In order to teach math skills, the head teacher who I work with has a couple games that help the kids to learn. For the children who are still learning to count and to add, she has a game called dice rolls, where they roll two 6-sided dice, count up the pips, and mark it on a sheet of paper. They have started to note trends like, “my sevens are winning” and some of them are able to understand why “because there are more ways to make seven than there are to make two or twelve,” but not all of them get that. They do all get the visual component of it.

For the children who are multiplying, they roll their dice, and instead of adding them and then marking them on a bar graph, they put them into a math equation, and multiply them. So they are practicing their multiplication tables without just rote memorization. They are using the skills they are building. And if they forget what 3×4 is, those students know that multiplication is adding in groups so they can count it up. Obviously, in this situation, they are only multiplying by 6s at the highest, but for first graders, that’s pretty good, from my understanding of where they “should be.”

Plus, the teacher has introduced multiplication to the other children in subtle ways so far, without calling it that yet, getting them familiar with the idea of counting by fives, and counting by threes, and counting by twos – which is really also what helps with multiplication. If you can count by threes, and then use your fingers to remember how many times you’ve counted by threes, you can do easy multiplication.

The teacher introduces these concepts all throughout the day; there are typically very few subject classes, though occasionally the whole class is engaged in a literacy activity or a math activity, but they are allowed to self-direct WHAT math activity they choose. Additionally, as part of the morning routine, the children are required to use math skills – they count attendance, and figure out the number day of school, and whether it’s even or odd, and what the pattern is, and add a cube to our rods of ten, and change the abacus.

The other game that the teacher has is called the trading game. In this game, the child rolls two dice. They pull out “ones” cubes for each pip. When they get ten cubes, they trade it in for one rod of “ten;” when they have ten rods of ten, they trade it in for one square of ten. When they have ten of those, they trade it in for a cube of a thousand. The children begin to see visually the concepts of counting by tens, but also of how the ones, tens, hundreds places all work. This is an important concept that I think many people also fail to understand in the early years that I’ve found hinders some of the college students I know who took computer programming, and had no basis for understanding how binary worked.

At any rate, my point from this post is that the teacher I work with has ways to develop the students math abilities that are engaging, deal in concrete examples that are meaningful because they are active participants – the act of rolling the dice lets them control the numbers they are adding and multiplying. This allows them to take ownership of their learning, and it just provides a much more engaging classroom than if they were sitting at desks and instructed how to add and count for an hour.

And yes, I think we should tell the kids that’s it’s “counting in groups” and not “repeated addition”.

I wonder if the multiplication policeare going cite you for saying “multiplication is repeated addition.” Technically, it’s not, but I still think using it in the way you have, also mentioning that it’s counting in groups, is a good way to phrase it.

Your web material looks great, BTW. So cool to see how you are weaving tech into your classrooms. Looks like those Vancouver kids are lucky.

Keep up the good fight!

Brian (a.k.a. Professor Homunculus at MathMojo.com )