mathbabe

My friend Josh Vekhter sent me this blog post written by someone who calls herself celandine13 and tutors students with learning disabilities.

In the post, she reframes the concept of mistake or “being bad at something” as often stemming from some fundamental misunderstanding or poor procedure:

Once you move it to “you’re performing badly because you have the wrong fingerings,” or “you’re performing badly because you don’t understand what a limit is,” it’s no longer a vague personal failing but a causal necessity.  Anyone who never understood limits will flunk calculus.  It’s not you, it’s the bug.

This also applies to “lazy.”  Lazy just means “you’re not meeting your obligations and I don’t know why.”  If it turns out that you’ve been missing appointments because you don’t keep a calendar, then you’re not intrinsically “lazy,” you were just executing the wrong procedure.  And suddenly you stop wanting to call the person “lazy” when it makes more sense to say they need organizational tools.

And she wants us to stop with the labeling and get on with the understanding of why the mistake was made and addressing that, like she does when she tutors students. She even singles out certain approaches she considers to be flawed from the start:

This is part of why I think tools like Knewton, while they can be more effective than typical classroom instruction, aren’t the whole story.  The data they gather (at least so far) is statistical: how many questions did you get right, in which subjects, with what learning curve over time?  That’s important.  It allows them to do things that classroom teachers can’t always do, like estimate when it’s optimal to review old material to minimize forgetting.  But it’s still designed on the error model. It’s not approaching the most important job of teachers, which is to figure out why you’re getting things wrong — what conceptual misunderstanding, or what bad study habit, is behind your problems.  (Sometimes that can be a very hard and interesting problem.  For example: one teacher over many years figured out that the grammar of Black English was causing her students to make conceptual errors in math.)

On the one hand I like the reframing: it’s always good to see knee-jerk reactions become more contemplative, and it’s always good to see people trying to help rather than trying to blame. In fact, one of my tenets of real life is that mistakes will be made, and it’s not the mistake that we should be anxious about but how we act to fix the mistake that exposes who we are as people.

I would, however, like to take issue with her anti-example in the case of Knewton, which is an online adaptive learning company. Full disclosure: I interviewed with Knewton before I took my current job, and I like the guys who work there. But, I’d add, I like them partly because of the healthy degree of skepticism they take with them to their jobs.

What the blogwriter celandine13 is pointing out, correctly, is that understanding causality is pretty awesome when you can do it. If you can figure out why someone is having trouble learning something, and if you can address that underlying issue, then fixing the consequences of that issue get a ton easier. Agreed, but I have three points to make:

1. First, a non-causal data mining engine such as Knewton will also stumble upon a way to fix the underlying problem by dint of having a ton of data and noting that people who failed a calculus test, say, did much better after having limits explained to them in a certain way. This is much like the spellcheck engine of Google works by keeping track of previous spelling errors, and not by mind reading how people think about spelling wrong.
2. Second, it’s not always easy to find the underlying cause of bad testing performance, even if you’re looking for it directly. I’m not saying it’s fruitless – tutors I know are incredibly good at that – but there’s room for both “causality detectives” and tons of smart data mining in this field.
3. Third, it’s definitely not always easy to address the underlying cause of bad test performance. If you find out that the grammar of Black English affects students’ math test scores, what do you do about it?

Having said all that, I’d like to once more agree with the underlying message that a mistake is a first and foremost a signal rather than a reflection of someone’s internal thought processes. The more we think of mistakes as learning opportunities the faster we learn.