# My Math Education Blog

"There is no one way"

## Tuesday, September 1, 2015

### Learning Styles, Teaching Styles

Over the years, many students, and a few teachers, have told me about what they consider their learning style, or in some cases, their learning differences. Meanwhile, over the years, I have been promoting what I call a tool-rich pedagogy, arguing that it helps reach students who have various learning styles.

And now I'm told that research shows that learning styles don't actually exist, or at any rate that there is no gain from teaching a student in a way that matches their supposed style. (See for example the Wikipedia entry.)

To be honest, I don't have the time or interest to evaluate that research, but I don't doubt its validity. As I see it, whether learning styles exist or not will have little impact on my advocacy of teaching in multiple modes. If an idea is important, I try to approach in many ways. As it turns out, this has nothing to do with learning styles.

For example, to get across the idea of function, I have students look at it numerically, graphically, and symbolically. These three representations have been enshrined in the curriculum since the advent of graphing technology, so I'm not saying anything original here. But why stop with three representations? I use function diagrams, which are not as well-known, but provide a powerful way to think about important aspects of functions. I also like to throw in geometric representations, such as perimeter and area patterns. Also: manipulatives, kinesthetic approaches, "real world" situations...

Multiple representations of important ideas is a key strategy if you care about reaching the full range of students. The more representations, the better. Here are some reasons:
• A student who doesn't get it the first way, gets more chances.
• A student who does get it the first way is not condemned to a boring repetition of the same lesson, which in any case, if it didn't work for everyone the first time, will still not work the second time.
• A student who does get it the first way, gets more depth of understanding, as expertise is to a large extent the ability to transfer knowledge between apparently unrelated contexts.
• For all students, extending exposure helps extend retention.
It's not that a visual approach, say, is for the visual learner. It is good for all students to understand the topic visually. Moreover, there is no magic at work here. It's not that doing something with manipulatives will guarantee understanding. Quite the opposite: the manipulatives just offer a context for reflection, discussion, and communication. It's not that physically moving provides instant insight, but it does provide an experience that is hard to forget. (Teacher explanations, in contrast, are hard to remember.)

Of course, teaching in different modes is not automatically successful. The same critical attitude needs to be applied to all modes: is the lesson interesting? is it intellectually demanding? does it carry the required curricular message? and so on...

All this to say that even if different learning styles do not actually exist, different teaching styles are a must.

--Henri

This post was inspired by Dylan Kane's post on the same topic at Five Twelve Thirteen.

Follow-up by Michael Goldenberg.