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What is Synthesis?

Here are some ways to think about synthesis:

Synthesis blends claims, evidence, and your unique insights to create a strong, unified paragraph. Assertions act as the threads, evidence adds texture, and your commentary weaves them together, revealing the connections and why they matter.

Beyond the sum of its parts: Synthesis isn't just adding one and one. It's recognizing how multiple sources, through their connections and relationships, create a deeper understanding than any single one could achieve.

Synthesis isn't just about what sources say, it's about how they say it. By digging into assumptions, interpretations, and even speculations, you uncover hidden connections and build a more nuanced picture.

Whereas analyzing involves dismantling a whole to understand its parts and their relationships, synthesizing involves collecting diverse parts and weaving them together to form a novel whole. Reading is an automatic synthesis process, where we connect incoming information with our existing knowledge, constructing a new, expanded "whole" of our understanding in the subject area.

You've been doing synthesis for a long time, the key now is being aware and organized in the process.

• Sharpen your research direction: Be clear about your main objective. This guides your reading and analysis to make the most of your time.
• Build a strong foundation: Use trusted sources like peer-reviewed journals, academic books, and reputable websites. Diverse sources add strength and credibility to your research.

Then Organize your Research:

• Dig deep and connect the dots: While reading, highlight key ideas, arguments, and evidence. Mark potential links between sources, like overlaps or contrasting arguments.
• Organize ideas by neighborhood: Group sources with similar themes or angles on your topic. This will show you where sources agree or clash, helping you build a nuanced understanding.
• Build a mind map of your research: Create a table of key themes, listing key points from each source and how they connect. This visual map can reveal patterns and identify any missing pieces in your research.

Finally, Build your synthesis:

• Lay out the groundwork: Kick off each section with a clear claim or theme to guide your analysis.
• Weave sources together: Briefly explain what each source brings to the table, smoothly connecting their ideas with transitions and language.
• Embrace the debate: Don't tiptoe around differences. Point out where sources agree or clash, and explore possible reasons for these discrepancies.
• Dig deeper than surface facts: Don't just parrot findings. Explain what they mean and how they impact your topic.
• Add your voice to the mix: Go beyond reporting. Analyze, evaluate, and draw conclusions based on your synthesis. What does this research tell us?

Tips & Tricks:

• Let the evidence do the talking: Back up your claims with concrete details, quotes, and examples from your sources. No need for personal opinions, just let the facts speak for themselves.
• Play fair with opposing views: Be objective and present different perspectives without showing favoritism. Even if you disagree, let readers see the other side of the coin.
• Give credit where credit is due: Make sure your sources get the recognition they deserve with proper citations, following your chosen style guide consistently.
• Polish your masterpiece: Take some time to revise and proofread your work. Ensure your arguments are crystal clear, concise, and well-supported by the evidence.
• Embrace the growth mindset: Remember, research and synthesis are a journey, not a destination. Keep refining your analysis as you learn more and encounter new information. The more you explore, the deeper your understanding will become.

Demonstrates how two or more sources agree with one another.

The collaborative nature of writing tutorials has been discussed by scholars like Andrea Lunsford (1991) and Stephen North (1984). In these essays, they explore the usefulness and the complexities of collaboration between tutors and students in writing center contexts.

Demonstrates how two or more sources support a main point in different ways.

While some scholars like Berlin (1987) have primarily placed their focus on the histories of large, famous universities, other scholars like Yahner and Murdick (1991) have found value in connecting their local histories to contrast or highlight trends found in bigger-name universities.

Accumulation

Demonstrates how one source builds on the idea of another.

Although North’s (1984) essay is fundamental to many writing centers today, Lunsford (1991) takes his ideas a step further by identifying different writing center models and also expanding North’s ideas on how writing centers can help students become better writers.

Demonstrates how one source discusses the effects of another source’s ideas.

While Healy (2001) notes the concerns of having primarily email appointments in writing centers, he also notes that constraints like funding, resources, and time affect how online resources are formed. For writing centers, email is the most economical and practical option for those wanting to offer online services but cannot dedicate the time or money to other online tutoring methods. As a result, in Neaderheiser and Wolfe’s (2009) reveals that of all the online options available in higher education, over 91% of institutions utilize online tutoring through email, meaning these constraints significantly affect the types of services writing centers offer.

[Taken from University of Illinois, "Synthesizing Research "]

The Writing Center at University of Arizona showcases how to create and use a synthesis matrix when reading sources and taking notes. It is a great, organized way to synthesize your research.

You can find it here .

Creativity in researching begins with developing a thorough understanding of your research topic; this is fundamental to streamlining the process and enriching your findings. This entails delving into its intricacies—exploring both similarities and divergences with related subject areas. Consider the most appropriate sources (and types of sources) for your study, critically engaging with all perspectives, and acknowledging the complex interplay between its positives, negatives, and broader connections.

Embrace interdisciplinary exploration. Delve deeper through transdisciplinary analysis, venturing beyond the immediate field to parallel professions and diverse academic arenas. Consider comparative studies from other cultural contexts to add fresh perspectives.

For example, researching rule changes in the NFL demands a nuanced approach. One might investigate the link to Traumatic Brain Injury, analyze case studies of impacted players, and even examine rule adjustments in other sports, drawing insights from their rationale and outcomes.

Remember, librarians are invaluable partners in this process. Their expertise in creative thinking and resource navigation can unlock a wealth of information, guiding you towards fruitful discoveries.

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Synthesis and Similarity in Science: Analogy in the Application of Mathematics and Application of Mathematics to Analogy

• First Online: 31 May 2022

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• Jordi Cat 11  

Part of the book series: Synthese Library ((SYLI,volume 453))

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Examining different cases, I show that, and how, analogies play a variety of roles in the application of mathematics. Different purposes may involve different cognitive and methodological tasks, some more descriptive – clustering –, others more heuristic – problem-solving and guiding metaphors – and others more evidentiary – robustness analysis and statistical inference in single studies and meta-analyses. Classification, generalization and justification cannot be easily reduced to basic standard patterns of analogical reasoning. I discuss two, however, main kinds of cases: the roles of analogy in the application of mathematics and, connectedly, the role of mathematics in the representation and implementation of analogical cognition.

Moreover, while the relevant similarities get a mathematical expression, the case of machine learning, including the case of similarity metrics and cluster analysis, shows that analogical cognition is not ultimately mathematical. And what I call the analogical circle is virtuous. But I also point to mathematical metaphors and, in relation to mathematical representations of similarity in clustering analysis, raise the issue of the possibility of mathematical representation of metaphoric function itself.

The different cases show in a new way also that the dependence on subjective judgment, research purpose, data characteristics and background information render the application of mathematics and analogical cognition, when connected, unavoidably contextual and plural.

The cases I have presented show also how analogy-driven or aided applications of mathematics connect analogical and synthetic tasks, and that they do so in different ways. They show, more specifically, also that each kind of task is a two-sided coin, so to speak, in scientific cognition and methodology. Synthesis involves also some form of differentiation or analysis, and connectedly, similarity is inseparable from dissimilarity.

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Maxwell’s methodological thinking about analogies borrowed from his interests in language and reasoning. He was educated and self-educated in the Aristotelian tradition of logic and rhetoric and in the new formulations of inductive scientific methodology of Herschel, Mill and Whewell. He was also an avid reader of romantic literature and poem writer and a prolific illustrator and draftsman of geometrical and ornamental designs (Cat, 2013 ). He viewed the application of mathematics accordingly, as a practice of exact but vivid language in the general representation of physical phenomena.

Maxwell was explicit about the role of formal analogies. Thus, Maxwell claimed (1) that the correctness of physical analogies depends on the mathematical analogy, namely, that related quantities belong in the same mathematical classes (Maxwell, 1856 , 157, 1870 , 219), and (2) that mathematical classes are in turn based on mathematical analogies (Maxwell, 1870 , 227). Those mathematical analogies are entertained in the mind, however, as far from purely symbolic and formal.

Maxwell’s analogies between mechanics and electricity or magnetism differed in this sense from William Thomson’s. As Nersessian puts it: ‘Maxwell did not make direct analogies between the domains. Rather, he constructed intermediary, hybrid models that embodied constraints from Newtonian sources and the electromagnetic target domain. Abstractive processes, especially generic modeling, enabled integrating selective constraints from the different domains because they were considered at a level of generality that eliminated the domain-specific differences.’ (Nersessian, 2018 , 60)

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Cat, J. (2022). Synthesis and Similarity in Science: Analogy in the Application of Mathematics and Application of Mathematics to Analogy. In: Wuppuluri, S., Grayling, A.C. (eds) Metaphors and Analogies in Sciences and Humanities. Synthese Library, vol 453. Springer, Cham. https://doi.org/10.1007/978-3-030-90688-7_6

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Higher Level Thinking: Synthesis in Bloom's Taxonomy

Putting the Parts Together to Create New Meaning

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Bloom’s Taxonomy  (1956 ) was designed with six levels in order to promote higher order thinking. Synthesis was placed on the fifth level of the Bloom’s taxonomy pyramid as it requires students to infer relationships among sources. The high-level thinking of synthesis is evident when students put the parts or information they have reviewed as a whole in order to create new meaning or a new structure.

The Online Etymology Dictionary records the word synthesis as coming from two sources:

"Latin synthesis  meaning a "collection, set, suit of clothes, composition (of a medication)" and also from the Greek  synthesis  meaning "a composition, a putting together."

The dictionary also records the evolution of the use of synthesis to include "deductive reasoning" in 1610 and "a combination of parts into a whole" in 1733. Today's students may use a variety of sources when they combine parts into a whole. The sources for synthesis may include articles, fiction, posts, or infographics as well as non-written sources, such as films, lectures, audio recordings, or observations.

Types of Synthesis in Writing

Synthesis writing is a process in which a student makes the explicit connection between a thesis (the argument) and evidence from sources with similar or dissimilar ideas. Before synthesis can take place, however, the student must complete a careful examination or close reading of all source material. This is especially important before a student can draft a synthesis essay.

There are two types of synthesis essays:

• A student may choose to use an explanatory synthesis essay in order to deconstruct or divide evidence into logical parts so that the essay is organized for readers. Explanatory synthesis essays usually include descriptions of objects, places, events or processes. Descriptions are written objectively because the explanatory synthesis does not present a position. The essay here has information gathered from the sources that the student places in a sequence or other logical manner.
• In order to present a position or opinion, a student may choose to use an argumentative synthesis. The thesis or position of an argumentative essay is one that can be debated. A thesis or position in this essay can be supported with evidence taken from sources and is organized so that it can be presented in a logical manner. 

The introduction to either synthesis essay contains a one-sentence (thesis) statement that sums up the essay's focus and introduces the sources or texts that will be synthesized. Students should follow the citation guidelines in referencing the texts in the essay, which includes their title and author(s) and maybe a little context about the topic or background information. 

The body paragraphs of a synthesis essay can be organized using several different techniques separately or in combination. These techniques can include: using a summary, making comparisons and contrasts, providing examples, proposing cause and effect, or conceding opposing viewpoints. Each of these formats allows the student the chance to incorporate the source materials in either the explanatory or the argumentative synthesis essay.

The conclusion of a synthesis essay may remind readers of the key points or suggestions for further research. In the case of the argumentative synthesis essay, the conclusion answers the "so what" that was proposed in the thesis or may call for action from the reader.

Key Words for the Synthesis Category:

blend, categorize, compile, compose, create, design, develop, form, fuse, imagine, integrate, modify, originate, organize, plan, predict, propose, rearrange, reconstruct, reorganize, solve, summarize, test, theorize, unite.

Synthesis Question Stems With Examples

• Can you develop a theory for the popularity of a text in English? 
• Can you predict the outcome of behavior in Psychology I by using polls or exit slips?
• How could you test the speed of a rubber-band car in physics if a test track is not available?
• How would you adapt ingredients to create a healthier casserole in Nutrition 103 class?'
• How could you change the plot of Shakespeare's Macbeth so it could be rated "G"?
• Suppose you could blend iron with another element so that it could burn hotter?
• What changes would you make to solve a linear equation if you could not use letters as variables?
• Can you fuse Hawthorne's short story "The Minister's Black Veil" with a soundtrack?
• Compose a nationalist song using percussion only.
• If you rearrange the parts in the poem "The Road Not Taken", what would the last line be?

Synthesis Essay Prompt Examples

• Can you propose a universal course of study in the use of social media that could be implemented across the United States?
• What steps could be taken in order to minimize food waste from the school cafeteria?
• What facts can you compile to determine if there has been an increase in racist behavior or an increase in awareness of racist behavior?
• What could you design to wean young children off video games?
• Can you think of an original way for schools to promote awareness of global warming or climate change?
• How many ways can you use technology in the classroom to improve student understanding?
• What criteria would you use to compare American Literature with English Literature?

Synthesis Performance Assessment Examples

• Design a classroom that would support educational technology.
• Create a new toy for teaching the American Revolution. Give it a name and plan a marketing campaign.
• Write and present a news broadcast about a scientific discovery.
• Propose a magazine cover for a famous artist using his or her work.
• Make a mix tape for a character in a novel.
• Hold an election for the most important element on the periodic table.
• Put new words to a known melody in order to promote healthy habits.
• Questions for Each Level of Bloom's Taxonomy
• Higher-Order Thinking Skills (HOTS) in Education
• Bloom's Taxonomy - Application Category
• How to Write a Good Thesis Statement
• An Introduction to Academic Writing
• Asking Better Questions With Bloom's Taxonomy
• Beef Up Critical Thinking and Writing Skills: Comparison Essays
• Bloom's Taxonomy in the Classroom
• Using Bloom's Taxonomy for Effective Learning
• What an Essay Is and How to Write One
• How to Construct a Bloom's Taxonomy Assessment
• Definition and Examples of Analysis in Composition
• How to Write a Critical Essay
• Tips on How to Write an Argumentative Essay
• How to Write a Solid Thesis Statement
• Composition Type: Problem-Solution Essays

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Mathematics > Optimization and Control

Title: data-driven distributionally robust system level synthesis.

Abstract: We present a novel approach for the control of uncertain, linear time-invariant systems, which are perturbed by potentially unbounded, additive disturbances. We propose a \emph{doubly robust} data-driven state-feedback controller to ensure reliable performance against both model mismatch and disturbance distribution uncertainty. Our controller, which leverages the System Level Synthesis parameterization, is designed as the solution to a distributionally robust finite-horizon optimal control problem. The goal is to minimize a cost function while satisfying constraints against the worst-case realization of the uncertainty, which is quantified using distributional ambiguity sets. The latter are defined as balls in the Wasserstein metric centered on the predictive empirical distribution computed from a set of collected trajectory data. By harnessing techniques from robust control and distributionally robust optimization, we characterize the distributional shift between the predictive and the actual closed-loop distributions, and highlight its dependency on the model mismatch and the uncertainty about the disturbance distribution. We also provide bounds on the number of samples required to achieve a desired confidence level and propose a tractable approximate formulation for the doubly robust data-driven controller. To demonstrate the effectiveness of our approach, we present a numerical example showcasing the performance of the proposed algorithm.

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