ZeroSum Ruler (home)

Blogging on math education and other related things

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.

Small Schools, SUPERSIZED Classrooms: Thanks a bunch, Bill GatesSeptember 3, 2010

School for Boston Public School teachers starts on Tuesday.  The kids come back Wednesday.  Three chairs at a table, eight tables, I have 24 seats in my classroom.  The class size limit in Boston is 31 per class.  -

37 students + 24 seats = success.  Solve for HOW.

-

So that I could get an idea of who I’ll be seeing on a daily basis and when, since I had many of the students I’ll have this year two years ago when they were 9th graders, I went onto mybps.com to download my class lists.  This will be the first year that all students get electives after four years of none (Thanks again, Bill Gates.  My students thank you too for the opportunity to go to a small school where they get to know each other so well that they fight like siblings and miss out on things like art, music, and… computer classes.  But to have computer classes would mean we’d need computers, so thanks for dropping the ball on that one, too.  “Good looks” as my kids would say, only I say it to you sarcastically, you mad scientist, you!)

side: What’s the difference between a real scientist and a computer scientist?  Real scientists can admit when they’re wrong and try, try, try again until they get it right.   You can’t Ctrl/Alt/Delete this one, Bill.

Anyway, so I downloaded my class lists and I see the following:

Math elective, period 3:            37 students

Algebra 2, period 4:                33 students

Algebra 2, period 5:                25 students

Algebra 2, period 6:                24 students

By my schedule, you can see I’m a math teacher.  As hard as calculus was, I got through it.  I even got through a java programming class that sucked 15 pounds out of my body.  But I just can’t seem to do the following problem:

37 students + 24 seats = success.  Solve for HOW.

I appreciate any and all suggestions on how to pull this one off.  These are the kinds of things people forget about us teachers.  We “get summers off”, we “only work 6 hours a day”, we “have tons of vacations”, we are “failing our kids”.  But no one ever comments on how we’re sometimes set up to fail before we even begin.

I’m scared for Wednesday, not because I don’t think I can teach 37 kids at a time but because I don’t know how to choose who gets a seat and who sits on the floor.