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Training mathematical thinking


LarrySanger
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I'd like to maximize my student's ability, and curiosity, to think through mathematical properties. I'll give you an example of one thing I loved to see the other day: he came out with the fact that the even numbers are all just the series of whole numbers, times two. He didn't put it just that way, but he was definitely thinking a mathy thought, and I liked that.

 

While our main math program right now is Spectrum Math, I've been having him do MEP as a supplement. We plan to continue doing that and I think that helps. Maybe it's enough...

 

We've also used Singapore Math but ultimately we liked Spectrum more, and we couldn't do Singapore, Spectrum, AND MEP...we tried. Basically, he does need something that introduces stuff straightforwardly and drills him, so that he knows how to do the problems.

 

Any other programs or techniques you know of, that you recommend for making math "theory" more interesting?

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Well not straightforward with drills....but I love Miquon. Your ds is at the perfect age to start and it will definitely make math interesting. Using Miquon along with Singapore and/or MEP is a great idea. Or use it along with Spectrum (I don't know anything about Spectrum). But Miquon works great along with the SM stuff.

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I was going to say Miquon + MEP + Singapore for building mathematical foundations, but Walking-Iris beat me to it. If I had to pick just one of those, it would be Miquon. Then AoPS in the later years when he's ready.

 

Yes, you also need to work on fluency & basic arithmetic. I'd personally skip the Spectrum workbooks and do something like Calculadders on the side (one daily concentrated dose of 10 - 15 minutes), with LOTS of card and board games that involve math and strategic reasoning. It's much more fun! That's how I raised a pair of strong mathematical thinkers.

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