Patterns in i? November 29, 2010

You can imagine my surprise at the end of last school year when, on my tutoree’s final online examination, the imaginary number i was everywhere.  “WHAT?” I thought, “There was just one small section of one small chapter on i in the textbook and here it is, on my students’ final exam, EVERYWHERE.”  At best, it was frustrating.  Sure, math is math, but different publishers tend to focus on different topics, and i was not on of those topics Glencoe included much of.

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For five years, I had taught Algebra 1 and loved it.  The kids loved me and I loved all of their “ooooh, I get it!”s.  But this year had been different because I was moved up to Algebra 2.  So I set my mind to teach this slightly more advanced Algebra (at least with Glencoe it’s only slight), brushed up during the summer, got my curriculum down pat, taught a rough year right up until the final exam and….

  

BOOM!  i! 

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Patterns are everywhere, especially in math.  The imaginary number i is no exception.  The number’s value follows an interesting and very distinct pattern, repeating itself every fourth iteration.  The pattern it DOES NOT fit is into a regular one in Glencoe’s Algebra 2 textbook.  I was mad that my students and I had worked so hard only to be sidelined by a final exam not connected to Glencoe at all.  

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So this year I changed.  I taught i first!  We wouldn’t be stopped!  If the “patterns_of_i.xls” sheet over there in the margin for you to download and use in your classes is not enough, I’d be more than happy to email you more.  You can reach me at sdonohue@post.harvard.edu. 

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I quit this year, jumped a sinking ship, really.  It was horrible leaving the kids- like I was going on maternity leave and never coming back.  But it was the decision I had to make so that I could focus on my thesis, my health and on finding a job where I would be respected.  What they say about finding happiness first before you can pass it on is true.  What they also say about not doing school part-time unless your job is also part-time is also true.    

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Now I’m finishing my thesis and looking for a new job, oh, and emailing you files to use in your classes.  I have thousands that I’ve made over the years that I’d love to share with you. 

 

  

Go i!

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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.