work. The course curriculum must provide space for the development of student evaluative and interpretive skills. This often comes with winnowing some course content as traditionally delivered through lengthy lectures (Calder, 2006). The process of winnowing involved using part of a summer break to critically review course materials to identify where unnecessary content was located that cluttered class time and reduced the capacity to develop student historical thinking skills. For example, a discussion of Civil War medicine and pro- and anti-U.S. imperialist arguments were removed given that they were peripheral to more important course themes. Further, those subjects tended to lead to more lecturing rather than active discussion. Rendon (1993) observed that “…many culturally diverse students do not learn best through lecture. Instead, we should focus on collaborative learning and dialogue that promote critical thinking, interpretation and diversity of opinion” (10).

Students can mine rich primary sources of the period as guided by research questions collaboratively developed by students and the instructor. Lectures are balanced with skill-building by doing – actively engaging students in learning how to develop researchable questions, engaging primary and secondary texts with critical lenses, forming interpretations from available evidence, and presenting results. Further, significant thought must be invested in designing course assignments and resources that enable skill development to occur and be assessed. Assessments must be constructed to evaluate student work in a manner consistent with skill development expectations. Class time invested in developing the foundational skills used within the discipline is necessary given that “…history teachers cannot simply present students with documents, tell them what to do, and then expect magical gains in the development of students’ historical sense. Much more elaborate and carefully thought out ‘scaffolding’ is needed to realize the potential of this approach” (Calder et al., 2002, 59).

This approach has significant student developmental implications. It may involve moving students and the course structure away from a dualistic form of learning history where questions are framed in terms of right and wrong response outcomes and there is strong dependency upon the instructor. Instead, there will be movement toward a course design wherein students are met with formulating questions within a course-related area of personal historical interest that has interpretive complexities associated within it (Donald, 2002, 3; Evans et al, 2010).

For example, rather than presenting students with a course design that asks them to identify within an exam three major outcomes of Reconstruction after the U.S. Civil War from lecture notes, students can experience the real problems of Reconstruction in depth by reading conflicting newspaper accounts in the North and the South regarding the political enfranchisement of African American men and the political balances of power that were at play (Langer, 1989). Rather than searching secondary and tertiary sources (such as many textbooks and lectures) alone for such information, students can mine rich primary sources of the period as guided by research questions collaboratively developed by students and the instructor. One research question that was developed in this manner focused on the tactics that some southern states utilized to stymie the voting capacity of black males following passage of the Fifteenth Amendment. In response, students were able to find and analyze different literacy tests for voting (the class even tried taking some of the tests which produced a high failure rate) and also details on the administration of poll taxes.

Such collaboration and student interpretive responsibilities can lead to movement from what psychologist Ellen Langer refers to as “mindlessness” wherein students are stuck with rote memorization and the search for the “right” answer rather than experiencing the rich contexts and possibilities that exist as part of the act of discovering and making meaning within disciplines (Langer, 1997). Langer notes that, “In math, teaching for understanding involves teaching students to think about what a problem means and to look for multiple solutions. Studies have confirmed that science is better taught through hands-on research and discovery than through memorization alone. In English, teaching for understanding means emphasizing the process of writing and exploring literature rather than memorizing grammar rules and doing drills. Understanding is encouraged in history by turning students into junior historians” (Langer, 1997, 71, 72). It is in that spirit that we developed history problems.

History Problems

 “As an interpretive historian using the primary source readings that are provided in this problem, how do you define Jim Crow?” This question, which seems deceptively simple at first, quickly exposes the complexities of Jim Crow as a comprehensive system within American society that touched every aspect of life. Each history problem is comprised of three essential parts: an introduction to the problem with concise contextual information; open-ended problem questions designed to provide students with interpretive space to utilize their voice and perspectives (rather than the instructor’s voice or that of the textbook); and a set of primary source materials that reflect diverse authors and views. Students are given three history problems throughout the semester and they have approximately four weeks to complete them given the complexity of the readings. Although there is no required page length for the problem responses, students often write seven pages or more for each problem. The history problems used during the Spring 2015 semester were based on student interests expressed at the beginning of the semester and involved the following topics: “The challenges of Jim Crow and the dynamics found within it;” “’Equal protection under the law:’ The challenges of separate but equal – The struggle for Brown v. Board of Education ;” and, “September 11, 2001.”

The history problem questions provide students with the ability to create responses based on their own interpretation of the material. The questions replicate real challenges and problems for historians that are consistent with the 5Cs of historical thinking that we use in class. Some questions expose students to the complexities of powerful systems of racial oppression such as Jim Crow. Other questions focus on establishing context or examining change over time. For example, in the problem examining Jim Crow, students were asked the following: “As an interpretive historian using the primary source readings that are provided in this problem, how do you define Jim Crow?” This question, which seems deceptively simple at first, quickly exposes the complexities of Jim Crow as a comprehensive system within American society that touched every aspect of life.

To assist in developing a definition of Jim Crow, the history problem packet includes a variety of primary sources that include memoirs, excerpts from scholarly books and novels, and a 1949 travel guide for African American motorists. Within this particular problem packet, the sources included pieces from W.E.B. Dubois’ The Souls of Black Folk (1903); Ralph Ellison’s Invisible Man (1952); John Hope Franklin’s autobiography, Mirror to America (2005); Howard Thurman’s The Luminous Darkness: A Personal Interpretation of the Anatomy of Segregation and the Ground of Hope (1965); Richard Wright’s Uncle Tom’s Children (1940); and, The Negro Motorist Green Book (1949). The Green Book was published to provide African American travelers with “…information that will keep him from running into difficulties, embarrassments and to make his trips more enjoyable” (1). These sources provided different views of and experiences with Jim Crow and, unlike a textbook, did not provide the definition and interpretation of Jim Crow for the students. Instead, the students worked with the different texts, situated them contextually in their particular time and place and with consideration of who wrote them, and gradually developed their own definition of Jim Crow. Further, the sources spanned a number of decades so that some consideration could be given to change over time in addition to complexity. The sources worked well in providing multiple perspectives of how Jim Crow, as a system, affected different parts of life and also a sense of the varieties of materials that historians use.

The same history problem also asked students to consider how the sources in the packet related to any prior readings we had used in the course (such as Frederick Douglass’ 1865 speech, “What the Black Man Wants”), so that students could further analyze and gain familiarity with context, change over time, complexity, contingency, and causality. Douglass’ speech was useful not only as an earlier expression of the challenges and contradictions that Jim Crow created within a nation that professed freedom and democracy, but also served as a source to explore the challenging concept of contingency. By expressing how black men wanted political participation through receipt of the right to vote and full recognition for their intellectual capacity to be informed contributors to democracy, Douglass’ speech highlighted contingencies necessary for breaking explicit bonds of enslavement and more diffuse societal systems of oppression. These varied course and problem-based primary sources enabled students to make complex connections between forms of evidence and further solidified historical thinking skills as expressed within the 5Cs. Providing approximately four weeks to work with each history problem gave plenty of in-class time to further discuss the sources, the context of the sources, and to practice the skills necessary to utilize them effectively.

Assessing the Results of Using a Problem-Based Approach to Learning History

We utilized several forms of assessment to evaluate the problem-based approach to learning history: 1) the evaluation of student written responses to history problems, 2) individual interviews with students, and, 3) an independently conducted end-of-semester student survey. In each assessment approach, it was important that student voices were prominent and listened to attentively (Patton, 1980). Each of these assessment forms is discussed below.

Written responses to history problems

Student written responses to the four history problems were evaluated carefully for progressive use of the elements of historical thinking. Each of the papers went through two evaluative reviews – one by the course teaching assistant and the other by the primary instructor. The papers were scored on a standard A-F grading scale and were preceded by smaller writing assignments that practiced discrete elements of five identified historical thinking skills. For example, the Frederick Douglass speech, “What the Black Man Wants,” was used early in the semester in part so students could practice establishing and expressing context and recognizing some elements of contingency. This was done with multiple other pieces of short reading and writing exercises that involved the voices and writing of diverse speakers and authors. With this practice experience in place, students could move with greater confidence in addressing contextual issues in the first history problem and those that followed. The papers were also useful in assessing student command or struggle with certain components of historical thinking. We discovered in multiple early papers that students did not fully understand the idea of contingency and, in response, were able to spend more time discussing and practicing it in class.

Toward the end of the semester as students worked with perhaps the most challenging history problem involving the September 11, 2001 attacks, we could detect that students were engaging in far more sophisticated historical reasoning and explicit use of historical thinking skills. For example, one student, a freshman, having studied the presence and role of the United States in the Middle East since the early twentieth-century (using maps, documents, interviews, reports, and political cartoons provided in the fourth history problem), constructed a complex contextual background in her written response to one set of the problem questions (“Using information from our class sessions and the materials provided within this problem packet, describe the relationships that existed and some of the events that occurred between the United States and the ‘Middle East’ region prior to 9/11. With these sources in mind, what are some of the possible motives for the 9/11 attack?”). She responded in part in her introduction,

The events of September 11th, 2001 came as a shock to millions of American citizens; however, a complex history of rocky foreign relations combined with the struggles regarding religion and government in the ‘Middle East’ suggest that the attack was only one part of several interconnected issues. As we examine the context of the events surrounding the 9/11 attacks, the complexity of the United States’ position in world affairs, the major causes leading up to the attack, and contingency of other nations’ histories on our own, we can begin to analyze the affect that each of these has had on the aftermath of 9/11 over time… [the] ten to fifteen years before the attacks on the Twin Towers… show a deeply complex relationship between different nations. While the Saudi Arabian government aided the United States [in the Gulf War by providing a U.S. military staging ground along the border with Kuwait] there were other entities such as Iraq that were pitted against the United States, resulting in conflict between the nations in that area regarding involvement of the United States. To add to this complexity is the idea of a theocracy and questions on how to rule a nation when military forces within those nations do not share the political philosophy or religious beliefs of those nations.

In this brief excerpt which was supported by lengthier supporting text and examples, we could easily detect the use of historical thinking skills (some of which were explicitly mentioned), including greater recognition of the deep complexities that long preceded the events of 9/11.

The written responses to the history problem questions were returned to the students with evaluative comments that served, in part, to prepare students for individual meetings with the course instructor and the graduate research assistant. With highly diverse students from different nations, it was important to provide different opportunities for the students to express how they approached the problems that extended beyond their written responses.

Individual meetings with students about the history problems

Individual student interviews were conducted on two of the problem set essays (history problems one and three). Each student was given the opportunity to schedule a conversation with us to discuss their responses and to further sharpen their historical thinking skills based on the 5Cs. During these meetings, the students could gain additional points (but no subtraction of points) by further clarifying their written responses and the processes that they used to construct them. The meeting questions were provided to each student in advance and included: Where did you encounter the greatest challenges in responding to this history problem? How did you approach the challenges? What do you believe you learned through engaging in this history problem? An opening question was designed to further probe each student’s writing by asking: “We found some engaging interpretations within your paper [if this was truthful] and also some places where we would like to know more. Can you further describe [this was customized for each student paper]….” The questions presented opportunities for students to further explain their own interpretations and how they approached the problems over time. Through the questions, students reflected on and expressed their own historical interpretations in a manner that replicates much of the way that historians utilize peers within their professional communities.

Within the second set of individual meetings on the third history problem, students began to express more of the 5Cs of historical thinking. During the first set of interviews regarding the “Challenges of Jim Crow and the dynamics found within it,” we met individually with twenty-three students who expressed a wide array of historical thinking skills. For example, one student, in expanding upon her interpretation of Jim Crow, remarked that developing her own definition of Jim Crow enabled her to “…go far below the surface to see the complexity of Jim Crow and its relationship to definitions of racism.” Further, the student explained that examining the use of Jim Crow-related art revealed to her the complex strategies of Jim Crow systems of oppression. Another student observed that reading primary source accounts of African Americans who lived within Jim Crow brought forth “contradictions” within the imagery and terms used within Jim Crow such as using ideas of “light” and “visibility” to describe American society while those who lived under the weight of Jim Crow described darkness, shadows, and invisibility. Within these comments, and many others, we observed students expressing different elements of historical thinking including complexity (very explicitly), as well as change over time, and causality as students considered and described the structures of Jim Crow messaging and how the messaging was delivered in different ways during specific spans of time.

Within the second set of individual meetings on the third history problem, students began to express more of the 5Cs of historical thinking. We used a slightly modified set of questions that included: Did you feel that you were able to utilize any particular historical thinking skills in this problem? Students commented more extensively and easily about historical thinking skills and demonstrated within their papers greater complexity in historical thinking. For example, one student expressed complex differences in how African American’s responded to racial oppression over time. She interpreted primary sources in the first history problem as being “defensive in nature – how persons responded or protected themselves within the Jim Crow system” whereas in the third history problem on the legal strategies that African American attorneys used to eventually prevail in the Brown v. Board of Education decision, the strategy was “more offensive in nature in that it showed black persons taking back their rights and being more confident in doing so.” This student, and others, expressed greater awareness and mastery of complexity, causality, and change over time in their interpretations of primary historical source materials.

Independently conducted end-of-semester student survey

At the request of the instructor, a grant-supported survey was developed and given to students in the history course at the very end of spring semester 2015. Among those who responded to the survey (50% of a class of 24 first-year students where this problem-based approach was fully implemented), the following are representative of their responses:

Question: What parts of the course were particularly effective for you in developing historical thinking skills and the capacity to be an effective historian? What parts were particularly ineffective?

• “The parts of this course that were effective in developing historical thinking skills were definitely the history problems and also the 5Cs. I learned so much through the history problems that I would have never learned through a test and I will remember the information much better by writing about it in a history problem. I didn’t feel like any part was ineffective.”
• “The history problems were effective because they allowed us to give our own opinion on the matter and we got involved instead of just mindless memorization.”
• “I think that the most effective things that we did in class to develop my historical thinking skills were definitely the problem sets and our class discussions. Both of those two platforms pushed us to think for ourselves and contribute to a larger group discussion. I loved the problem sets because they forced me to think and form my own opinions using the historical thinking skills that we were given.”
• “The history problems really helped me see how contemporary historians actually applied their skills to modern problems.”

Question: Do you believe that you know and can apply the essential elements of historical thinking, as a result of this course? Please explain.

• “Yes, I have already applied it to other classes and feel very comfortable doing it.”
• “Yes, the history problems gave us that opportunity.”
• “I do believe that I could apply the elements of historical thinking into other classes and in my everyday life as a historian. I feel confident that I know the 5Cs of historical thinking and could use them in other situations. They were drilled into us, I won’t forget them.”
• “Yes. I believe that using the 5Cs from the beginning of this course helped me to gain further knowledge and also to help me dig deeper into historical problems and questions.”
• “I definitely feel that this course has aided my skills in critical analysis and historical thinking and I can see how to use these skills in different contexts and subjects besides history.”

Student survey responses found that 1) history thinking elements of the 5C’s gave them a grasp of historical thinking skills; 2) established a process whereby students could formulate their own interpretations of historical sources thereby moving from mindless memorization to mindfulness and, 3) students were able to utilize their own lived experiences and interests as historians engaged in investigating historical problems.

The use of history problems in our course stems from a twofold purpose. First, we want students to experience the discipline of history as actively engaged historians who use primary sources in addressing challenging questions of historical interpretation through use of well-defined historical thinking skills. Second, we want to facilitate personal interaction with the discipline by using sources and stories that are reflective of the diversity of our students and enabling their interpretive voices to emerge and be respected in our assessments of their learning. Through the use of history problems, unlike our past exams, we noticed the disappearance of instructor voice in student interpretations of historical source materials and an increase in deliberate use of the 5Cs of historical thinking: context, change over time, contingency, complexity, and causality. Continued exploration of the use of history problems in developing more focused development of particular historical thinking skills will occur in our future work as will the capacity to assess those skills effectively through combinations of written work and in-person conversational interactions with students.

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Acknowledgements

Facilitation and evaluation of this project was enabled by the invaluable support and guidance of Ilene Alexander, Jeff Lindgren, and J.D. Walker. We also acknowledge the work and influence of the following excellent undergraduate teaching assistants who, over the last seven years, contributed to the development, implementation, and the strengthening of the problem based approach to teaching and learning: Emily DePalma, Emily McCune, Julianna Ryburn, Jade Beauclair Sandstrom, and Chris Stewart

Innovative Learning and Teaching: Experiments Across the Disciplines Copyright © 2017 by Individual authors is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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Problem-solution history

History gets a bad rap. Most people find it boring—as did I, throughout all my school years, until I finally got excited about it in my mid-twenties and began catching up on my education. The problem is the way it is written and taught.

History is often presented as a collection of facts. The facts might be a jumble, or hopefully organized in an understandable sequence. I call this name-and-date history . It’s the boring history that most people associate with the subject and that most people suffer through in school. At its best, a historian can pick out the most interesting or exciting facts, and tell them in an engaging, lively manner. I call this storytime history . The material is somewhat motivated and it’s at least entertaining. But in any case the student doesn’t retain much if anything, and what little they retain is not very useful, because it isn’t connected to anything and doesn’t represent a deep understanding.

The better historians go beyond name-and-date history. They integrate facts into casual sequences to create coherent narratives. I call this cause-and-effect history. At this level the student actually has a chance of achieving real understanding. Even at this level, though, the ideas can quickly become overwhelming. At its best, cause-and-effect history simplifies, condenses and essentializes until it reaches a high level of integration. This is big-picture history , a term coined by Scott Powell (to whom I am indebted for most of the perspective just outlined). With big-picture history the student can not only understand, but retain that understanding in a usable package.

What I am trying to do in this blog is something I’m calling problem-solution history . Since I’m telling the story of human progress, I want to tell not only what happened, not only why it happened, but why we decided to make it happen . To do that, I need to clearly explain the problems humans face and how almost every aspect of the modern world is a solution to one of those problems.

Only in this context can you appreciate, protect, and defend what we have accomplished so far—and be inspired to push progress further, faster. Without this background, it’s easy to hate DDT without realizing that it was a replacement for arsenic , to despise plastic without realizing that it saved the elephants , or to be disgusted by industrial furnaces without realizing that they averted worldwide famine . It’s easy to propose doing away with modern technolgy and reverting to a seemingly halcyon past, without realizing that this means un-solving problems that those who came before us worked so hard to solve.

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Whale explosion debacle: Oregon's unforgettable lesson in problem-solving

54 years ago, the Oregon coast was the scene of an unforgettable event now known in history as the "Exploding Whale." In 2020, the Oregon Historical Society released footage of this extraordinary occurrence.

As IFLScience reported, led by the navy, the highway patrol tried to remove a dead whale from the beach using dynamite. This unconventional method resulted in "whale meat rain," The event was documented and then restored to 4K quality by AV Geeks from Raleigh, North Carolina.

8 tons of meat

In November 1970, an 8-ton sperm whale washed ashore in Oregon. After consulting with the navy, the local highway patrol decided to handle the situation with an explosion. The idea was to use dynamite to disperse most of the whale’s remains into the sea. The assumption was that smaller, more easily digestible pieces would be more beneficial for marine life.

Unexpected consequences of the unusual solution

Despite thorough consultations, the explosion had vastly different effects than expected. Walt Umenhofer, an entrepreneur with a background in explosives, expressed his doubts about the highway patrol's plan and recommended using less TNT. Nevertheless, his suggestions were overlooked, leading him to observe the disastrous explosion from a safe distance.

Upon detonation, large chunks of whale blubber were flung far and wide, causing damage to, among other things, Umenhofer's brand-new car. Journalist Paul Linnman, in his coverage, likened the explosion to a "massive shot of tomato juice." Ironically, despite the initial debacle, the Oregon community has embraced this peculiar event, incorporating it into their regional culture.

This unconventional attempt to solve the problem of a dead whale on an Oregon beach reminds us that novel solutions to challenges can have both disastrous and culturally enriching effects.

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Watch CBS News

Teens come up with trigonometry proof for Pythagorean Theorem, a problem that stumped math world for centuries

By Bill Whitaker

May 5, 2024 / 7:00 PM EDT / CBS News

As the school year ends, many students will be only too happy to see math classes in their rearview mirrors. It may seem to some of us non-mathematicians that geometry and trigonometry were created by the Greeks as a form of torture, so imagine our amazement when we heard two high school seniors had proved a mathematical puzzle that was thought to be impossible for 2,000 years. 

We met Calcea Johnson and Ne'Kiya Jackson at their all-girls Catholic high school in New Orleans. We expected to find two mathematical prodigies.

Instead, we found at St. Mary's Academy , all students are told their possibilities are boundless.

Come Mardi Gras season, New Orleans is alive with colorful parades, replete with floats, and beads, and high school marching bands.

In a city where uniqueness is celebrated, St. Mary's stands out – with young African American women playing trombones and tubas, twirling batons and dancing - doing it all, which defines St. Mary's, students told us.

Junior Christina Blazio says the school instills in them they have the ability to accomplish anything. 

Christina Blazio: That is kinda a standard here. So we aim very high - like, our aim is excellence for all students. 

The private Catholic elementary and high school sits behind the Sisters of the Holy Family Convent in New Orleans East. The academy was started by an African American nun for young Black women just after the Civil War. The church still supports the school with the help of alumni.

In December 2022, seniors Ne'Kiya Jackson and Calcea Johnson were working on a school-wide math contest that came with a cash prize.

Ne'Kiya Jackson: I was motivated because there was a monetary incentive.

Calcea Johnson: 'Cause I was like, "$500 is a lot of money. So I-- I would like to at least try."

Both were staring down the thorny bonus question.

Bill Whitaker: So tell me, what was this bonus question?

Calcea Johnson: It was to create a new proof of the Pythagorean Theorem. And it kind of gave you a few guidelines on how would you start a proof.

The seniors were familiar with the Pythagorean Theorem, a fundamental principle of geometry. You may remember it from high school: a² + b² = c². In plain English, when you know the length of two sides of a right triangle, you can figure out the length of the third.

Both had studied geometry and some trigonometry, and both told us math was not easy. What no one told  them  was there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible, … and that was the bonus question facing them.

Bill Whitaker: When you looked at the question did you think, "Boy, this is hard"?

Ne'Kiya Jackson: Yeah. 

Bill Whitaker: What motivated you to say, "Well, I'm going to try this"?

Calcea Johnson: I think I was like, "I started something. I need to finish it." 

Bill Whitaker: So you just kept on going.

Calcea Johnson: Yeah.

For two months that winter, they spent almost all their free time working on the proof.

CeCe Johnson: She was like, "Mom, this is a little bit too much."

CeCe and Cal Johnson are Calcea's parents.

CeCe Johnson:   So then I started looking at what she really was doing. And it was pages and pages and pages of, like, over 20 or 30 pages for this one problem.

Cal Johnson: Yeah, the garbage can was full of papers, which she would, you know, work out the problems and-- if that didn't work she would ball it up, throw it in the trash. 

Bill Whitaker: Did you look at the problem? 

Neliska Jackson is Ne'Kiya's mother.

Neliska Jackson: Personally I did not. 'Cause most of the time I don't understand what she's doing (laughter).

Michelle Blouin Williams: What if we did this, what if I write this? Does this help? ax² plus ….

Their math teacher, Michelle Blouin Williams, initiated the math contest.

Bill Whitaker: And did you think anyone would solve it?

Michelle Blouin Williams: Well, I wasn't necessarily looking for a solve. So, no, I didn't—

Bill Whitaker: What were you looking for?

Michelle Blouin Williams: I was just looking for some ingenuity, you know—

Calcea and Ne'Kiya delivered on that! They tried to explain their groundbreaking work to 60 Minutes. Calcea's proof is appropriately titled the Waffle Cone.

Calcea Johnson: So to start the proof, we start with just a regular right triangle where the angle in the corner is 90°. And the two angles are alpha and beta.

Bill Whitaker: Uh-huh

Calcea Johnson: So then what we do next is we draw a second congruent, which means they're equal in size. But then we start creating similar but smaller right triangles going in a pattern like this. And then it continues for infinity. And eventually it creates this larger waffle cone shape.

Calcea Johnson: Am I going a little too—

Bill Whitaker: You've been beyond me since the beginning. (laughter) 

Bill Whitaker: So how did you figure out the proof?

Ne'Kiya Jackson: Okay. So you have a right triangle, 90° angle, alpha and beta.

Bill Whitaker: Then what did you do?

Ne'Kiya Jackson: Okay, I have a right triangle inside of the circle. And I have a perpendicular bisector at OP to divide the triangle to make that small right triangle. And that's basically what I used for the proof. That's the proof.

Bill Whitaker: That's what I call amazing.

Ne'Kiya Jackson: Well, thank you.

There had been one other documented proof of the theorem using trigonometry by mathematician Jason Zimba in 2009 – one in 2,000 years. Now it seems Ne'Kiya and Calcea have joined perhaps the most exclusive club in mathematics. 

Bill Whitaker: So you both independently came up with proof that only used trigonometry.

Ne'Kiya Jackson: Yes.

Bill Whitaker: So are you math geniuses?

Calcea Johnson: I think that's a stretch. 

Bill Whitaker: If not genius, you're really smart at math.

Ne'Kiya Jackson: Not at all. (laugh) 

To document Calcea and Ne'Kiya's work, math teachers at St. Mary's submitted their proofs to an American Mathematical Society conference in Atlanta in March 2023.

Ne'Kiya Jackson: Well, our teacher approached us and was like, "Hey, you might be able to actually present this," I was like, "Are you joking?" But she wasn't. So we went. I got up there. We presented and it went well, and it blew up.

Bill Whitaker: It blew up.

Calcea Johnson: Yeah. 

Ne'Kiya Jackson: It blew up.

Bill Whitaker: Yeah. What was the blowup like?

Calcea Johnson: Insane, unexpected, crazy, honestly.

It took millenia to prove, but just a minute for word of their accomplishment to go around the world. They got a write-up in South Korea and a shout-out from former first lady Michelle Obama, a commendation from the governor and keys to the city of New Orleans. 

Bill Whitaker: Why do you think so many people found what you did to be so impressive?

Ne'Kiya Jackson: Probably because we're African American, one. And we're also women. So I think-- oh, and our age. Of course our ages probably played a big part.

Bill Whitaker: So you think people were surprised that young African American women, could do such a thing?

Calcea Johnson: Yeah, definitely.

Ne'Kiya Jackson: I'd like to actually be celebrated for what it is. Like, it's a great mathematical achievement.

Achievement, that's a word you hear often around St. Mary's academy. Calcea and Ne'Kiya follow a long line of barrier-breaking graduates. 

The late queen of Creole cooking, Leah Chase , was an alum. so was the first African-American female New Orleans police chief, Michelle Woodfork …

And judge for the Fifth Circuit Court of Appeals, Dana Douglas. Math teacher Michelle Blouin Williams told us Calcea and Ne'Kiya are typical St. Mary's students.  

Bill Whitaker: They're not unicorns.

Michelle Blouin Williams: Oh, no no. If they are unicorns, then every single lady that has matriculated through this school is a beautiful, Black unicorn.

Pamela Rogers: You're good?

Pamela Rogers, St. Mary's president and interim principal, told us the students hear that message from the moment they walk in the door.

Pamela Rogers: We believe all students can succeed, all students can learn. It does not matter the environment that you live in. 

Bill Whitaker: So when word went out that two of your students had solved this almost impossible math problem, were they universally applauded?

Pamela Rogers: In this community, they were greatly applauded. Across the country, there were many naysayers.

Bill Whitaker: What were they saying?

Pamela Rogers: They were saying, "Oh, they could not have done it. African Americans don't have the brains to do it." Of course, we sheltered our girls from that. But we absolutely did not expect it to come in the volume that it came.  

Bill Whitaker: And after such a wonderful achievement.

Pamela Rogers: People-- have a vision of who can be successful. And-- to some people, it is not always an African American female. And to us, it's always an African American female.

Gloria Ladson-Billings: What we know is when teachers lay out some expectations that say, "You can do this," kids will work as hard as they can to do it.

Gloria Ladson-Billings, professor emeritus at the University of Wisconsin, has studied how best to teach African American students. She told us an encouraging teacher can change a life.

Bill Whitaker: And what's the difference, say, between having a teacher like that and a whole school dedicated to the excellence of these students?

Gloria Ladson-Billings: So a whole school is almost like being in Heaven. 

Bill Whitaker: What do you mean by that?

Gloria Ladson-Billings: Many of our young people have their ceilings lowered, that somewhere around fourth or fifth grade, their thoughts are, "I'm not going to be anything special." What I think is probably happening at St. Mary's is young women come in as, perhaps, ninth graders and are told, "Here's what we expect to happen. And here's how we're going to help you get there."

At St. Mary's, half the students get scholarships, subsidized by fundraising to defray the $8,000 a year tuition. Here, there's no test to get in, but expectations are high and rules are strict: no cellphones, modest skirts, hair must be its natural color.

Students Rayah Siddiq, Summer Forde, Carissa Washington, Tatum Williams and Christina Blazio told us they appreciate the rules and rigor.

Rayah Siddiq: Especially the standards that they set for us. They're very high. And I don't think that's ever going to change.

Bill Whitaker: So is there a heart, a philosophy, an essence to St. Mary's?

Summer Forde: The sisterhood—

Carissa Washington: Sisterhood.

Tatum Williams: Sisterhood.

Bill Whitaker: The sisterhood?

Voices: Yes.

Bill Whitaker: And you don't mean the nuns. You mean-- (laughter)

Christina Blazio: I mean, yeah. The community—

Bill Whitaker: So when you're here, there's just no question that you're going to go on to college.

Rayah Siddiq: College is all they talk about. (laughter) 

Pamela Rogers: … and Arizona State University (Cheering)

Principal Rogers announces to her 615 students the colleges where every senior has been accepted.

Bill Whitaker: So for 17 years, you've had a 100% graduation rate—

Pamela Rogers: Yes.

Bill Whitaker: --and a 100% college acceptance rate?

Pamela Rogers: That's correct.

Last year when Ne'Kiya and Calcea graduated, all their classmates went to college and got scholarships. Ne'Kiya got a full ride to the pharmacy school at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University.

Bill Whitaker: So wait a minute. Neither one of you is going to pursue a career in math?

Both: No. (laugh)

Calcea Johnson: I may take up a minor in math. But I don't want that to be my job job.

Ne'Kiya Jackson: Yeah. People might expect too much out of me if (laugh) I become a mathematician. (laugh)

But math is not completely in their rear-view mirrors. This spring they submitted their high school proofs for final peer review and publication … and are still working on further proofs of the Pythagorean Theorem. Since their first two …

Calcea Johnson: We found five. And then we found a general format that could potentially produce at least five additional proofs.

Bill Whitaker: And you're not math geniuses?

Bill Whitaker: I'm not buying it. (laughs)

Produced by Sara Kuzmarov. Associate producer, Mariah B. Campbell. Edited by Daniel J. Glucksman.

Bill Whitaker is an award-winning journalist and 60 Minutes correspondent who has covered major news stories, domestically and across the globe, for more than four decades with CBS News.

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LSU Provost’s Fund Invests $1.2 Million in Highly Competitive Research Teams

May 14, 2024

In a second round of Big Idea seed grants, the largest internal funding program in LSU history, the Provost’s Fund for Innovation in Research is investing $1.2 million in 15 interdisciplinary research teams. Aligned with LSU’s Scholarship First Agenda, the teams and their projects aim to solve pressing problems in Louisiana and everywhere.

“This substantial investment marks a strategic advancement in growing competitively and federally funded research at LSU,” Executive Vice President and Provost Roy Haggerty said. “It directly supports our mission to address critical challenges in Louisiana and to elevate LSU as a comprehensive, leading research university on the national stage.”

Projects include how to restore river deltas and protect coastlines by leveraging the land-building capabilities of soil-microbe-plant ecosystems; develop new treatments for drug-resistant cancers; improve human-robot collaboration; and support the health and performance of student athletes, warfighters, astronauts and first responders as well as older Black people who are four times more likely to suffer from frailty than their white counterparts.

In total, the funded projects will engage 65 faculty across nine colleges and schools on LSU’s flagship campus in Baton Rouge, extending collaboration to LSU Athletics, LSU AgCenter, Pennington Biomedical Research Center and LSU Health New Orleans. Two projects support advances in agriculture; seven projects drive discovery in biomedicine; six projects elevate the coast and environment; six projects protect the state and nation through stronger defense and cybersecurity; and six projects help secure the future of energy.

The goal of the Provost’s Fund is to provide seed funding to transform new ideas into nationally competitive research programs that are likely to attract external support and bring significant federal funding to Louisiana. Beyond the Big Idea grants, the Provost’s Fund also awards Faculty Travel Grants (this spring, to 37 faculty across the disciplines), Research & Creative Activity Support (this spring, to 14 faculty in the arts, humanities, social and behavioral sciences) and Seminar & Collaborator Support (this year, to 10 faculty).

This year’s Big Idea awards are categorized into five Phase 1 grants at $25,000 each (increased from $10,000 last year) to help researchers get organized; eight Phase 2 grants at $75,000 to develop preliminary data and create long-term research agendas; and two Phase 3 grants at $250,000 to develop large, center-scale grant proposals for national impact.

“In Louisiana, we face serious economic and social challenges related to insurance, extreme weather as well as infrastructural and community challenges in the face of natural hazards. Our future prosperity depends on our collective capacity to innovate and problem-solve in the fields of risk management and resilience,” said Thomas Douthat, assistant professor of environmental sciences at LSU and principal investigator for one of the two Phase 3 awards. “This funding will enable collaboration between LSU and LSU AgCenter in coastal sciences, resilient construction, energy, design and policy, and strengthen partnerships and nation-leading research in this field.”

“Our goal, the development of a Center for Exercise Science and Sports Medicine at LSU, is the natural progression of the existing partnership between LSU researchers and members of the LSU Athletics family,” said Guillaume Spielmann, associate professor of kinesiology and principal investigator on the other Phase 3 award. “Together, we will work to maximize holistic health, safety and well-being, culminating in the enduring success of LSU Athletics.”

Learn more about the funded projects and how they will improve lives for everyone in Louisiana and beyond.

Abbi Rocha Laymoun

LSU Media Relations

LSU Office of Research & Economic Development

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How Biden Adopted Trump’s Trade War With China

The president has proposed new barriers to electric vehicles, steel and other goods..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

From “The New York Times,” I’m Sabrina Tavernise, and this is “The Daily.”

[MUSIC PLAYING]

Donald Trump upended decades of American policy when he started a trade war with China. Many thought that President Biden would reverse those policies. Instead, he’s stepping them up. Today, my colleague, Jim Tankersley, explains.

It’s Monday, May 13.

Jim, it’s very nice to have you in the studio.

It’s so great to be here, Sabrina. Thank you so much.

So we are going to talk today about something I find very interesting and I know you’ve been following. We’re in the middle of a presidential campaign. You are an economics reporter looking at these two candidates, and you’ve been trying to understand how Trump and Biden are thinking about our number one economic rival, and that is China.

As we know, Trump has been very loud and very clear about his views on China. What about Biden?

Well, no one is going to accuse President Biden of being as loud as former President Trump. But I think he’s actually been fairly clear in a way that might surprise a lot of people about how he sees economic competition with China.

We’re going after China in the wrong way. China is stealing intellectual property. China is conditioning —

And Biden has, kind of surprisingly, sounded a lot, in his own Joe Biden way, like Trump.

They’re not competing. They’re cheating. They’re cheating. And we’ve seen the damage here in America.

He has been very clear that he thinks China is cheating in trade.

The bottom line is I want fair competition with China, not conflict. And we’re in a stronger position to win the economic competition of the 21st century against China or anyone else because we’re investing in America and American workers again. Finally.

And maybe the most surprising thing from a policy perspective is just how much Biden has built on top of the anti-China moves that Trump made and really is the verge of his own sort of trade war with China.

Interesting. So remind us, Jim, what did Trump do when he actually came into office? We, of course, remember Trump really talking about China and banging that drum hard during the campaign, but remind us what he actually did when he came into office.

Yeah, it’s really instructive to start with the campaign, because Trump is talking about China in some very specific ways.

We have a $500 billion deficit, trade deficit, with China. We’re going to turn it around. And we have the cards. Don’t forget —

They’re ripping us off. They’re stealing our jobs.

They’re using our country as a piggy bank to rebuild China, and many other countries are doing the same thing. So we’re losing our good jobs, so many.

The economic context here is the United States has lost a couple of million jobs in what was called the China shock of the early 2000s. And Trump is tapping into that.

But when the Chinese come in, and they want to make great trade deals — and they make the best trade deals, and not anymore. When I’m there, we turn it around, folks. We turn it around. We have —

And what he’s promising as president is that he’s going to bring those jobs back.

I’ll be the greatest jobs president that God ever created. I’ll take them back from China, from Japan.

And not just any jobs, good-paying manufacturing jobs, all of it — clothes, shoes, steel, all of these jobs that have been lost that American workers, particularly in the industrial Midwest, used to do. Trump’s going to bring them back with policy meant to rebalance the trade relationship with China to get a better deal with China.

So he’s saying China is eating our lunch and has been for decades. That’s the reason why factory workers in rural North Carolina don’t have work. It’s those guys. And I’m going to change that.

Right. And he likes to say it’s because our leaders didn’t cut the right deal with them, so I’m going to make a better deal. And to get a better deal, you need leverage. So a year into his presidency, he starts taking steps to amass leverage with China.

And so what does that look like?

Just an hour ago, surrounded by a hand-picked group of steelworkers, President Trump revealed he was not bluffing.

It starts with tariffs. Tariffs are taxes that the government imposes on imports.

Two key global imports into America now face a major new barrier.

Today, I’m defending America’s national security by placing tariffs on foreign imports of steel and aluminum.

And in this case, it’s imports from a lot of different countries, but particularly China.

Let’s take it straight to the White House. The president of the United States announcing new trade tariffs against China. Let’s listen in.

This has been long in the making. You’ve heard —

So Trump starts, in 2018, this series of tariffs that he’s imposing on all sorts of things — washing machines, solar panels, steel, aluminum. I went to Delaware to a lighting store at that time, I remember, where basically everything they sold came from China and was subject to the Trump tariffs, because that’s where lighting was made now.

Interesting.

Hundreds of billions of dollars of Chinese goods now start falling under these Trump tariffs. The Chinese, of course, don’t take this lying down.

China says it is not afraid of a trade war with the US, and it’s fighting back against President Trump with its own tariffs on US goods.

They do their own retaliatory tariffs. Now American exports to China cost more for Chinese consumers. And boom, all of a sudden, we are in the midst of a full-blown trade war between the United States and Beijing.

Right. And that trade war was kind of a shock because for decades, politicians had avoided that kind of policy. It was the consensus of the political class in the United States that there should not be tariffs like that. It should be free trade. And Trump just came in and blew up the consensus.

Yeah. And Sabrina, I may have mentioned this once or 700 times before on this program, but I talk to a lot of economists in my job.

Yeah, it’s weird. I talk to a lot of economists. And in 2018 when this started, there were very, very, very few economists of any political persuasion who thought that imposing all these tariffs were a good idea. Republican economists in particular, this is antithetical to how they think about the world, which is low taxes, free trade. And even Democratic economists who thought they had some problems with the way free trade had been conducted did not think that Trump’s “I’m going to get a better deal” approach was going to work. And so there was a lot of criticism at the time, and a lot of politicians really didn’t like it, a lot of Democrats, many Republicans. And it all added up to just a real, whoa, I don’t think this is going to work.

So that begs the question, did it?

Well, it depends on what you mean by work. Economically, it does not appear to have achieved what Trump wanted. There’s no evidence yet in the best economic research that’s been done on this that enormous amounts of manufacturing jobs came back to the United States because of Trump’s tariffs. There was research, for example, on the tariffs on washing machines. They appear to have helped a couple thousand jobs, manufacturing jobs be created in the United States, but they also raised the price of washing machines for everybody who bought them by enough that each additional job that was created by those tariffs effectively cost consumers, like, $800,000 per job.

There’s like lots of evidence that the sectors Trump was targeting to try to help here, he didn’t. There just wasn’t a lot of employment rebound to the United States. But politically, it really worked. The tariffs were very popular. They had this effect of showing voters in those hollowed-out manufacturing areas that Trump was on their team and that he was fighting for them. Even if they didn’t see the jobs coming back, they felt like he was standing up for them.

So the research suggests this was a savvy political move by Trump. And in the process, it sort of changes the political economic landscape in both parties in the United States.

Right. So Trump made these policies that seemed, for many, many years in the American political system, fringe, isolationist, economically bad, suddenly quite palatable and even desirable to mainstream policymakers.

Yeah. Suddenly getting tough on China is something everyone wants to do across both parties. And so from a political messaging standpoint, being tough on China is now where the mainstream is. But at the same time, there is still big disagreement over whether Trump is getting tough on China in the right way, whether he’s actually being effective at changing the trade relationship with China.

Remember that Trump was imposing these tariffs as a way to get leverage for a better deal with China. Well, he gets a deal of sorts, actually, with the Chinese government, which includes some things about tariffs, and also China agreeing to buy some products from the United States. Trump spins it as this huge win, but nobody else really, including Republicans, acts like Trump has solved the problem that Trump himself has identified. This deal is not enough to make everybody go, well, everything’s great with China now. We can move on to the next thing.

China remains this huge issue. And the question of what is the most effective way to deal with them is still an animating force in politics.

Got it. So politically, huge win, but policy-wise and economically, and fundamentally, the problem of China still very much unresolved.

Absolutely.

So then Biden comes in. What does Biden do? Does he keep the tariffs on?

Biden comes to office, and there remains this real pressure from economists to roll back what they consider to be the ineffective parts of Trump’s trade policy. That includes many of the tariffs. And it’s especially true at a time when almost immediately after Biden takes office, inflation spikes. And so Americans are paying a lot of money for products, and there’s this pressure on Biden, including from inside his administration, to roll back some of the China tariffs to give Americans some relief on prices.

And Biden considers this, but he doesn’t do it. He doesn’t reverse Trump’s tariff policy. In the end, he’s actually building on it.

We’ll be right back.

So Jim, you said that Biden is actually building on Trump’s anti-China policy. What exactly does that look like?

So Biden builds on the Trump China policy in three key ways, but he does it with a really specific goal that I just want you to keep in mind as we talk about all of this, which is that Biden isn’t just trying to beat China on everything. He’s not trying to cut a better deal. Biden is trying to beat China in a specific race to own the clean-energy future.

Clean energy.

Yeah. So keep that in mind, clean energy. And the animating force behind all of the things Biden does with China is that Biden wants to beat China on what he thinks are the jobs of the future, and that’s green technology.

Got it. OK. So what does he do first?

OK. Thing number one — let’s talk about the tariffs. He does not roll them back. And actually, he builds on them. For years, for the most part, he just lets the tariffs be. His administration reviews them. And it’s only now, this week, when his administration is going to actually act on the tariffs. And what they’re going to do is raise some of them. They’re going to raise them on strategic green tech things, like electric vehicles, in order to make them more expensive.

And I think it’s important to know the backdrop here, which is since Biden has taken office, China has started flooding global markets with really low-cost green technologies. Solar panels, electric vehicles are the two really big ones. And Biden’s aides are terrified that those imports are going to wash over the United States and basically wipe out American automakers, solar panel manufacturers, that essentially, if Americans can just buy super-cheap stuff from China, they’re not going to buy it from American factories. Those factories are going to go out of business.

So Biden’s goal of manufacturing jobs in clean energy, China is really threatening that by dumping all these products on the American market.

Exactly. And so what he wants to do is protect those factories with tariffs. And that means increasing the tariffs that Trump put on electric vehicles in hopes that American consumers will find them too expensive to buy.

But doesn’t that go against Biden’s goal of clean energy and things better for the environment? Lots of mass-market electric vehicles into the United States would seem to advance that goal. And here, he’s saying, no, you can’t come in.

Right, because Biden isn’t just trying to reduce emissions at all costs. He wants to reduce emissions while boosting American manufacturing jobs. He doesn’t want China to get a monopoly in these areas. And he’s also, in particular, worried about the politics of lost American manufacturing jobs. So Biden does not want to just let you buy cheaper Chinese technologies, even if that means reducing emissions.

He wants to boost American manufacturing of those things to compete with China, which brings us to our second thing that Biden has done to build on Trump’s China policy, which is that Biden has started to act like the Chinese government in particular areas by showering American manufacturers with subsidies.

I see. So dumping government money into American businesses.

Yes, tax incentives, direct grants. This is a way that China has, in the past decades, built its manufacturing dominance, is with state support for factories. Biden is trying to do that in particular targeted industries, including electric vehicles, solar power, wind power, semiconductors. Biden has passed a bunch of legislation that showers those sectors with incentives and government support in hopes of growing up much faster American industry.

Got it. So basically, Biden is trying to beat China at its own game.

Yeah, he’s essentially using tariffs to build a fortress around American industry so that he can train the troops to fight the clean energy battle with China.

And the troops being American companies.

Yes. It’s like, we’re going to give them protection — protectionist policy — in order to get up to size, get up to strength as an army in this battle for clean energy dominance against the Chinese.

Got it. So he’s trying to build up the fortress. What’s the third thing Biden does? You mentioned three things.

Biden does not want the United States going it alone against China. He’s trying to build an international coalition, wealthy countries and some other emerging countries that are going to take on China and try to stop the Chinese from using their trade playbook to take over all these new emerging industrial markets.

But, Jim, why? What does the US get from bringing our allies into this trade war? Why does the US want that?

Some of this really is about stopping China from gaining access to new markets. It’s like, if you put the low-cost Chinese exports on a boat, and it’s going around the world, looking for a dock to stop and offload the stuff and sell it, Biden wants barriers up at every possible port. And he wants factories in those places that are competing with the Chinese.

And a crucial fact to know here is that the United States and Europe, they are behind China when it comes to clean-energy technology. The Chinese government has invested a lot more than America and Europe in building up its industrial capacity for clean energy. So America and its allies want to deny China dominance of those markets and to build up their own access to them.

And they’re behind, so they’ve got to get going. It’s like they’re in a race, and they’re trailing.

Yeah, it’s an economic race to own these industries, and it’s that global emissions race. They also want to be bringing down fossil-fuel emissions faster than they currently are, and this is their plan.

So I guess, Jim, the question in my mind is, Trump effectively broke the seal, right? He started all of these tariffs. He started this trade war with China. But he did it in this kind of jackhammer, non-targeted way, and it didn’t really work economically. Now Biden is taking it a step further. But the question is, is his effort here going to work?

The answer to whether it’s going to work really depends on what your goals are. And Biden and Trump have very different goals. If Trump wins the White House back, he has made very clear that his goal is to try to rip the United States trade relationship with China even more than he already has. He just wants less trade with China and more stuff of all types made in the United States that used to be made in China. That’s a very difficult goal, but it’s not Biden’s goal.

Biden’s goal is that he wants America to make more stuff in these targeted industries. And there is real skepticism from free-market economists that his industrial policies will work on that, but there’s a lot of enthusiasm for it from a new strain of Democratic economists, in particular, who believe that the only chance Biden has to make that work is by pulling all of these levers, by doing the big subsidies and by putting up the tariffs, that you have to have both the troops training and the wall around them. And if it’s going to work, he has to build on the Trump policies. And so I guess you’re asking, will it work? It may be dependent upon just how far he’s willing to go on the subsidies and the barriers.

There’s a chance of it.

So, Jim, at the highest level, whatever the economic outcome here, it strikes me that these moves by Biden are pretty remarkably different from the policies of the Democratic Party over the decades, really going in the opposite direction. I’m thinking of Bill Clinton and NAFTA in the 1990s. Free trade was the real central mantra of the Democratic Party, really of both parties.

Yeah, and Biden is a real break from Clinton. And Clinton was the one who actually signed the law that really opened up trade with China, and Biden’s a break from that. He’s a break from even President Obama when he was vice president. Biden is doing something different. He’s breaking from that Democratic tradition, and he’s building on what Trump did, but with some throwback elements to it from the Roosevelt administration and the Eisenhower administration. This is this grand American tradition of industrial policy that gave us the space race and the interstate highway system. It’s the idea of using the power of the federal government to build up specific industrial capacities. It was in vogue for a time. It fell out of fashion and was replaced by this idea that the government should get out of the way, and you let the free market drive innovation. And now that industrial policy idea is back in vogue, and Biden is doing it.

So it isn’t just a shift or an evolution. It’s actually a return to big government spending of the ‘30s and the ‘40s and the ‘50s of American industrialism of that era. So what goes around comes around.

Yeah, and it’s a return to that older economic theory with new elements. And it’s in part because of the almost jealousy that American policymakers have of China and the success that it’s had building up its own industrial base. But it also has this political element to it. It’s, in part, animated by the success that Trump had making China an issue with working-class American voters.

You didn’t have to lose your job to China to feel like China was a stand-in for the forces that have taken away good-paying middle-class jobs from American workers who expected those jobs to be there. And so Trump tapped into that. And Biden is trying to tap into that. And the political incentives are pushing every future American president to do more of that. So I think we are going to see even more of this going forward, and that’s why we’re in such an interesting moment right now.

So we’re going to see more fortresses.

More fortresses, more troops, more money.

Jim, thank you.

You’re welcome.

Here’s what else you should know today. Intense fighting between Hamas fighters and Israeli troops raged in parts of Northern Gaza over the weekend, an area where Israel had declared Hamas defeated earlier in the war, only to see the group reconstitute in the power vacuum that was left behind. The persistent lawlessness raised concerns about the future of Gaza among American officials. Secretary of State Antony Blinken said on “Face the Nation” on Sunday that the return of Hamas to the North left him concerned that Israeli victories there would be, quote, “not sustainable,” and said that Israel had not presented the United States with any plan for when the war ends.

And the United Nations aid agency in Gaza said early on Sunday that about 300,000 people had fled from Rafah over the past week, the city in the enclave’s southernmost tip where more than a million displaced Gazans had sought shelter from Israeli bombardments elsewhere. The UN made the announcement hours after the Israeli government issued new evacuation orders in Rafah, deepening fears that the Israeli military was preparing to invade the city despite international warnings.

Today’s episode was produced by Nina Feldman, Carlos Prieto, Sidney Harper, and Luke Vander Ploeg. It was edited by M.J. Davis Lin, Brendan Klinkenberg, and Lisa Chow. Contains original music by Diane Wong, Marion Lozano, and Dan Powell, and was engineered by Alyssa Moxley. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

That’s it for “The Daily.” I’m Sabrina Tavernise. See you tomorrow.

• May 14, 2024   •   35:20 Voters Want Change. In Our Poll, They See It in Trump.
• May 13, 2024   •   27:46 How Biden Adopted Trump’s Trade War With China
• May 10, 2024   •   27:42 Stormy Daniels Takes the Stand
• May 9, 2024   •   34:42 One Strongman, One Billion Voters, and the Future of India
• May 8, 2024   •   28:28 A Plan to Remake the Middle East
• May 7, 2024   •   27:43 How Changing Ocean Temperatures Could Upend Life on Earth
• May 6, 2024   •   29:23 R.F.K. Jr.’s Battle to Get on the Ballot
• May 3, 2024   •   25:33 The Protesters and the President
• May 2, 2024   •   29:13 Biden Loosens Up on Weed
• May 1, 2024   •   35:16 The New Abortion Fight Before the Supreme Court
• April 30, 2024   •   27:40 The Secret Push That Could Ban TikTok
• April 29, 2024   •   47:53 Trump 2.0: What a Second Trump Presidency Would Bring

Hosted by Sabrina Tavernise

Produced by Nina Feldman ,  Carlos Prieto ,  Sydney Harper and Luke Vander Ploeg

Edited by M.J. Davis Lin ,  Brendan Klinkenberg and Lisa Chow

Original music by Diane Wong ,  Marion Lozano and Dan Powell

Engineered by Alyssa Moxley

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Donald Trump upended decades of American policy when he started a trade war with China. Many thought that President Biden would reverse those policies. Instead, he’s stepping them up.

Jim Tankersley, who covers economic policy at the White House, explains.

On today’s episode

Jim Tankersley , who covers economic policy at the White House for The New York Times.

Background reading

Mr. Biden, competing with Mr. Trump to be tough on China , called for steel tariffs last month.

The Biden administration may raise tariffs on electric vehicles from China to 100 percent .

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We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

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Luke Vander Ploeg is a senior producer on “The Daily” and a reporter for the National Desk covering the Midwest. More about Luke Vander Ploeg

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