Big Patterns in math and in life

I spent some time tutoring a student in math yesterday. This girl, like many of my students, struggles in math; when I started working with her a few months ago, it became clear that she has a hard time remembering how to do specific types of problems, and often ends up stumped, or she applies the wrong technique or a haphazard one, which naturally results in a wrong answer.

Today, after some discussion and some probing questions, I discovered that she wasn’t able to visualize a number line in her head in order to have an intuitive feel for the relationship between numbers. She also didn’t see and understand many of the large patterns in math processes that make it much easier to remember and apply the specific steps necessary to solve a given problem.

This is, unfortunately, a common thing in my students.

But it makes me wonder — why is this so devastatingly common? So many of my students see math or chemistry or biology as a collection of entirely unrelated facts that must be memorized in a sadistic ritual that they must get through to be allowed into the adult world.

Is that how they’re being taught? If so (and I suspect that it is so) is it because their teachers look at the subject as a collection of entirely unrelated facts that they just happened to be reasonably good at memorizing, or is it because the teachers were taught to teach as if that were the case, and they don’t know how to do it any different? Or maybe a combination of the two?

And the big problem is that this is doing the students and the society that they will eventually be contributing adults within, a serious disservice, because not only does this make school tortuous and frustrating, it also discourages the students from ever going and learning things on their own, since their only experiences of learning are so horrible and frustrating.

It also means that as adults in larger society, they don’t have the mental tools to make sense of larger patterns. It means they don’t have the ability to look at the wide variety of data pointing to how our climate is changing and see why scientists are saying that this is a long term negative pattern that we need to do something about. It means that they don’t have the mental tools to look at the sweep of history to see how we got where we are socially and politically, and how we might change that for the better. It means that they don’t have the mental tools to see and understand patterns in their own lives of how they sabotage their personal or professional trajectories.

Because teachers only ever gave them unrelated facts to memorize, instead of showing them patterns and concepts that made the details understandable, and thus memorable. If they learned to see the patterns and connections, they did it on their own, perhaps despite their teachers, rather than because of them.

That’s why I try to do things differently with my students. Teach them the big concepts, the big patterns, the connections, the relationships, because by doing so, I’m not just teaching them math, I’m teaching them the tools to think at different scales, and go out to find other big, meaningful patterns that will illuminate the details.

I’m not entirely sure that I’m successful at this. But I sure hope I am, because we surely need people in the world with those mental tools, and those perspectives. Now more than ever.

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