In part 5 of this series I summarized the “features” of the Math Academy system, i.e., the learning strategies that it implements, as described in the book The Math Academy Way. I now look at the question of what responsibilities Math Academy customers need to take on, either on their own or with the help of others, as discussed in Part IV of The Math Academy Way, “Coaching.”
As in previous posts, the following sections are my paraphrases of the content of The Math Academy Way; my own comments are [enclosed in square brackets]. You should interpret statements not in brackets as being prefaced by “The book says . . .” or “The author claims that . . .” Terms in boldface are key concepts relevant to the Math Academy system.
Chapter 24. Parental Support (In Progress)
Because deliberative practice requires effort, students need support and encouragement to do it, and need to be held accountable by responsible others (parents or teachers) when they don’t do it. Otherwise students lose motivation and give up on Math Academy.
[This is the only place thus far where teachers are mentioned as potentially assisting students using the Math Academy system.]
The above is the bare minimum needed. The ideal level of support is similar to that characteristic of the families of competitive musicians (and other high-achieving performers), which include daily supervised practice, ongoing evaluation and discussion of progress, motivation through rewards and encouragement, and so on.
[This chapter does not mention it, but even the bare minimum is going to be hard to maintain in families where work, illness, poverty, single parent, etc., make ongoing support and supervision difficult.]
Chapter 25. In-Task Coaching
The main point emphasized in this incomplete chapter is the negative effect of a student using reference material while completing a task in the Math Academy system. This is because they’re using the reference material as a crutch instead of trying to retrieve the material from memory (effortful retrieval).
[I have occasionally done this while using the Math Academy system, looking back at a prerequisite topic before beginning a lesson on a topic I felt a little uncomfortable taking on, or copying down a formula discussed in the example section of a lesson before embarking on answering the questions. As the book says, though, this is generally not a good idea, and I try to do it only occasionally.]
[I’ve also done something related but a little different: Before beginning a series of questions, I sometimes write out from memory the formulas that I’ll need. Other times, if I can’t remember a formula I’ll try to derive it from other formulas I know. For example, one time I couldn’t remember the formula for the derivative of the tangent function, so I worked it out using the definition of the tangent function (sine divided by cosine), the formula for differentiating the quotient of two functions, and the formulas for the derivatives of the sine and cosine functions. It’s not clear to me whether either of these practices are a violation of the advice in this chapter.]
This concludes my discussion of Part IV of The Math Academy Way. In part 7 of this series I’ll discuss Part V of the book, “Technical deep dives,” which decribes in more detail the “technologies” that support the learning strategies discussed in Part III.