nix the trix? Maybe.

Posted on September 9, 2013

7


   My twitter feed got me a link to a new site called “nix the trix.”   I like its premise:   that understanding math is better than memorizing mnemonics, and that those mnemonics can make it harder to understand the math, especially when they get in the way.   Classic example is when my guys are telling me -3 + -4 is +7 because “two negatives make a positive, don’t they???”   

   However, the tone of the page makes me want to cry on behalf of so many of my students. The first Trick to Nick goes like this: 

“Nix Same-Change-Change or Keep-Change-Change (Integer Addition)

Because it’s meaningless

Fix: there is no need for students to memorize a rule here. They should be able to reason about adding integers (and extrapolate to the reals) without difficulty. Students are comfortable adding integers on the number line, all they need to add to their previous understanding is that a negative number is the opposite of a positive number.

2 + 5 ⇒ start at 2, move to the right 5 spaces

2 + (–5) ⇒ start at 2, move to the right –5 spaces ⇒ start at 2, move to the left (opposite of right) 5 spaces

2 – 5 ⇒ start at 2, move to the left 5 spaces

2 – (–5) ⇒ start at 2, move to the left –5 spaces ⇒ start at 2, move to the right (opposite of left) 5 spaces

 —————————————————————

Okay.   First.   Don’t should on me, and I won’t should on you.   I work, every day, with students who  … wait for it…

They.

Do.

Have.

Difficulty.  

    There is zero, zilch, zip, nada in this description of the teacher’s responsibility for getting the students to that understanding.   It’s full of “Don’t use the rule, this is EASY!!!!”  There is *nothing* about how to help students understand the nature of negative integers, and there *is* a lot about how easy it is.   Which is fine, if it’s easy for you.  If not…. 

    And we wonder why people get this mindset that they can’t do math?   

    These are the students who will either not look for help and fail, or look for help, and somebody will tell them the trick and they’ll say, “Why didn’t somebody just tell me that?”

  “Same change change” is, I assume, referring to changing subtraction to adding the opposite.   For the verbal learner, that’s where meaning takes its roots, and then gets applied to the number line. (Pointing at self, here.)   It’s okay to use the number line trick  to get to the idea of opposite — why is it “meaningless” to change subtraction to its opposite and the sign of the number being subtracted to its opposite?   I’ve seen people do visual routines with numberlines that are meaningless, too.  

    Now, I don’t know the teacher posting this.   S/he could be very nurturing and supportive of many pathways to understanding.   I hope so! 

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