Knowing and Teaching Elementary Mathematics

Phew!!! I made it.

This is absolutely not my style of reading, but I promised myself that I would read it, and I did it. Hooray for me!

Knowing and Teaching Elementary Mathematics was originally written as a graduate paper by Liping Ma, and it reads as such, Dry. Dry. Dry. But – it is revealing, and worth wallowing through.

My kids are just beginning their journey into the world of math, so I’ll focus there, although the book discusses much more.

Undertaking the task of teaching young children sounds easy: 1 + 1, great, got it! ABC, okay, what’s next? Oh, how very wrong that thought is. Simple concepts are the building blocks for bigger, more complex concepts. The sturdiness of the foundation is absolutely key to a great education.

As a kid, I was a good student, but honestly, never developed a great understanding of math. Sure, I passed algebra, calculus, and trigonometry, but I never knew why the procedures worked. I simply memorized formulas, plugged in the right numbers and spit out an answer. Now, years down the road, I neither remember the formulas, nor the purpose that they were designed to perform. I want something better for my own kids. Enter Ma’s book.

In essence, the author urges teachers to develop a profound understanding of fundamental mathematics, not just knowing the surface of the procedures that they teach, but deeply understanding the theory behind mathematical actions. “It is not enough to know how, one must also know why.”

What I took away from this book was a greater dedication to speak the truth to my children in regards to math. Statements such as “We can’t subtract a bigger number from a smaller one” or “Just borrow a one from the next column,” slip easily off my tongue, and I need to break these habits. It is easier to teach the truth once, and to teach it well. In the best case scenario, each lesson will reinforce my kids’ previous learning, rather than causing them to have to start over with a new concept.

The reasons behind facts are more powerful than individual procedures. Period. My goal is to intentionally make these connections tangible and obvious for my kids, so that they can fully understand how all of their math lessons are related and how/why they work in real life.

So, despite its difficult writing style, my copy of Knowing and Understanding Elementary Mathematics has been underlined, highlighted, and written all over. It is full of excellent information, and is sure to be re-read.