Sunday, February 20, 2011

Investigations Math in action: crashing and burning with large numbers

A third grade girl attempts, unsuccessfully, to add several large numbers using an Investigations Math strategy. She then adds them successfully using traditional "stacking" (disallowed at school) in a fraction of the time the Investigations method took her:




Filmed and edited by a fellow concerned parent who is a specialist in math remediation.

9 comments:

Obi-Wandreas, The Funky Viking said...

Investigations, like the other curriculum used in my district (Connected Math) was listed on the What Works Clearinghouse as not having a single valid study supporting the conclusions they claimed.

delta_dc said...

So the issue is that the camera operator and parent was frustrated with the time that it took? The third-grader was asked to show her thinking and did a nice job of it. Making our thinking visible is not a simple task and it takes time.

I would be concerned if I knew for sure that the teacher was prohibiting a particular approach but I've worked with enough elementary children to know that they can mix-up instructions. I might have said, "You should use an approach that makes sense to you." and the child would hear, "You cannot use stacking because it doesn't make sense, yet." But there's nothing for sure based on the video - so let's move on.

I also thought it was nice that the child could evaluate the two methods and decide for herself which approach was more efficient; this is something that is a problem if only one way (either way) is shown. It was also nice that she could identify where she might have gone wrong (counting) using the representations.

I wish the camera operator hadn't said that the stacking work "looks right." I would have been interested in hearing the child's rationale for which answer was right.

All in all, watching this 3rd grader, I'd say we have a mathematician in our midst.

Anonymous said...

Good grief! How can we ever expect our children to progress in math and science without some rote memory of simple "number facts". I think the Investigations approach may teach logic, but at a terrible price to pay!

delta_dc said...

I'm not sure what number facts Anon is speaking of - 1,568+1,423+680 is a number fact to be memorized? Sorry, I'm being snarky. It's late. Anyway, it seems she has her facts memorized.

As for logic or speed, I'll go with logic. Neither Einstein nor Bohr would have won a game of "Around the World" with flashcards but we consider them brilliant. We need more long thinkers like the young lady in this video.

Katharine Beals said...

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Anonymous said...

And this new math differs from counting on your fingers, how?

Bon Crowder said...

First, there's nothing wrong with using your fingers. Second, as a previous commentator indicated, "I would be concerned if I knew for sure that the teacher was prohibiting a particular approach but I've worked with enough elementary children to know that they can mix-up instructions." Kids hear a few words from teachers and interpret them.

Regardless, I'm not a fan of forcing any kid to do math in any particular way. They should be allowed to choose (a this little on did eventually).

Anonymous said...

I agree with delta_dc's remarks. It would be sad if an elementary teacher imposes as an exclusive algorithm an approach that is meant to elucidate the meaning of numbers. Mathematics is about problem solving, explanations, and connections. The girl in the video is clearly developing those skills.

I thought the problem itself was interesting. How did Betty know that she had bought 1,568 stickers initially? Perhaps she bought a package that stated it contained 1,568 stickers. If not or if Betty wanted to check, I hope that she did not simply count 1, 2, 3, ..., 1568--the likelihood of error is high. Instead, I hope she counted the stickers into small equal-size piles, then grouped the small piles into bigger equal-size piles, and finally counted the bigger piles, smaller piles, and left overs. If the piles were of size ten, then the connection with our decimal numeration system may be made. If the piles were of a different size, another numeration basis might be discovered. Some pretty cool math!

Barry Garelick said...

I agree with delta_dc's remarks. It would be sad if an elementary teacher imposes as an exclusive algorithm an approach that is meant to elucidate the meaning of numbers.

The girl explicitly said the teacher doesn't allow stacking, and the Investigations program does not teach the standard "stacking" algorithm until 4th grade. That means she has to do it the pictorial and first principles method each and every time.

Singapore's program uses an explanation similar to what she has done but links the pictorial immediately to the abstract numerical (i.e "stacking" ) representation so that the connection is made while getting the explanation.