Categorizing Learners: Bad Uses for Good Tools

by Kyle Skinner

Over the last couple of years, while becoming more invested in developing myself as a teacher, I’ve been asked to take the VARK inventory three or four times. VARK was presented to me as a learning style inventory, or a sort of personality quiz that tells you what kind of “learner” you are—visual, auditory, read/write, and/or kinesthetic. If you haven’t taken the VARK inventory before, you can take it for free here. Whether you’ve taken it or not, you’ve probably taken something like it before. Quizzes or inventories of learning styles like VARK, Kolb’s Learning Styles Inventory, or the Honey and Mumford Learning Styles Questionnaire are easy to find and seemingly ubiquitous. While they follow slightly different models from one another, they are all built to sort students into categories of learners. One study included a list of more than seventy available learning style models, and another even cites statements on an old version of our very own Yale Graduate Teaching Center website to demonstrate the extent to which the idea of learning styles has become popular in the world of pedagogy.

When asked to take these inventories in the context of teaching workshops, facilitators often justify their use of the quiz with vague allusions to the “matching hypothesis,” or the notion that learning outcomes can be improved by matching your presentation of course material to the style of learning that individual students prefer.

I have always been suspicious of VARK and learning inventories like it, but the last time I was asked to take it I got stuck on one particular question:

You are helping someone who wants to go to your airport, the center of town or railway station. You would:

-write down the directions.
-draw, or show her a map, or give her a map.
-go with her.
-tell her the directions.

One of the things I like about the VARK inventory is that you can select multiple answers to any question. But this question in particular (and a few other similar questions) makes me want to explain myself. Depending on whether the recipient of my directions is a beloved friend or a stranger, I might have different feelings about walking her to the airport. I might decide to write down directions instead of drawing a map if the directions would be simple and my piece of paper was small. Most importantly, I might give directions in different ways based on the navigational prowess of the recipient (my sister has such good directional memory that I could give her verbal directions once, but I would rather just put my mother in an Uber to save us both the inevitable frustration). The way I would answer this question would be dependent on context, not on my own personal learning preferences.

Even if the questionnaire did accurately diagnose my learning preference, I find myself skeptical that such diagnoses for my students would be particularly helpful to me as a teacher. When asked what their favorite days of class were over the course of a semester, I would be disappointed but not surprised were some of my more honest students to rank the lessons featuring active learning and hard work below the one day I screened a film. And I wouldn’t blame them—everyone needs an easy day every once in a while, but if curriculum were driven simply by what our students prefer to do, I think we’d see very little learning while YouTube would see a moderate increase in ad revenue.

My intuition seemed to pan out as I looked for evidence-based considerations of the usefulness of the matching hypothesis. A meta-analysis of relevant research revealed no reason to believe that the matching hypothesis is real. I far prefer to learn by reading silently to myself—but that’s because I’m impatient as a listener (as many close friends and former girlfriends would agree) and find that diagrams make me work too hard. But I could probably learn a lot more by becoming a better listener and analyzing diagrams. In fact, when I “match” my learning style, my intuition is that I get less out of it because I end up putting less effort into the learning.

I was feeling pretty misled about the VARK inventory and the like until I found this punnily named article, co-authored by a higher-ed consultant and Neil Fleming, the designer of the VARK questionnaire. I was surprised and delighted to find out that the questionnaire was never designed to be diagnostic, but rather was intended to be the starting point of useful conversations about meta-cognition that might help students themselves become better learners by thinking more about circumstances that aid or stifle learning:

“I sometimes believe that students and teachers invest more belief in VARK than it warrants. It is a beginning of a dialogue, not a measure of personality. It should be used strictly for learning, not for recreation or leisure. Some also confuse preferences with ability or strengths. You can like something, but be good at it or not good at it or any point between. VARK tells you about how you like to communicate. It tells you nothing about the quality of that communication.”

Using VARK as a diagnostic tool to determine what “kind of learners” our students are is a missed opportunity. Used to determine how we can match our teaching to our students’ learning styles, VARK encourages a one-sided teacher-centric classroom. For example, after finding out which learning modalities my students prefer, I can change my curriculum to match their preferences. Teachers should, of course, tailor their curricula to make sure they are meeting learners half-way, but providing information only in a student’s preferred learning modality means the student won’t get practice in learning in other styles. Instead of using VARK to dictate how we should teach or to inform our students that they should focus on particular methods of learning, the inventory could be used as the first step in a series of conversations with students about metacognition, ultimately helping them to develop their own notions of how to learn most effectively in the classroom or while studying on their own time.

There’s nothing wrong, I think, with the VARK inventory. Or any of the learning styles inventories you might find—but even the best tools are only useful when used well.


  1. Coffield, F., Moseley, D., Hall, E., & Ecclestone, K. (2004). Learning styles and pedagogy in post-16 learning. A systematic and critical review. London: Learning and Skills Research Centre.
  2. Fleming, Neil, and David Baume. “Learning Styles Again: VARKing up the Right Tree!” Educational Developments 7.4 (2006): 4-7. Web. 12 Jan. 2016. <>.
  3. Fleming, Neil. “Introduction to VARK.” VARK. VARK Learn Limited, n.d. Web. 12 Jan. 2016. <>.
  4. Fleming, Neil. “The VARK Questionnaire.” VARK. VARK Learn Limited, n.d. Web. 12 Jan. 2016. <>.
  5. Pashler, Harold, Mark Mcdaniel, Doug Rohrer, and Robert Bjork. “Learning Styles: Concepts and Evidence.” Psychological Science in the Public Interest 9.3 (2009): 105-19. Web. 19 Jan. 2016. <>.

Mindfulness of the Mind


Jared Rovny

I. Mental frameworks

The brilliant French mathematician and Einstein’s contemporary, Henri Poincaré, was mid-vacation in the town of Coutances, mid-conversation, and mid-stride — one foot stretched to step into his bus — when the solution to his problem suddenly appeared in his consciousness and seared itself in his mind. He had no time to write down and verify the mathematics, but also no need, so he continued his conversation. Without working on his problem or even actively thinking about it, his subconscious mind had presented him with the solution in a single moment.1 Controversial and perennially misunderstood, occurrences like these fascinated the earliest students of human academic thought, and help motivate the broader goal of this piece: to take a step back and ask “What can we learn about effective teaching by thinking about the minds of students?”

And so I want to briefly explore: what constitutes a framework of knowledge, how is it built, and how can we be more effective teachers by thinking about these things?

Inspired by a series of lectures by Poincaré in 1937, Jacques Hadamard (also a renowned French mathematician) wrestles issues like the above in his short work The Psychology of Invention in the Mathematical Field. While a powerfully thought-provoking piece in its own right, I am particularly interested in his questions to prominent scientists of the day, including Albert Einstein, as to how they “did their thing.” Did they think in words? Imagine mathematical symbols? Interestingly enough, Hadamard notes that “practically all of them… avoid not only the use of mental words but also, just as I do, the mental use of algebraic or any other precise signs; also as in my case, they use vague images.” [i] Einstein reports the following famously fascinating observations:

The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be “voluntarily” reproduced or combined… The above mentioned elements are, in my case, of visual and some of muscular type.” [i]

The “muscular type”? Yes, Einstein could “feel the abstract spaces he was dealing with, in the muscles of his arms and fingers.” [ii][iii]

I love reading things like this, both because I myself rarely think (scientifically) in words or symbols, and because I wonder at the possibilities— how many ways are there to think?2 How can I improve my understanding of the world around me by exploring modes of thought? But back to the point: what implication does this have for our students?

II. Synthesis as a context for learning

If we agree that our students mentally work in unpredictably unique ways, how can we introduce them to a subject in a way that they can build a useful framework in their own minds, according to their own way of thinking? An answer to this, in many regards, is what Hadamard calls “synthesis,” and by which I mean the active process of discovery, or of actively incorporating new ideas into one’s own mental model. In the classroom, by actively working to understand or apply a new concept, the student builds a mental framework organically consistent with his or her own mode of thinking.3

How do we teach in a way that promotes this active synthesis for our students? This can be especially difficult since in mathematics (and possibly in other fields) we often have to communicate in a language foreign to our own — or our students’— actual mode of operational understanding. Here’s an example: a well-known law in physics and mathematics is called “Gauss’s Law.” I know this law well, but like the scientists mentioned above, it exists in my mind only as a sort of image or impression. Even though the law is elegant and simple, I cannot convey it as such. Instead I have to conjure my mental image, and interpret it into a series of mathematical relationships, which is a common language between my students and myself. Is it then sufficient to derive a mathematical law by simply presenting a series of individually consistent steps?

According to Poincaré (who we started with), this is necessary, but is not usually sufficient. As he puts it:

Context is everything. [viii]

Context is everything. [viii]

To understand the demonstration of a theorem, is that to examine successively each syllogism composing it and ascertain its correctness, its conformity to the rules of the game? … For some, yes; when they have done this, they will say, I understand. For the majority, no. Almost all are much more exacting; they wish to know not merely whether all the syllogisms of a demonstration are correct, but why they link together in this order rather than another…Doubtless they are not themselves just conscious of what they crave…but if they do not get satisfaction, they vaguely feel that something is lacking. [i]

Teaching by simple progression, one abstract idea to the next, leaves a student missing something; Hadamard more clearly states exactly what’s missing:

In this way of working, which seems to be the best one of getting a rigorous and clear presentation for the beginner, nothing remains, however, of the synthesis… But that synthesis gives the leading thread, without which one would be like the blind man who can walk but would never know in what direction to go. [i]

The missing piece is synthesis, the original context by which the idea came to fruition. Of course, this is commonplace. We discover something through a particular thought-process, then rewrite and rework our logic a dozen times before presenting our work anywhere else. The advantages are concise and logical publications; the disadvantages are the production of learning materials that can leave us feeling led, but blind. This is a pitfall for textbooks especially, which are as rigorous as reference manuals, but are often lacking in synthesis, context, or motivation.

A further example to conclude: suppose this week you become fascinated by a close relative of “Gauss’ law”, called “Stokes theorem” (we use this in introductory Physics, so naturally you are enthralled). You look it up on Wikipedia only to read:

“In vector calculus, and more generally differential geometryStokes’ theorem is a statement about the integration of differential forms on manifolds… Stokes’ theorem says that the integral of a differential form ω over the boundary of some orientable manifold Ω is equal to the integral of its exterior derivative dω over the whole of Ω.” [iv]

Well good luck sipping knowledge from that fire hose. It is logical, concise, defensible, and largely useless, links and all (exactly 6 clicks deep into the first links will lead you to the “philosophy” page anyways—again, good luck) [v][vi][vii]. But Hadamard’s point is deeper than this— he claims that even if you “understood” the above statement, meaning you could verify each part yourself, you are still lacking the synthesis, the ideas and thoughts and problems that could lead a person to such a formulation as a whole.

So both Poincaré and Hadamard claim that synthesis is an important ingredient in the teaching process: by presenting the topic in the fullness of its historical or logical context as much as possible (the context in which the idea was synthesized in the first place), the mind of the student is automatically set to contextualizing and reframing that problem according to their own mental processes as they search for a solution.4

III. Application: lessons from my own teaching

To incorporate synthesis in my teaching, I have borrowed from the examples of my own teachers, who were an unbroken chain of great mentors, especially my undergraduate advisor and friend at the University of Dallas, Dr. Richard Olenick. With them in mind, I try to make synthesis a habitual practice in my teaching, using the following two methods:

  1. Provide the context for synthesis. To do this, I always try to connect, contextualize, then motivate the material. Connect: Each and every student sits down in class with something different on their mind: food, sleep, relationships, intimidation, excitement, and more. I’ve found it highly effective to allow the first sixty seconds or so be content-free. Discussing the course, upcoming assignments, or their current course load gives each mind time to adapt and settle in to their surroundings, and build attention towards you and the class. Only a few seconds are needed and provide a very high return on investment. Contextualize: I can then easily discuss a background to the topic and properly motivate it. In the sciences particularly, history has been my friend; a short background to your topic is a powerful incentive, human and logical. Motivate: With some background, however brief, the material is ready to be motivated: why is this interesting? How does it impact your life? Why did it fascinate the people who came up with it? Reasons and goals are great allies.
  1. Provide tools for synthesis. Even with the proper context and motivation, you can’t actively search for answers (synthesize) if you don’t understand the question. With complicated material, I’ve found it helpful to first provide simple overviews of the topic, verbally and visually. This reduces intimidation and clarifies the topic, allowing students to be more receptive to the material itself. With a basic overview and understanding of the relationship among different aspects of a topic, students have a mental “scaffold” on which to place the more complicated material as it arises, providing mental space and the prerequisite knowledge to begin active problem-solving and synthesis.

To frame this according to modern research: “To develop competence…students must: (a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a conceptual framework, and (c) organize knowledge in ways that facilitate retrieval and application” [xii]. That is, competence requires knowledge, in a framework and organized. So, to restate: with complicated material, I find that first exposing students to a clarifying framework5 of a topic can help them retain the knowledge itself. Students are then better equipped to synthesize and create mental organization as they internalize the knowledge. To accomplish this, I first discuss the larger framework (“how are all these ideas connected?”) using simple versions of the ideas, only then to follow through with more detailed explanations.

IV. Conclusion

Innovative thoughts about metacognition from over fifty years ago provide insights into thought and pedagogy that remain highly relevant today. The sources referenced here gave me important mental models for understanding active learning and backward design as a teacher, but student metacognition has also been shown to produce learning gains [xiii]—so as your students learn and synthesize, have them think about how ideas fit into their own broader understanding. Everyone benefits from being mindful of the mind!

By looking into the foundations of education research, we can continue to find innovative ways to relate current research to our own teaching. This innovation “is highly important for the further development of educational professions… and for our development as a knowledge society.”6 In our rapidly accelerating information era, we can foster effective pedagogy by applying research old and new. I hope you find ways to apply mindful teaching in your own discipline, and I hope you tell me how you do it! I’d love to hear.


1 “At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidian geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience’ sake, I verified the result at my leisure.”

2 Some would say there is only one way to think. I would refer them to the broader discussion on [i] and documentation on alternative mental processes such as synesthesia.

3 For more on active learning, a good starting place is the CTL’s overview [ix].

4 Ever had a student reach the “a-ha” moment, and then explain the concept back to you in a strange way? “OH! So it’s just like [insert unanticipated or confusing analogy here].” But you realize their analogy does make some sort of sense. That’s the concept being adopted and adapted into their particular mental framework, and being re-expressed.

5 While the full meaning of a “knowledge framework” is the subject of much discussion, here I simply use “framework” in the very specific sense discussed in the prior paragraph: a basic overview of a topic with stated relationships among its various components.

6 This importance was recently emphasized in Review of Educational Research [x].


[i] Jacques Hadamard, The Mathematician’s Mind: The Psychology of Invention in the Mathematical Field. Princeton University Press, Princeton NJ. 1945. Pages cited: 84, 143, 104-106.

[ii] L’Enseignement Mathematique, Volumes 4 and 6. International Committee on the Teaching of Mathematics.


[iv] (subject to change without notice, especially after publication of this article)

[v] (subject to change without notice, but less likely)





[x] M. Thurlings, A. Evers, M. Vermeulen, “Towards a Model of Explaining Teachers’ Innovative Behavior: A Literature Review.” 2015. Review of Educational Research, Vol. 85, No. 3, pp. 430-471. DOI: 10.3102/0034654314557949.

[xi] For further thoughtful commentary about Hadamard’s book (and other topics), see

[xii] M. Donovan, J. Bransford, and J. Pellegrino, How People Learn: Bridging Research and Practice. Committee on Learning Research and Educational Practice, National Research Council. 1999. Page cited: 12.

[xiii] K. Tanner, “Promoting Student Metacognition.” 2012. Life Sciences Education, Vol. 11, pp. 113-120. DOI: 10.1187/cbe.12-03-0033.