Teaching

We’ve talked about several types of math manipulative that homeschooling parents might use to help their children learn math (see part 1 and part 2), but we never stopped to ask the most basic question:

Why use math manipulatives at all?

Math manipulatives are a tool for solving educational problems, so we should first decide what problem we are trying to solve. That will help us know which tool to use.

Continue reading Homeschool Musings: Math Manipulatives Part 3

In my previous post, I examined fingers and found items (beans, buttons, leaves, and so on) as tools that can help our children learn math. This time, we move on to the kinds of math manipulatives you’ll find in stores or packaged with your favorite curriculum.

Standard base ten blocks

The standard base ten blocks consist of plastic or wooden cubes, a rod with the length of ten cubes, a flat shape the size of ten rods side-by-side, and a large cube equivalent to ten of the flat shapes stacked atop each other.

These are used primarily for modeling place value as a means of developing the standard arithmetic algorithms for addition and subtraction.

They can also be used for modeling decimals as a place value notation, without relying on fraction concepts. And with a bit of imagination (“Pretend the rods are stretchy, so we don’t know how long they really are”) they can model simple algebraic expressions.

Continue reading Homeschool Musings: Math Manipulatives Part 2

I stumbled across another blogger’s post on the common question, “What are the best math manipulatives for homeschooling?”

My answer to this question has changed over the years, as I’ve grown in my understanding of math and of education. As my current stance is far different from much of what I read from other homeschoolers, I’m going to lay out my reasoning below.

I’d love to hear your thoughts, especially if you disagree, because comparing ideas with one another is a great way to learn.

Continue reading Homeschool Musings: Math Manipulatives Part 1

I was asked to do an interview for a new podcast called Learning is Disruptable, and that got me thinking…

Is Math Education Ripe for Disruption?

Math education is not working. Too many people come out of school with math avoidance, math anxiety or even phobia, a profound conviction that math is not for them.

Generally, humans enjoy success, the feeling that things make sense, that they are capable of understanding big ideas. People like subjects that give them this type of success, where they are meeting and making sense of new ideas, growing in mastery.

But they hate subjects that make them feel like a failure, where things don’t make sense and there seems to be no real chance of success.

Therefore, understanding our students’ attitude toward math gives us a solid indication of how well they are learning.

Continue reading Musings: School Math vs. Real Math

There’s a great new homeschool math program that can radically transform your children’s experience of math, building understanding through creative exploration.

First, a bit of history…

What Is Algebra Before Arithmetic?

Back when I was still homeschooling, I read a couple of articles by Keith Devlin about the benefits of teaching children algebra, even before they study numbers.

As a homeschooler leaning toward Charlotte Mason-style education, I found the notion of algebra-first math intriguing. What if we could introduce students to the big ideas of math, the foundational concepts that explain how numbers relate, before they get distracted by details like math facts and memorized rules?

Continue reading A Revolutionary New Approach to Homeschool Math