Nothing really that new under the sun, Dept.

There is a continuing chorus of complaints about how math is taught from those who seek to reform math education. The chief complaint is the lack of transfer of knowledge. That is, students cannot seem to take their prior knowledge and apply it to problems that rely on the same knowledge but are in new or novel settings.

The reformers then talk about how we need to build students’ “depth of knowledge” to get to the holy grail of “deeper understanding”.

I’ve taken a sample of a PowerPoint which is similar to many others that have been making the rounds over the years. In it, the problem is presented as follows:

Students appear to demonstrate “deep, authentic command of mathematical concepts” when given commonly used problems.
However with more challenging problems, the same students seem
to no longer demonstrate that command.

First, we must have a clear understanding about why…