## Monday, October 29, 2007

### Learning styles

I've been puzzled by the fact that the IEP of one of my students describes the student as a "visual learner," while I would have said that visual information is what she has the most trouble with. This student is pretty good at algebraic manipulations, but understanding graphs has been a challenge. In particular, she quickly learned how to compute the slope of a line given the coordinates of two points, but learning to find the slope by inspecting the graph - by counting the units of vertical and horizontal change - required a lot of effort and repetition. And even then it seemed to be easier for her to first determine the coordinates of a couple points on the graph and then to plug these into the slope formula, rather than to just read the rise and the run off the graph. Also, she apparently really struggled with Geometry last year.

Her IEP recommends that she be placed near the front of the classroom so that she, being a visual learner, can see the board well, and all of that seems perfectly sensible and easy to accommodate. However, I am wondering about what exactly is meant by these learning styles categories: Are we talking about the mode of input - about which senses are used - or rather about the character of the information processed? I'll admit from the start that I have not done my homework in terms of reading the academic literature on learning styles - just those bullet-pointed short versions used in alternative credentialing programs - and maybe the most appropriate response to my questions would just be a reference to some standard text on these matters. Which would be fine.

In trying to distinguish 'mode of input' from 'character of information' (or whatever; if anyone knows any official terminology in this area, let me know) I'm reminded of Bach-y-Rita's little devices for transmitting visual information by tactile means. Starting in the 60s, he experimented with optical sensors attached to arrays of tiny electrodes attached to blind subjects' backs. Initially, candidates just experienced random tingling sensations from the electrodes, but with some time and practice this gave way to an immediate experience of rudimentary vision, enough to find their way while walking. They could, for example, "see" if an object was placed in front of another, blocking the latter from "view." When a candidate equipped with such an apparatus learns about his or her world by using information transmitted through tiny electrodes attached to the skin, is this candidate acting a as a "visual" learner or rather as a "kinesthetic" learner? I'd say the former, even though the mode of input is tactile.

Presumably the information needed to navigate a sidewalk could instead be given in verbal form, as a list of instructions about when to move and when to stop, and this language-based information could be accessed aurally, from directions read aloud, or the mode of input could be tactile, as when reading the list of steps in Braille. However, if the information were provided as a list of instructions about how to walk, reading these instructions would hardly make the information "visual" even though the mode of input were now visual, and reading them in Braille presumably would not make it more suitable for kinesthetic learners. Similarly, I would think that if a student learns most readily by a visual approach, then the student's needs are hardly met by the information being available as words on a screen or board, because even though the mode of input is certainly visual, the character of the information is verbal - and being able to see well is quite compatible with having a language-based learning disability.

In teaching my students about the number line I have come to wonder whether I am over-emphasizing a visual approach because such an approach happens to be mine. I guess I compare numbers by mentally placing them on the number line, and that is how I have always made sense of the rules for negative numbers. However, my (mathematically adept) husband insists that he does not think of numbers this way - and certainly the magnitude of a number and its position on a line are not the same thing. After all, the Ruler Postulate, which tells us that we can define a one-to-one correspondence between numbers on the one hand and positions on a line on the other, and in such a way that differences between numbers correspond to distances between points, is not a trivial statement. Besides, I have this unclear notion that Geometry developed for centuries without numbers attached in any important way, while Algebra did without Coordinate Geometry and number lines for the longest time (but I've never actually studied History of Mathematics, and don't really know). Anyway, students who have trouble distinguishing left and right might conceivably be more confused by the number line approach while still being perfectly capable of reasoning with signed numbers. It might be interesting to try and think of approaches to the material that are less visually oriented, instead of just assuming that this approach pretty much defines understanding, since that is the way I, um, see it!

Not that it matters that much in practical terms. I'm sure that in terms of learning outcomes for my students, they'd have been better served by my spending this time on getting their papers back to them quickly instead of writing all these words. But, whatever.