The boys' school uses Investigative Math in their curriculum. I do not understand it well enough to give a fair critique but there are plenty of people who lambast it, a simple google will confirm this. What I do like about Investigative Math, however, is that it challenges the child to explain to other children how he solves a particular math problem (I'll write about what I do not like another time :)). This is not as easy as it sounds. It can be very frustrating for a child who just sees it, to force himself to slow down and spell out all the steps required to get to the solution.
I wrote in my Squares & Stuff post that after some time, the child will be able to visualise the boxes required to solve multiplication problems. Sean is now able to visualise squares from 1x1 till 23x23, ie, solve these equations without pen & paper; I tested him during dinner yesterday (to counter my boredom when feeding him).
I then asked him to explain in his own words (which Investigative Math encourages) how he's using The Method . He refused but relented when I told him he'll be helping other children, hehe. Here's the video with full transcript below.
My conclusion: He understands how to use The Method, but I don't think he truly understands what's behind it.
I'm doing 23x23.
First I have to do the equation.
Hmmmm...23 equals...What? You don't know? Okay.
First I have to put 400 here, which is 20x20. I also have to write down, I have to write 60, which is three 20s to do it or you can call it 3x20 or 20x3, because I'm doing 23x23.
Hmmm...you need another 60, don't you think you need one? Of course you do. You need another 60.
Here's your 9. And don't forget your little tiny 9...
First you add 60 to 400 to make 460 and then you add another 60 to make it 520 and you also have to add your little 9, and here's the equation (he means answer of course), 529.