This month, we will focus on math on our blog. Homeschool math tends to trigger strong emotions in both parents and students, whether positive or, more often, negative. I happen to like math, and my family has had a lot of fun exploring math concepts over the years. I, too, feel strongly about math – I believe that when math is taught properly, it can be simple and enjoyable.
There are two aspects to math: concepts and techniques. Concepts form the foundation of math. With a proper foundation, students can appreciate the techniques and understand when and how to apply them. Unfortunately, too many math teachers and curricula emphasize techniques over concepts. That leads to students not only missing the basic concepts but unable to use the techniques as well.
For example, a friend’s son was having trouble with math. When I tried to help, the friend spoke about him not remembering his multiplication facts. However, when I spoke to him, it quickly became clear that he was missing not only the multiplication table but the basic understanding of what multiplication was about. Even though he knew that 5 * 5 = 25, he had no idea that what it meant was adding five 5s together. In other words, he didn’t realize that 5 * 5 was the same as 5 + 5 + 5 + 5 + 5.
Even children that have no trouble with the four basic operations, or with other techniques, like adding fractions, often don’t know when to apply these techniques. They are able to follow the steps of the technique without understanding what they are actually doing and why. Then they get to word problems and find themselves completely lost.
The way to prevent these issues is to build a strong conceptual foundation first. Sure, the techniques are important. But without the concepts, they are not very useful. So while I certainly spend time teaching my children the techniques, I focus on the concepts much more.
When my children were young, I used lots of manipulatives to illustrate math concepts. By manipulatives I don’t necessarily mean fancy, expensive math kits you buy in a specialty store. Anything that can be counted can be used as manipulatives. In my house, that means things like blocks, Legos, or even beans and Cheerios.
Before I even mentioned the multiplication table, my kids would play with piles of manipulatives, dividing them into smaller piles of equal size, then combining the piles again. There were no questions, tests, or right answers. There was no pressure. It was purely exploration – and fun!
As my children got older and moved on to more complicated math problems, we switched from manipulatives to pen and paper. I would illustrate the concepts, making sure they understood them clearly before we moved on to techniques. These days, there are also many visual explanations of math concepts available on the computer.
Throughout this month, I am planning to bring you more information about homeschool math curricula and resources. There are lots of great resources out there to help you out! As always with homeschooling, choose the one that works best for your family.
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