Tuesday, September 8, 2009

Math, Math, Math

My school is piloting a Math program that focuses on mathematical thinking. There are some really good things about it. Below is an example of an invented strategy we would try to get the kids to generate based on multiplication.

35 X 6 =
10 x 6 = 60
10 x 6 = 60
10 x 6 = 60
5 x 6 = 30

60 + 60 + 60 = 180
180 + 30 = 210

35 X 6 = 210

As you can see, a child who understands this has a thorough grasp on the concept of multiplication. As time goes on, kids are supposed to derrive a strategy based on the distributive property. Below is an example:

44 x 28 =
(40 + 4) (20 + 8) =
40 x 20 = 800 40 x 8 = 320
4 x 20 = 80 4 x 8 = 32
800 + 320 = 1120
32 + 80 = 112
1120 + 112 = 1232

We are supposed to avoid the evil algorythm (ie anything that involves carrying numbers) because kids don't know what it is. I'm sure they can't explain why the algorythms work. I would have to think really hard to explain that! Yet, they are efficient. This invented Math can be extremely cumbersome at times.

When I taught fifth grade, I thought it was because the fifth grade curriculum called for big numbers. It's still cumbersome in third grade.

I like investigations as a supplementary tool, but skill and drill is also important at this stage of learning.

1 comment:

luckeyfrog said...

Agreed that these are great for introducing or explaining a concept- but the algorithms aren't evil. You just have to teach the 'why' behind them as much as you can.

We're teaching regrouping in addition and borrowing in subtraction, and I really worked with my group on showing what was happening with manipulatives and making them explain what that 1 meant (You're carrying 1 WHAT?). I think they actually get it, and I'm so excited, but they still know how to use the quick algorithm too.