My Harvard Math for Teaching Thesis: Complete! And ready to share… March 20, 2011

After many many years of jumping through many many hoops, I am finally graduating with my MA in Mathematics for Teaching in May.  My thesis, Negative Number Misconceptions in High School: An Intervention Using the ZeroSum Ruler is right now at the printers being printed and bound.  I don’t know about you, but that instantaneous feeling of relief after taking a final exam or passing in a final paper stopped hitting me sometime in college.  So now, I’m just feeling a bit burnt out.  OK, completely burnt out.  But I’m sure it will hit me soon since it kind of needs to; I need to now get in a post-Bach program to get my Initial teaching license.  I like to do things backwards.

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So here it is for download!  For all to read!  Or maybe to just glance.  In my study, the ZeroSum ruler proved effective in reducing eleventh grade error on integer addition and subtraction problems (especially with negative integers).  If I wasn’t so burnt out, I’d want to test it with younger kids.  Imagine how our world would be if my eleventh graders actually mastered integers when they learned them in, and only in, 7th grade.  But that’s in my thesis.]

 

All too common math mistakes! June 16, 2010

 

One of my grad school professors called the mistake (a+b)^2 = a^2 + b^2 the “freshman dream”.  I guess he meant freshmen in college, but freshmen in high school make the same mistake.  Come to think of it, a lot of people make the same mistake.  What other mistakes are common in Algebra?

 

Here are just a few I can think of:

 

x = 1.     NO.  Well, sometimes, but definitely not always.

  

-7 + 5 = -12.  NO.  This one’s a never and the reason I developed the ZeroSum ruler.

  

(a+b)^2 = a^2 + b^2.  NOPE.  There’s a middle term in there.  Write it out.  Don’t be lazy.  Find it. 

  

1/2 = 2.  NO.  “1 out of 2″ is not 2.

  

(x + 2) + (x - 5) = x^2 – 3x - 10.  NO.  This is an addition problem, not a multiplication problem.

  

(x+2) – (x - 5) = -3.  NOPE again.  That little – sign is a -1 in disguise and needs to be distributed.

  

(2/5)(7/3) = ….<blank>….  NO.  Multiply the numerators together and the denominators together to get 14/15.  Easy!

  

“Thirty percent of 140 = 140/.3″.  NO.  You’re going to get a huge number.  “OF” means to multiply, not divide.

  

|-5| = 5, so |5| = -5.  NO.  Absolute value is always a positive number.  It represents a distance.  Even if you walk backwards, you’re still moving some distance.

  

“find x^2 if x = -5″.  Answer: -25.  NO.  Jut because the TI-83 says -25 doesn’t mean it’s right.  Calculators use PEMDAS, which states multiplication comes after exponents.  Remember a few mistakes back that the little – sign is a -1 in disguise.  It’s the same here.  If you put “-5^2″ into the calculator, the calculator will square 5 and then multiply by -1.  To square the entire -5, use ( ).  Or just remember that a negative number raised to any even power will always be positive. 

 

(x^4)(x^5) = x^20.  NO!  This is a common mistake kids make.  But if they start by thinking about what “x^4″and “x^5″ mean, it’s easy to see that (x^4)(x^5) expands to (xxxx)(xxxxx).  Parenthesis right next to each other tell us to multiply, so you end up with (xxxxxxxxx) or x^9 or x^(4+5).

 

(x^4)^5 = x^9.  No, too.  x^4 = (xxxx) and the “^5″ means you have 5 (xxxx)’s.  So (x^4)^5 expands to (xxxx)(xxxx)(xxxx)(xxxx)(xxxx).  Parenthesis right next to each other still say “multiply” so we have 20 x’s in a row, or x^20.

 

I know there are more.  What did I miss?

 

 

Webpage blocked! [possibly] May 25, 2010

 

I found a great video at http://adgonzalezmath.wordpress.com/ in the “February 2010 archives” that lead to what could [possibly] be the greatest collection of math videos on all of the interweb superhighway: http://justmathtutoring.com/  I say “possibly” because, like many things that could be useful to students, the site is blocked here at school!

 

So I’ll check it out at home.  My bet is, based on the video I saw on adgonzalezmath’s page, the videos are going to be nice.  So if you know how to save videos from the internet onto your computer, I’d love to hear from you.  I know of one site that may [possibly] do this, but it’s blocked here.  Though even if it weren’t, I’d have nothing to upload!