How Do Students Think? By Using Their Hands

09.18_thinking-with-our-hands

I’m willing to bet that you believe you don’t ever use your hands to think. After all, you think with your brain, and your brain is in your head. Care to wager?


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I’m willing to bet that you believe you don’t ever use your hands to think. After all, you think with your brain, and your brain is in your head. Care to wager?

We normally think of writing as a fine supplement to speaking because it allows us to communicate over vast stretches of time and space. For example, I can read what Cervantes wrote four centuries ago and, in the next moment, communicate with a colleague half a world away. But writing is more than a medium of communication because we also use it to help us think. In this regard, most of us have an intuitive understanding that it helps. For example, here is what the eminent anthropologist Claude Lévi-Strauss (1961, 291) wrote:

Writing is a strange thing. It would seem as if its appearance could not have failed to wreak profound changes in the living conditions of our race, and that the transformations must have been above all intellectual in character. . . . Yet nothing of what we know of writing, or of its role in evolution, can be said to justify the conception.

He is unsure of exactly how writing helps. But I believe there is an explanation, and I’ll sketch it here.

Some time ago, my sister Joanne, a lawyer, asked me to tell her something interesting about the research I was doing. I thought for a moment and replied, “When you do serious legal thinking, you always use your hands.” She looked at me like I had five heads and responded categorically that she used her head to think. I then asked her how she prepared for an important cross-examination, knowing that she would tell me she wrote it out on a legal pad with her favourite fountain pen. When she did, I came back with “So you use your hands to think.” She looked at me, thought for a moment, and said, “I might use my hands, but my mind is telling my hands what to do. My head is driving the whole process.” “OK,” I said, “but what if I took away the pad and pen? Could you put together a cross-examination?” At this point, a lightbulb appeared to go on, and she conceded my claim, remarking that she’d never really thought about it that way.

My sister was under the mistaken impression that her mind alone was responsible for her thinking. This belief is not uncommon and cognitive scientists refer to it as neurocentrism. The early cognitive scientists viewed the mind as a computer. The individual turns their mind on, begins to process internal knowledge much as a computer processes 1s and 0s, and with some effort, arrives at ideas. But we’ve now accumulated significant evidence that we use artifacts in the environment to help us think. For example, professional cooks will order the ingredients going into a dish so that they don’t have to read the directions later in the cooking process. To teach arithmetic, a primary school teacher often has students use manipulatives. To solve 5 − 2, for instance, a child will begin with five counters (uniform objects like disks or chips) and then remove two counters to arrive at the answer, 3. Eventually, the child will internalize the thinking and no longer require manipulatives. The discovery that some of our thinking requires the support of external artifacts dates to the early 1990s. Those cognitive scientists who believe our thinking requires external artifacts are called integrationists.

Let me be clear about what I mean by writing. For some, writing is the visual equivalent of speech. It’s words, sentences, and paragraphs inscribed on a visual medium (paper, computer screen, clay tablets, etc.). But some of our thinking requires us to inscribe the medium with other kinds of symbols, like the symbols of mathematics, or music notation, or the language of computer codes, or special constructs like pictures, tables, graphs, and data. To avoid any confusion, I want a term that includes all these possibilities. So, I’ve chosen the word exographics. Exographics includes not only writing but any other set of symbols that are meaningful to the inscriber.

Let’s now look at a few more examples of how writing can help us discover ideas. Consider the problem of getting the answer to the arithmetic problem 847 × 86. The idea I am trying to discover is 847 × 86 = 72,842. Before I begin my thinking, I don’t know the answer, but I have the recipe I learned in primary school to get it, and I plan to apply that recipe. For the moment, I am not going to allow myself to use my hands (i.e., no exographics). I’ll just sit with my hands neatly folded and try to figure it out using only my mind. I find such mental calculations difficult. What’s difficult is remembering the result of a calculation I’ve just made for use later in the computation. At the same time, if I can use exographics, I’m able to store these intermediate calculations externally (usually with pencil and paper) so that I don’t have to remember them internally. With this external help that exographics provides, I can discover the idea 847 × 86 = 72,842 in a matter of seconds.

I’m offering this arithmetic problem as a simple metaphor for much larger, more difficult problems whose solutions lead to important ideas. For example, consider Einstein and the idea of special relativity. By his reporting, we know that his thoughts usually involved some kind of highly visual thought experiment. The one that eventually led to special relativity (including his discovery that E = mc2) involved a moving train, lightning bolts, and observers. He analyzed this vision with mathematics (exographics) and ended up with the theory of special relativity, just one of the highlights of his annus mirabilis (1907). What is clear from any reading of his biographies is that he was always anxious to get to pen and paper to see whether the mathematics of one of these thought experiments would lead to an interesting idea. He could do vivid visual thought experiments at will but could not do their associated maths without pen and paper. Einstein needed exographics (and his hands to operate the exographics technology) to discover special relativity.

I do not mean to suggest that exographics was the key driver to discover special relativity, because it wasn’t. The key was Einstein and his incredible imagination. But it’s also true that Einstein needed exographics to take full advantage of his imagination.

My research suggests that exographics as an external memory aid to help us thinkis not the complete explanation. What our species is especially good at is the invention of abstract concepts that we can then manipulate and combine into important ideas. Mathematics is a good example. There is no such thing as the number 23 in the real world. It’s not like ducks and baseball bats. But we were able to invent the concept and use it. The key to our using it is this ability we have to represent it in our visual field using exographics. Once we write “23” on a piece of paper, it’s just as real as a duck, and we can manipulate it with along with other abstract concepts to our heart’s content. We’ve been manipulating objects in our visual fields for at least two and half million years, so it’s pretty much second nature to us. I refer to this externalization of abstract concepts with exographics as reification, and it’s been critical to our ability to generate the material culture we have today. You can’t go to the moon, or compose Adagio for Strings, or build a smartphone without the reification that comes with exographics.

So there are two critical aspects of exographics to thinking: we use it as an external memory aid and to reify abstract concepts.

Let’s now think about the complete collection of ideas we’ve discovered since the dawn of consciousness, a collection we can partition into ideas that have required exographics to discover—what I term A-class ideas—and those that don’t. Surveys of the A class suggest that it’s been growing exponentially for the last millennium and there is no reason to think this growth will not continue. The techno-literate society we enjoy today, with all its A-class material artifacts, is the direct result of our discovery of the technology of writing.

Let’s now think about the importance of exographics to education. Exographics is fundamental to college and university study. Students use it to take class notes, to do rough work as they put together assignments and essays, to record lab results, to write exams, and more. Professors use it extensively in teaching and especially in their research. Exographics is endemic to every subject students could possibly study at university. The other side of exographics is reading. When reading, we’re generally embracing someone else’s ideas.

I believe that high school, college, and university students would benefit from a course in exographics, the fundamental technology they use to support their thinking and learning. Such a course would explain embodied thinking, the nature of the A class, the fundamentals of individual thought, the foundations of our collaborative networked thought, the history of the exographics technology and how it’s affected the generation of ideas, and the role of exographics in explaining the marked differences between those societies with it and those without it.

In closing, my hook was to suggest that you use your hands to think. While that’s true, the real story is how exographics helps us to generate abstract ideas. What is clear is that without exographics, we’d be living the lifeways of an oral indigenous society. Given human nature, this would be a thoroughly satisfying existence, but it would be one without many of the material accoutrements that come with human imagination supported by exographics.

Now, about that wager . . .

Reference

Lévi-Strauss, Claude. 1961. Tristes Tropiques. Translated by John Russell, New York: Atheneum.


Bill Hurley, PhD, is a professor in the Department of Mathematics and Computer Science at the Royal Military College of Canada and has recently published the book Catching Unicorns: How Writing Enables Our Imaginations (Kendall Hunt, 2023), which puts meat on the bones of argument outlined in this piece.