Thursday, October 22, 2015

Thoughts About Math

I warn you ahead of time: these thoughts are disjointed.

I'm not a math person. By that I mean that I do not enjoy math, I don't do math in my spare time, and when I am forced to do a bit of math I have to use my whole, aching brain. But I did well in math in school. I can do it if I have to.
Ha!!!
Adam is a math geek. He took AP math and tested out of 2 years of college calculus. (So did Philip.) He had to drop out of his math major because of the tinnitus that plagued his brain, but he remained a math whiz. He took all the course work online for the math degree at MIT. He got to know MIT math people and now he proofs work for them as they do big whoopie math. The math people he does proofs for live from Turkey to southern Africa. None of them are Americans. Do Americans get higher level math degrees at MIT anymore? I don't know, but foreigners apparently still think of the U.S. as a place to come to for the programs. How can we still provide the universities but not the students? That's a mystery to me.

Recently I heard someone talking about Common Core math in North Carolina. I've heard a lot of negatives about CC, so I was interested to hear a cheerleader, someone with deep knowledge of CC and its implementation. I was told that CC is designed to compensate for years of horrible math instruction in US schools. That CC is designed to give conceptual and procedural understanding -- a thorough, deep understanding of how math works instead of the hokey short-cuts we used. The "I-don't-know-why-this-works-to-solve-the-problem-but-I'm-doing-it-because-the-teacher-told-me-to" method of math.

I remember being a hokey short-cut math student. But I also know that over the years of math instruction I did learn math concepts. I did understand the why's behind the solutions. It was rote memorization at the beginning, but by high school the work was complicated enough that understanding the concepts behind the steps was necessary. I think that's true.

So I was surprised to hear that my math education had created generations of dummies. I was also surprised to hear that Common Core, with its lengthy approach to teaching multiple ways of understanding the math and solving the problems, including videos and lots of manipulatives, is a dream curriculum for Special Ed. kids, and is a great solution for all the average kids. But I heard that it is really frustrating for the advanced students, and that those whiny students, and their equally whiny and lazy parents, complain about all the work. That the advanced students just want the short-cuts because they want to get the answer, get done, finish the work, and get their grade. Because they're just grade hogs.

I found that description of them to be offensive, so I challenged it, and the person backed off a bit. I argued that many advanced math students have an impressive intuitive understanding of why math works the way it does -- they grasp the concepts and the steps quickly and don't need it drawn out repeatedly three different ways.

I was told that we really don't have many kids like that in our county because we mostly have poor, dumb kids here who don't perform at that level. Okay, the person didn't use "dumb" but we all knew what was meant. We don't expect that level of understanding from our local kids. Maybe that's part of the problem!

Some friends noted that there's less actual work done by students at home -- maybe three problems instead of ten. The kids aren't required to do lots of repetitions of the work to reinforce it. And this is apparently true! In fact, a teacher may assign 3 problems to child A, 5 problems to child B, and twenty problems to child C. I was told that repetition is not a good thing; if the child is doing the work incorrectly, lots of repetition will only reinforce the wrong methods! And then it's hard to reverse that ... so it's better to do very few problems. I don't even want to begin to investigate how wrong-headed that thinking is!

People, where did we go wrong? Adam noted to me that back in the 1950's and 1960's, we produced rocket scientists and math geniuses. What math were those kids taught in the '30's and '40's? Can we go back to that?

I'll end with Julia, and our anecdotal homeschooling evidence. Julia is me -- not a "math person." She dislikes it. In fact, of all her homeschooling work, the class that finally ended it all for us ... was math. She and Adam came to an impasse. They could not do math anymore without fighting. Math is important to Adam; it's beautiful and eternal and reflects the mind of God. And to have his middle school daughter repeatedly dismiss and insult math was just painful. We tried textbooks, Khan Academy, less supervision, more supervision -- nothing helped. In 9th and 10th grades, her math study was rather pitiful, and I was worried. I didn't know where she was, to be honest. Finally we realized we'd better get her into a community college for a math course (and chemistry, because I didn't want to do labs at home) if she were ever to finish high school.

She enrolled in pre-calculus algebra. She ended up dropping chemistry because this math course was so, SO stressful. She got a 70 on her first test. She complained and whined and made our lives miserable. Oh My Word, was it awful! It was as bad as homeschooling her in math! But we told her flatly that she must do this if she ever wanted to go to college. Her next score was a 73, and then gradually her scores climbed into the 80's and 90's. Her last two tests were 103 and 104, the highest score this teacher gives on tests. She's clearly mastered the material and is excelling, even though she's not a math geek, even though she still dislikes it.

Is it just her brain? I don't know. What did we do right all those years of Math Suffering? I haven't a clue, except as homeschoolers we tried to teach her to THINK, to problem-solve, to stick to it, to reason well. We never, ever taught to a test, and we did not focus on assessment. We valued the information itself, even if she didn't.

If we, who did such a poor and incomplete job teaching our daughter math, could see her flourish this way after only two months in a community college, why can't our public school system, with all its resources, do better? I look at the Common Core work that kids are dong now, and  scratch my head. I do believe the intend is noble: to improve conceptual and procedural understanding of the work. But for some reason I don't think this convoluted curriculum will work. In spite of what I was told recently, I don't think kids are being taught basic math facts. They are not memorizing them. They are confused. They need better thinking skills, better problem-solving skills, but I don't think they're learning them in those classrooms. I hope -- I dearly hope -- I'm wrong.

I don't write any of this with a political agenda. I don't give a flying fig if either political party endorses or opposes Common Core; they're always looking for the latest football to fight over. I care about the kids and what we are doing with their minds during the many hours they are in our care in school. Both kids and teachers are desperately eager to perform well on EOG tests. This test-desperate approach makes them desperate for the answers -- not the concepts, not the procedures, not the deep understanding. They want the answer and the grade. Until we reduce the pressure to perform there, we will not make student minds eager for understanding. I feel we do not need more, but less. I would love to know any thoughts from readers out there who know more about math, or Common Core, than I do, or who have experiential knowledge from teaching. That should be about 90% of you!

2 comments:

  1. I like the poster that says, "Another day when I didn't use algebra once."
    Ha!
    I had horrible math instruction and I still don't think like a numbers girl. I've survived. I'm thankful.

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  2. Math to me was always a four-letter word. Endless frustration. You know, I actually found some of those old feelings return as I read this post. Yikes.

    Regarding Common Core, the federal government needs to stay completely out of education. It should be under local control. Just my two cents!

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