For Math Mastery, Allow Time For Struggle And Collaboration

A few posts ago, we pondered whether the trend in math we’ve observed with some of our students, i.e. taking more complicated classes at earlier and earlier ages – something we labeled “math push-down” – was a viable choice for most students in improving math mastery as they progress through school. Two pieces in this past week’s New York Times, one concerning American mathematics pedagogy, and the other, an opinion from a university mathematics professor encouraging parents to turn math into a game and take a “coaching” perspective, have us feeling confident that the position we took, calling the push-down trend into question, was justified.

Our work in tutoring math requires us to regularly assess a student’s understanding of just what it is that s/he is doing, correcting misunderstanding through Socratic instruction and practice, and attempting to provide the student with examples of how the material is used in the “real-world” so that the student can place his/her learning in a broader context and learn how math works. Sadly, we regularly meet students whose approach to math is so mechanical and procedure-focused that the student is most certainly not assimilating the “big picture” about the material being studied.

In the above-mentioned piece on math pedagogy, one of the main points cited is the professional practice difference between American and Japanese teachers of math. The gist is that Japanese teachers spend significantly more time honing their craft by way of collaboration about the methods they use in classroom teaching. Japanese teachers discuss, debate and learn from one another as they attempt to refine their in-class methods. Broadly speaking, spending time thinking about what one is doing, discussing alternative approaches and struggling to improve are all excellent means of mastering a subject and a practice.

This is where we again are compelled to point out the problems we see with “math push-down” and indeed, with one of the structural learning challenges we witness. The upshot is that time and time again, we meet students that are so pressed for time, so focused on “next,” and so thinly stretched that they simply do not have the ability to spend the necessary time struggling with and discussing math.

Let us be clear here too about the relationship between one’s math grades and “mastery.” It may come as a surprise to many, but one’s grade in math is not a perfect indicator of one’s mastery. We’ve met some very resourceful students over the years that have cleverly (and honestly) learned how to achieve good grades in math without necessarily achieving mastery in the subject. That’s an unfortunate reality that may make some in our achievement-obsessed culture a bit uncomfortable, but the sooner it’s acknowledged, the better.

We believe that the process of struggle is an essential component to developing a big picture view, and thus developing mastery. Productive struggle requires time. This is time that we are generally not giving to our students so their response has been to learn to “perform,” without learning deeply. As we did in our piece on push-down, we must ask, “What is the hurry?”

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