In today’s students, I really see a lack of ability to understand math because of (for one thing) a lack of retention of math because of, in turn, a lack of memorization. Memorization is anathema to the philosophically corrupt modern intellectual, to the modern theorist of education. It, along with drill, was attacked vigorously when I was getting my Texas Teacher Credentials, and still is, as such attack is implied by a broader perspective on mind and thought: the perspective of John Dewey. (Ultimately, Dewey and the Deweyans believe, consensus creates reality, nothing abides, so why remember anything when it will become outdated? Dewey even claimed that Aristotle’s logic worked so long, it had to be wrong. So A is no longer A: things do not have a nature or identity; their apparent nature changes; things are what we as a group want them to be.)
I’d highly recommend students memorize and be drilled in, at the least, their multiplication facts, working (adding, subtracting, multiplying, dividing) with fractions, and the perfect squares. Students should memorize definitions and methods, as well. These facts are universal and timeless. A is A.
If knowledge is not ingrained and remembered, then it is not there to utilize and build on. What’s more, memorization and understanding reinforce each other.
Let’s not sell our children out; let’s not be comprachicos distorting their minds and souls.