Wednesday, January 12, 2011

Math problems of the week: subtraction strategies in Investigations vs. Singapore Math

1. From the 4th grade Investigations Student Math Handbook, pp. 13-15, given out in January:







2. From the 3rd grade Singapore Math Primary Mathematics 3A Textbook, about midway through the first half of 3rd grade, pp. 54-59:













3. Extra Credit:

Are the six demonstrations of a single algorithm, as seen in the Singapore Math textbook, an instance of "rote" teaching--as opposed to the single demonstrations of four different methods in the Investigations handbook?

By 5th grade, Investigations students are two years behind Singapore Math students. Is it because of "Chinese mothering," or might there be some other factor at work here?

3 comments:

Deirdre Mundy said...

Good grief! After trying to read through the "Investigations" worksheet, *I* felt less competant at subtraction! It's confusing--even though I understand the concept, it's more difficult and less accurate than the normal algorithm.

I can only imagine what it would do to a kid who was still working on learning the material!

kcab said...

Well, I think there must be less resistance to the curriculum than to Chua's parenting style!

What strikes me about the Investigations sheets is that I do use these techniques, or variants, when doing mental math. I don't usually visualize the standard subtraction algorithm, though sometimes I have. I'd never choose to use the strategies that Investigations presents for written work though.

I guess I can see one advantage... for those problems where the kids are supposed to explain how they got their answer they'd have a bit more to say.

FedUpMom said...

Ugh. The Investigations handbook reminds me of a phenomenon that computer programmers call "creeping featuritis". It's the tendency to keep throwing new features at a program, until the original function is completely obscured by the tangled undergrowth of extras.

I saw this in action once when I went to buy a new dishwasher, after the old one broke down.

Dishwasher salesman: "See, there's 8 different kinds of rinse cycle, and a dish warmer, and you can set it for delicate or tough dishes, and you can set the amount of time you want it to take!"

Me: "Show me one button I can push to get the dishes washed."

It turns out there is such a button, labeled "Normal Wash".

We wound up buying the dishwasher, and we've had it for many years. To this day, I have only ever pressed the "Normal Wash" button. I can't be bothered thinking about all the different possible varieties of washing the damn dishes.

Similarly, it would be better to teach the kids one method of subtraction, and make sure they can all use it competently.

Oh look! Here's an algorithm people have been using for centuries! Let's use that!