The more I post on this site, the clearer it becomes to me that what I need is a “basics” series: a series in which I explain how I introduce the fundamental building blocks of elementary mathematics. Only in the context of these definitions will the work I do with my kids make sense.
What I focus on with my kids are the fundamental mental models that underpin much of elementary mathematics. These include place value, the four elementary arithmetic operations, and the concept of equality. I primarily focus on these concepts and the interactions between them, largely forgoing “extras” like telling time, using money, naming unusual shapes, and many other things that often gets stuffed into modern curricula. In my opinion, these topics are best encountered informally “in the wild.” As a child becomes more proficient with the basic models of arithmetic, they will be able to apply arithmetic to a wider range of questions. However, in my opinion, including these topics in the curriculum wastes valuable time best spend on the fundamentals.
Another early concept I spend a lot of time on is the concept of a variable. Algebra is a generalization of arithmetic: it is arithmetic done with an arbitrary number instead of a specific number. The right time to start generalizing one’s observations about numbers is when one is working with numbers in a hands-on way. And similarly, the right time to build a robust mental model of a variable is when one is doing arithmetic.
When taken together, these basics form a large part of our elementary mathematics program. I hope this series helps explain how we approach our journey!
This is the introduction to a series of posts about our basic approach. Here’s are my first and second posts about place value. Here’s a post about arithmetic operations. I will soon also add posts about equality, variables, and a couple of detailed examples of our daily lessons.