http://www.nixthetricks.com is the site that the twitterfeed led me to last Sept. 9. Seems I didn’t directly link to it, else the author might have noticed … but as I said in my reply, I’m still figuring out how to get things to ping in the right places, and am confident that as soon as I figure it out, it will change.
I wholeheartedly agree with the premise of the site/book (which is a free-to-download pDF and I wholeheartedly like that, too): we should teach students to understand, not to learn quick tricks. (If one doesn’t gather that from my assorted diatribes against emphasis on procedure, I don’t know what to say.)
The intro includes teacher rationales for “tricks” —
“But it’s just to help them remember – I taught them the concept!” — and we’re told we should have students invent their own mnemonics — “each by each” instead of FOIL.
More important is this one:
——————–
“”My students can’t understand the higher level math, but they do great with
the trick.”
If students do not understand, they are not doing math. Do not push
students too far, too fast…asking children to mindlessly follow an
algorithm is not teaching them anything more than how to follow instructions.
There are a million ways to teach reading and following directions, do not
reduce mathematics to that single skill.”
————————–
To which I can only say: +1 // Amen // Huzzah!
the other thing I really like is the recognition of what students do to our quick run-through of a concept, finishing with the short version… they grab the “short version.”
My only concern — and it’s a biggie — is that for an *awful lot* of students, it takes serious time and practice and reinforcement to build the abstract concepts, including creating and confronting cognitive dissonance and then whittling away at the misconceptions again and again. Misconceptions don’t die easily, per http://www.learner.org/resources/series26.html (and all those silly Facebook math questions invoking the order of operations, which most people have forgotten). If knowing that 2/3 + 3/8 isn’t 5/11 because “the shoes have to be the same to dance together,” you’ve got a chance to get that right long after you’ve forgotten what all that notation means. (Here’s where my population may be different from your population — many of my students have been away from evn basic math notation for a while. It’s still easy to forget that *we* go over *exactly the same* math year after year — of course we know it by heart!) WHile I don’t like students using tricks, I think that going over the concepts too quickly for them and *not* having a shortcut at the end is even worse.
Also, just because a student *can* flush out comprehension with a trick doesn’t make it so. Some of my most industrious students absolutely *rely* on verbal “tricks” to connect to a concept and procedure. There are so many of them. These students would ‘get’ the concept you’re teaching… but without the trick at the end, would not have a hook to get back to it. I have mixed feelings about FOIL too, but don’t think it’s any worse than SOH CAH TOA, which I used yesterday finishing Lab 1 for my Spring class.
I really, really like the “teach concepts, not tricks” idea… but am not comfortable with assuming that our teaching is really building those concepts. The “tricks” are like an electric assist in a bicycle. Throwing it away means a student has to find a different way to get up the hill — but often they’ll design their own “tricks” that are much worse than the standard ones (grabbing a bumper of a passing car). If you remove one “lifeline,” I want more assurance that you’ll redesign that bike and its gearing so that more students can get up the hill…
Resource Room Dot Net Blog 
Tina C.
January 2, 2014
Hi There! Still not the right link 😉 NixTheTricks.com (I may be a math teacher but I still like to spell things properly.) I totally agree that this all takes time, but I would argue that we should be pushing back against the testing pressure rather than pushing back against concept development. Every year my department gets together and tries to guess which topics in Geometry are least likely to be on the state test, then we leave those topics for after the exam and do our very best to teach the other topics well. I would rather send students into the test with solid reasoning skills to rely on than teach them a couple formulas for inscribed angles in 20 minutes with the false hope they’ll be able to apply that to an exam question. Thanks for writing this post because writing this response is the first draft of a paragraph I’ve been meaning to add to the introduction!
xiousgeonz
January 2, 2014
Edited and fixed.
I have never pushed back against concept development. Could you tell me what led you to think I was?
Jo Boaler has lots of good support for the idea that if you’re learning to *think* you end up doing better on any test, period. I really enjoyed her “How to Learn Math” MOOC last year (and her “What’s math got to do with it” book).
Pushing back against tricks is not the same as pushing back against tests. While we’re trying to push, our students are still having to take those tests. That is their focus.
I will question things done in the name of concept development, because an awful lot of well-intentioned things are… that don’t succeed. One huge problem, as I said, is the reality that math teachers *think* they’re “teaching” a concept. (See previous posts and http://www.carnegiefoundation.org/carnegie-perspectives/what-were-learning/what-community-college-developmental-mathematics-students-understand-about-math .) Many of the students who come to see me don’t even think there’s a concept to be learned. Yup.
Presenting them with “simple logic” (almost always based on concepts they don’t already have and delivered too quickly and too symbolically), is interpreted as “this is your version of the tricks to solve this problem — but my friend/the INternet/ knows a quicker trick. WHy do you hate me and make me do this longer, more confusing trick?”
It ends up, ironically, that the effort to teach concepts nails down even harder the notion that they are not in the elite group that is able to comprehend math. Guess what? I’ve no intention of stopping my pushback against that.
I dont’ question teaching the concept. I question the notion that if we stop teaching shortcuts and present concepts, that students will learn them.
I’m not in a position to pushback against the bizarre test-prep policies; happily, I am in a position to help students prepare for our placement test with tutorials that develop concepts,and get to work with faculty to have our basic courses prepare for college level ones conceptually (instead of ramming through every procedure in arithmetic one more time as if it worked the last n times).
xiousgeonz
January 3, 2014
… okay, **now** it’s edited and fixed (but I’ll check later to make sure).