Wednesday, May 28, 2008

Math problems of the week: grade 2 Trailblazers vs. Singapore Math

1. From the Trailblazers 2nd grade workbook:

Solve the problem three different ways. Problem: 68 + 12.
First way:
Second way:
Third way:

2. From the Singapore Math 2nd grade workbook:
Add or subtract.
(a) 324 + 149 =
(b) 440 + 76 =
(c) 569 + 283 =
In requiring the child to solve one problem in three different ways, I suspect Trailblazer's agenda extends beyond showing kids that there's no one "right" way, to making sure that they solve the problem at least twice without using the dreaded addition algorithm (here, carrying a 1 to the tens place).

While not the only "right" way, the standard algorithm is generally the most efficient, particularly when one moves beyond the easy, carefully-contrived problems of Reform Math (where, above, it's easy to add the 60 and the 10 first, hold the sum in memory, and then add the additional 10 from 8 + 2).

Imagine what happens to a 7-year-old's working memory load if s/he tries to solve problem (c) of the Singapore problems without using the standard algorithm:
500 + 200 is 700.  60 plus 80 is... Well, 6 + 6 is 12 (I know my doubles) so 60 + 60 is 120, and 20 more is 140.  700 plus 140 is 840.  9 plus 3 is 12.  840 + 12 is... Well 840 plus 10 is 850, and 2 more is 852.
569 is one less than 570.  283 is three more than 280.  500 plus 200 is 700.  70 plus 80 is... well 70 + 70 is 140, and 10 more is 150.  150 plus 700 is 850.  Then we have one less and three more, which is two more, so we get 852.

Enjoying and progressing through math means freeing up working memory for higher-level concepts, not burdening it with contortions like these.


Dawn said...

I recently realized that why I loved the 'creative' approach, the solve-it-3-ways problems, is because I have 35 years of life and math behind me and I'm well equipped to solve a problem 3 ways. My kids don't have that yet. They need one way. They need a trunk with roots then, when they've got that, they can branch out and explore two or three or four different ways.

I don't think the people who design the Trailblazers crap understand this.

lefty said...

That's interesting. In focusing on left-brainers, I hadn't considered whether the multiple solutions approach might be a bad idea for most students--at least those who, as you say, are young enough that they like lack the breadth of experience that multiple solutions may require.

I'm wondering if there are other things I've written here specifically about left-brainers that might apply more broadly?

K9Sasha said...

I recently asked a group of 5th graders to find the mean of the following numbers: 9, 11, 12, 14, 17, 17, 25.

I don't know what he had been taught about math, or what he thought he was doing, but one poor kid had filled his page with tally marks! Guess what? He didn't get the right answer.

Why can't we just teach kids math???