Friday, September 10, 2010

Finding a New Groove With Math

At the end of last week, P complained, "Math isn't fun any more this year." I'd been giving her 5 review problems daily, same as last year, while working on a new concept. It may be that I wasn't approaching the concept of place value in a way that worked with her learning style, or that she had forgotten several of the review items, but I felt that the main problem was that I was requiring too much writing of her. We've been doing math at the end of the school day, right before lunch, and by that time, she has already done a page in her handwriting workbook, written a list of 10 spelling words, often done copywork for language arts, and frequently completed part of a science worksheet.

At the same time, I was busy reading this article. If you don't have time to read 25 pages of sometimes over-emotional diatribe about what ails math education, here's my summary: Math is actually an art form - finding the beauty of patterns in conceptual objects (numbers, triangles, etc). Math education has removed all the art and beauty from math, and turned it into a purely mechanical exercise requiring memorization without creativity. It would be better to teach no math at all than to ruin the subject the way it is ruined by teachers who don't know better because they've never seen math, either.

I don't fully agree with the author, but the article did make me think about how I'm going about teaching math to P. I decided to try to include more unguided discovery, as well as more guided discovery, into our lessons and our review. I started by revamping the 5-a-day review process. Instead of having her write anything with pencil and paper, I'm looking at what concepts we need to review and trying to find games to play that will require understanding of those concepts. Sometimes, failing to come up with anything creative, I simply have her do a problem on the chalkboard, which she at least prefers to pencil and paper.

I've been doing lesson prep for math on Tuesday nights, but Ari and I watched the first half of "Gone With the Wind" last Tuesday night instead, so I had no plan for Wednesday. Fortunately, the math video which once was lost now is found, so I simply let them watch that. "Professor Justin" reviews a number of concepts that we covered a while ago, and even E was really getting into shouting out the answers before Justin said them.

On Thursday, I used an idea gleaned from the Sonlight forums for our science experiment - demonstrating the water cycle. We put water in a pot (the "ocean") and heated it on the stove (the "sun") until it began to evaporate. I then held a bowl about 20cm above the pot and let the water vapour condense inside it ("clouds") until the droplets got big enough to "rain" back into the "ocean". Once the experiment was over, the kids begged to bake something with the boiled water. I had been planning on making bread (and, for vocabulary enrichment and additional science, discussing the differences between whole wheat flour and enriched unbleached flour). Our recipe calls for 3 cups of warm water and 1/2 cup of honey, so I added the 1/2 cup of honey to the boiled water to dissolve it easily. This turned into a lesson in adding fractions - "We have 1 1/2 cups of liquid in our measuring cup, and we need 3 1/2 cups of liquid. We've added all the honey we need, so how much water do we need to add?" P needed a bit of hand-holding, but she grasped it pretty well once I explained it in a couple of different ways. She easily remembered, while helping me make pizza dough this afternoon, that 2 1/2 cups of flour was the same as 5 half-cups of flour. Kitchen math is an excellent way to work with fractions - I plan to incorporate it into our days more often, since both big kids love baking with me. (B does too, if you count him sticking his hand into the dough when I'm not paying attention and then smearing it all over my recipe books).

Today's math lesson, I decided to introduce P to some patterns that I find fascinating. In the RightStart games package which we bought in May, there are games involving the "long chain" and "short chain". I had never heard of these, but they are patterns similar to Fibonacci in that they only require simple addition, but simpler because they only take into account the ones digit. Since we're working on place value and I'd like to help P get more comfortable with her addition facts, I thought they'd be valuable for her as well as enjoyable - she has a thing for patterns. For example, the one I started her out on is "4 2 6 8 4 2 6 8..." - the nth number is the ones digit of the sum of the (n-1)th and (n-2)th numbers. P loved this, and I had her figure out "0 5 5 0..." for herself. I also showed her the trivial case, "0 0 0...". She said, "That isn't a pattern. It's just zero." I neglected to introduce the vocabulary word "trivial", but she clearly grasps its concept. I then demonstrated, with some participation from her, the "long chain", which starts like Fibonacci (0 1 1 2 3 5 8) but, because it only contains the ones digit, repeats after 60 digits. She doesn't have the patience to do that much addition! But she liked the idea of a repeating pattern of numbers, so I imagine we'll play with that again.

Now, I'm off to figure out some hands-on, real-life activities for her 5-a-day reviews this coming week, and see if they lend themselves to any interesting patterns. I like this challenge - it's real mathematics.

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