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!
Resource Room Dot Net Blog 
Cal Armstrong (@sig225)
September 9, 2013
I’m fortunate enough to know the organizing author of the website and she’s the definition of “very nurturing and supportive of many pathways to understanding.” I’d view the initial draft of this nascent project as only the beginning of a much larger conversation.
xiousgeonz
September 9, 2013
Thanks 🙂 I”ve worked with too many students who have been told “you should have no trouble with this!” Hopefully the project will include pathways to understanding instead of missives about how easy it is!
Kate MacInnis
September 9, 2013
I think it’s important to make a distinction between what we tell each other, and what we tell students. Saying to another instructor that students (of a certain type/class/developmental level) don’t tend to have difficulty with a certain concept is very different from telling the students that it’s easy.
xiousgeonz
September 9, 2013
That’s absolutely true! I do, though, sometimes find that language tends to work its way from one world to the other, specifically that “should” language… and I also find that many many many the student frustrated with math has *heard* the message, whether or not it was intended to be delivered.
Tina C.
December 30, 2013
Hi! I’m the author and I just happened upon this post while testing out our SEO. I really wish you’d shared this sentiment on one of the google docs or via the commentary form. I totally agree that the wording there wasn’t good. I changed the “should” to “are” in the final version but forgot to delete the “be,” it now says “students are be able” which somehow no one has caught! Thanks for alerting me to that typo and I hope you’ll read the new version and share your commentary. NixTheTricks.com
xiousgeonz
December 31, 2013
Hi! Thanks so much for finding this and responding. I had/have no idea where “the google docs” and commentary forms are, or I’d have given direct feedback. I’m still getting the hang of getting things to “ping” in the right places (and it will change as soon as I figure it out). It was also hard to figure out whether that would be worth my while — I know too many math teachers who deeply and serenely believe that really, students “should understand” an awful lot of things “without difficulty,” and in the name of nixing tricks, actually drive students even faster towards them… and they’re perfectly likable, earnest people… As Kate pointed out in the comments, what we tell students and what we tell each other are two different things (because we already know the math, among other things…) Off to read teh commentary …
xiousgeonz
December 31, 2013
(I’ve found said forms … I’m not sure they were as easily accessible in September…)