I like this approach. I can see how it might be difficult to implement for a large group and requires more from the teacher. But - that could be good, right? Don't you want to exercise your brain too, Kriston? (For that matter, why are you terrified of math? ) And I'm thinking too that I should search out that article on Finland's schools, this is reminding me of that for some reason ... will see if connects later.

So here's some thoughts:
- I think the point is to start with teaching ideas and to think, rather than teach formulas. Eventually you'll need to introduce notation, but the ideas come first as motivation for the notation. So, in the case of volume and popsicle, think about it with the child and figure things out. Try to think of different ways of figuring the volume out, of comparing it to other volumes. You can bring in thermo too .... compare frozen volume to liquid. What happens with different mixtures.... Could be a very rich topic and you could go in lots of different directions.

- this method intrinsically provides motivation for math. One of the things that drives my DD(newly)11 crazy is word problems with helpless people in them - she'll rail, "Why should I figure out how many apples Mr. X has, why can't he figure it out himself!" or something of the sort. I think the point behind word problems is to show how computation might come up in the real world, but it would be better for it to actually arise in the real world.

- Might take longer to achieve math whizziness, but the understanding might be greater.

- Math questions come up everywhere, if you look for them. Part of the challenge to the teacher here is in recognizing the opportunities.

- Prior to 1st grade, DH and I thought our DD had good math intuition. She wasn't way out there, but she had good conceptual understanding. However, having to do only 3 minutes a day of computation drill homework (plus whatever they did at school) killed any interest in math that she had. She's been gaining it back recently, but it took teaser introduction of more advanced topics before she would even consider caring about math again. Which is just to say that I think it's valid to fear that you could diminish your DS's love of math.

Well, whatever. What do I know anyway! smile I do think it sounds like a more intense and challenging way to teach. I bet it could feel like taking away the safety net. Of course, that could be more exciting too.
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kcab