Wednesday, August 13, 2008

The special draw of the standard algorithms... even when there's an easier way out

One hallmark of Reform Math is a preference for problem-specific shortcuts.

E.g., subtracting 55 from 350 by first subtracting 50 to get 300, and then counting 5 backwards to 295.

Reformists also argue that such solutions are more appealing and accessible to students.

Consider, however, my seven-year-old daughter.

Faced with a problem like 350 - 55, as she often is, in the 2nd Grade Singapore Math book she's been working her way through this summer (which also has much harder problems like 964-87), she immediately puts the 55 under the 350 and proceeds to borrow from the 10's to the 1's and then from the 100's to the 10's.  ("Fifty equals forty ten"; "three hundred and forty equals two hundred and fourteenty").

She does this even when, surprising myself at my Reformist reaction, I suggest that there might be an easier way out.

Perhaps she's mindlessly applying an algorithm that autocrats have mindlessly drilled into her head.

Except that I'm the only autocrat around here, and I've spent no more than half an hour showing her the subtraction algorithm.  And she rarely gets it wrong.

Here's another possibility: perhaps kids like her actually prefer using a general method consistently, even for those many carefully chosen Reform problems for which there's an easier, case-specific solution.

1 comment:

Anonymous said...

Liz from I Speak of Dreams here.

I haven't been commenting much, but have been reading and thinking. Thanks for the continuing series.

Please allow me to make the following comment:

proceeds to borrow from the 10's to the 1's

No, not borrowing, which isn't mathematically correct*/**. Your daughter is regrouping.

I took a class in teaching math to k-5 students. While a lot of the content was constructivist, the instructor was very clear on using mathematically-correct language.

*Or linguistically: "borrowing" implies "repaying", which isn't what happens in regrouping.

**If you are teaching this level of arithmetic using the CRA approach (concrete, representational, abstract), it becomes clear. The concrete (introductory level) requires manipulatives. The problems are carefully staged, so that a problem-solver (student) first becomes experienced in exchanging one "ten-stick" for "ten units", and only after exhibiting mastery in the 10s place/1s place exchange, is introduced to the idea of exchanging a "100s square" for 10 "ten-stick".

It is hard to describe this verbally, without having the manipulatives to demonstrate.

It is also hard to describe verbally the scaffolding of skills to mastery.

Here's an article on the CRA Approach. What would be better is some videos of the approach across grade levels.