(Click chart to enlarge)
Schmidt, William H., Wang, Hsing Chi., McKnight, Curtis C., J Curriculum Studies, 2005, volume 37, number 5, pages 525–559
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Negative Numbers. OH NO! October 6, 2010
In our BPS high school, there’s a big focus on the “broken window theory”, made famous recently in The Tipping Point. One broken window we’ve identified in the school as far as discipline goes is hats and ipods. So, there’s been a big push to get rid of them.
I’d like to mention to you a “broken window” that has somehow gotten lost in the mess of school closings, going charter, union fighting, pension plans, longer days, MCAS scores. As a high school math teacher, the biggest broken window I face – in fact, it’s a gaping hole not even bothered to be temporarily covered with plastic- is… negative numbers.
What do I mean by negative numbers? I’ve done my research as they’re the topic of my Harvard thesis. Students using the TERC Investigations curriculum in Boston elementary schools do not do problems like “-22 + 5″. One TERC representative told me they “leave that topic to middle school”. So, I looked at the middle school Connected mathematics Project 2 (CMP2) curriculum, and negative integer problems, like “-22 + 7″ are taught for 20 days total in the 7th grade. 20 days. From then on, students are assumed to know how positives and negatives interact and to be able to evaluate “-22 + 5″.
Then students get to me, their 11th grade Algebra 2 teacher, and they can’t solve for y in “y + 22x = 5x – 7″ because they don’t know what “5 – 22″ is. The kids think -22 + 5 = -27. Why? Maybe the rules of multiplication get mixed in. I don’t know. Or maybe it’s because these problems were taught to them for a total of 20 days four years earlier and were never touched n again except in the context of other problems. Understanding why and how kids think is beyond the scope of my thesis and my means for data collection. What I can tell you is that because my students don’t know what “5 – 22″ is, they can’t solve y + 22x = 5x – 7 for y. Because they can’t solve the equation for y, they can’t graph the equation. I assume you know where I’m going with this.
Please, as someone on the front lines of math education in Boston, I’m telling you that the biggest difficulty our students have in math is adding and subtracting positive and negative integers. It seems ridiculous and that there are bigger fish to fry, some of which I have listed, but if you want more competency in math, please, heighten the focus on negative numbers. It will lead to better test scores, more understanding, but most of all, to students who feel good about themselves when they’re not still making silly 7th grade mistakes in high school.
