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5 Ways to Stop Thinking for Your Students

Too often math students lean on teachers to think for them, but there are some simple ways to guide them to think for themselves.

Who is doing the thinking in your classroom? If you asked me that question a few years ago, I would have replied, “My kids are doing the thinking, of course!” But I was wrong. As I reflect back to my teaching style before I read Building Thinking Classrooms by Peter Liljedahl (an era in my career I like to call “pre-thinking classroom”), I now see that I was encouraging my students to mimic rather than think .

My lessons followed a formula that I knew from my own school experience as a student and what I had learned in college as a pre-service teacher. It looked like this: Students faced me stationed at the board; I demonstrated a few problems while students copied what I wrote in their notes. I would throw out a few questions to the class to assess understanding. If a few kids answered correctly, I felt confident that the lesson had gone well. Some educators might call this “ I do, we do, you do .”

What’s wrong with this formula? When it was time for them to work independently, which usually meant a homework assignment because I used most of class time for direct instruction, the students would come back to class and say, “The homework was so hard. I don’t get it. Can you go over questions 1–20?” Exhausted and frustrated, I would wonder, “But I taught it—why didn’t they get it?”

Now in the “peri-thinking classroom” era of my career, my students are often working at the whiteboards in random groups as outlined in Liljedahl’s book. The pendulum has shifted from the teacher doing the thinking to the students doing the thinking. Do they still say, “I don’t get it!”? Yes, of course! But I use the following strategies to put the thinking back onto them.

5 Ways to Get Your Students to Think

1. Answer questions with a refocus on the students’ point of view. Liljedahl found in his research that students ask three types of questions: “(1) proximity questions—asked when the teacher is close; (2) stop thinking questions—most often of the form ‘is this right’ or ‘will this be on the test’; and (3) keep thinking questions—questions that students ask so they can get back to work.” He suggests that teachers acknowledge “proximity” and “stop thinking questions” but not answer them.

Try these responses to questions that students ask to keep working:

• “What have you done so far?” 
• “Where did you get that number?” 
• “What information is given in the problem?” 
• “Does that number seem reasonable in this situation?”  

2. Don’t carry a pencil or marker. This is a hard rule to follow; however, if you hold the writing utensil, you’ll be tempted to write for them . Use verbal nudges and hints, but avoid writing out an explanation. If you need to refer to a visual, find a group that has worked out the problem, and point out their steps. Hearing and viewing other students’ work is more powerful .

3. We instead of I . When I assign a handful of problems for groups to work on at the whiteboards, they are tempted to divvy up the task. “You do #30, and I’ll do #31.” This becomes an issue when they get stuck. I inevitably hear, “Can you help me with #30? I forgot how to start.”

I now require questions to use “we” instead of “I.” This works wonders. As soon as they start to ask a question with “I,” they pause and ask their group mates. Then they can legitimately say, “ We tried #30, and we are stumped.” But, in reality, once they loop in their group mates, the struggling student becomes unstuck, and everyone in the group has to engage with the problem.

4. Stall your answer. If I hear a basic computation question such as, “What is 3 divided by 5?” I act like I am busy helping another student: “Hold on, I need to help Marisela. I’ll be right back.” By the time I return to them, they are way past their question. They will ask a classmate, work it out, or look it up. If the teacher is not available to think for them, they learn to find alternative resources.

5. Set boundaries. As mentioned before, students ask “proximity” questions because I am close to them. I might reply with “Are you asking me a thinking question? I’m glad to give you a hint or nudge, but I cannot take away your opportunity to think.” This type of response acknowledges that you are there to help them but not to do their thinking for them.

When you set boundaries of what questions will be answered, the students begin to more carefully craft their questions. At this point of the year, I am starting to hear questions such as, “We have tried solving this system by substitution, but we are getting an unreasonable solution. Can you look at our steps?” Yes!

Shifting the focus to students doing the thinking not only enhances their learning but can also have the effect of less frustration and fatigue for the teacher. As the class becomes student-centered, the teacher role shifts to guide or facilitator and away from “sage on the stage.”

As another added benefit, when you serve as guide or facilitator, the students are getting differentiated instruction and assessment. Maybe only a few students need assistance with adding fractions, while a few students need assistance on an entirely different concept. At first, you might feel like your head is spinning trying to address so many different requests; however, as you carefully sift through the types of questions you hear, you will soon be comfortable only answering the “keep thinking” questions.

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Spirit of Mathematics Critical Thinking Skills (CTS)

S Syafril 1 , N R Aini 1 , Netriwati 1 , A Pahrudin 1 , N E Yaumas 1 and Engkizar 2

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 1467 , Young Scholar Symposium on Science Education and Environment 2019 4-5 November 2019, Lampung, Indonesia Citation S Syafril et al 2020 J. Phys.: Conf. Ser. 1467 012069 DOI 10.1088/1742-6596/1467/1/012069

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1 Universitas Islam Negeri Raden Intan Lampung, Indonesia

2 Universitas Negeri Padang, Indonesia

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The mathematical critical-thinking skill is a process of thinking systematically to develop logical and critical thinking on mathematical problems, which characterize and demand to learn in the 21st century. This conceptual paper aims to analyze the spirit of critical thinking skill, and various approaches that can be applied in mathematics learning. Based on the analysis of several theories and research findings from various countries in the world, it can be concluded that the mathematical critical-thinking skill is very important for students, too; (i) help rational thinking in making decisions to express an idea, (ii) dare to make conclusions with alternative logical thinking, and (iii) able to examine and disregard various complex problems in learning Mathematics. Indeed, mathematics learning does not occur, if the learning process has not demonstrated the spirit of developing mathematical critical thinking skills.

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Critical thinking definition

Critical thinking, as described by Oxford Languages, is the objective analysis and evaluation of an issue in order to form a judgement.

Active and skillful approach, evaluation, assessment, synthesis, and/or evaluation of information obtained from, or made by, observation, knowledge, reflection, acumen or conversation, as a guide to belief and action, requires the critical thinking process, which is why it's often used in education and academics.

Some even may view it as a backbone of modern thought.

However, it's a skill, and skills must be trained and encouraged to be used at its full potential.

People turn up to various approaches in improving their critical thinking, like:

• Developing technical and problem-solving skills
• Engaging in more active listening
• Actively questioning their assumptions and beliefs
• Seeking out more diversity of thought
• Opening up their curiosity in an intellectual way etc.

Is critical thinking useful in writing?

Critical thinking can help in planning your paper and making it more concise, but it's not obvious at first. We carefully pinpointed some the questions you should ask yourself when boosting critical thinking in writing:

• What information should be included?
• Which information resources should the author look to?
• What degree of technical knowledge should the report assume its audience has?
• What is the most effective way to show information?
• How should the report be organized?
• How should it be designed?
• What tone and level of language difficulty should the document have?

Usage of critical thinking comes down not only to the outline of your paper, it also begs the question: How can we use critical thinking solving problems in our writing's topic?

Let's say, you have a Powerpoint on how critical thinking can reduce poverty in the United States. You'll primarily have to define critical thinking for the viewers, as well as use a lot of critical thinking questions and synonyms to get them to be familiar with your methods and start the thinking process behind it.

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Critical Thinking in Mathematics Education

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• Logical thinking
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• Mathematical literacy
• Critical judgment
• Goals of mathematics education

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Jablonka, E. (2014). Critical Thinking in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_35

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Thinking About Kahneman’s Contribution to Critical Thinking

A nobel laureate on contributions on the importance of 'thinking slow.'.

Updated April 10, 2024 | Reviewed by Lybi Ma

• Kahneman won a Nobel Memorial Prize in Economics for his work.
• He found that people are often irrational about economics.

During my Ph.D. studies, I recall focusing on reconceptualising what we know of as critical thinking to include reflective judgment (not jumping to conclusions and taking your time in your decision-making to consider the nature limits, and certainty of knowing) on par with the commonly accepted skills and dispositions components. The importance of reflective judgment wasn’t a particularly novel idea – a good deal of research on reflective judgment and similar processes akin to critical thinking had already been conducted (see King and Kitchener, 1994; Kuhn, 1999; 2000; Stanovich, 1999). However, reflective judgment – as opposed to intuitive judgment – didn’t seem to have ‘the presence’ in the discussion of critical thinking that it does today.

The same month I submitted my Ph.D. back in 2011, a book was released that massively helped to accomplish what I had been working to help facilitate – changing the terrain of thought surrounding critical thinking: Thinking, Fast, and Slow . Its author, Daniel Kahneman, passed away a couple of weeks ago at age 90. Psychology students will likely recognise the name associated with Amos Tversky and their classic work together in the 1970s on the availability, representativeness, and anchoring and adjustment heuristics (for example, Tversky and Kahneman, 1974). Indeed, such heuristics, alongside the affect heuristic (Kahneman and Frederick, 2002; Slovic and colleagues, 2002) play a large role in how we think about thinking and barriers to critical thought. In 2002, Kahneman won a Nobel Memorial Prize in Economics for his work on prospect theory concerning loss aversion and people’s often irrational approach to economics. Indeed, Kahneman’s resume is full of awards and achievements.

However, the accomplishment I will remember him best for is the publication of Thinking, Fast, and Slow and its contribution to the field of critical thinking. Funny enough, I don’t recall the term, critical thinking being used very often in the book, if at all – and I read it two or three times. No, critical thinking was not the focus of his book; rather system 1 (fast) and 2 (slow) thinking (see also Stanovich, 1999) – intuitive and reflective judgment. Not only did this book put into the spotlight many of the mechanics of reflective judgment for fellow academics and researchers of cognitive psychology, it also did so l for non-academic audiences – becoming a New York Times bestseller. Moreover, it won the Los Angeles Times Book Award for Current Interest, and the National Academy of Sciences Communication Award for Best Book (both in 2011). Good thinking was cool again in popular culture.

In the critical thinking literature, reflective judgment – regardless of what you want to call it (for example, system 2 thinking, epistemological understanding, ‘taking your time’) – is becoming more accepted as a core component of critical thinking. The field of critical thinking research and psychology more broadly, owes Kahneman a debt of gratitude for his contributions in helping shine a light on the importance of ‘thinking slow’. Thank you .

Kahneman, D. (2011). Thinking, fast and slow . 2UK: Penguin.

Kahneman, D., & Frederick, S. (2002). Representativeness revisited: Attribute substitution in intuitive judgment. Heuristics and biases: The Psychology of Intuitive Judgment , 49 (49-81), 74.

King, P. M., & Kitchener, K. S. (1994). Developing Reflective Judgment: Understanding and Promoting Intellectual Growth and Critical Thinking in Adolescents and Adults. CA: Jossey-Bass.

King, P. M., & Kitchener, K. S. (2004). Reflective judgment: Theory and research on the development of epistemic assumptions through adulthood. Educational Psychologist, 39 (1), 5–15.

Kuhn, D. (1999). A developmental model of critical thinking. Educational Researcher , 28 (2), 16-46.

Kuhn, D. (2000). Metacognitive development. Current Directions in Psychological Science , 9 (5), 178-181.

Slovic, P., Finucane, M., Peters, E., & MacGregor, D. G. (2002). Rational actors or rational fools: Implications of the affect heuristic for behavioral economics. The Journal of Socio-economics , 31 (4), 329-342.

Stanovich, K.E. (1999) Who is rational? Studies of individual differences in reasoning. Mahwah, Erlbaum.

Tversky, A., & Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases: Biases in judgments reveal some heuristics of thinking under uncertainty. Science , 185 (4157), 1124-1131.

Christopher Dwyer, Ph.D., is a lecturer at the Technological University of the Shannon in Athlone, Ireland.

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