cheesemonkey wonders

cheesemonkey wonders

Sunday, June 19, 2011

Mathematical Language Manifesto — including mathematical language skills in SBG

Yeah, I'm talking to you. But mostly I'm really writing this for myself.

One of the biggest holes I see in our SBG skills lists is the skill of using correct mathematical language. Not just the names of things, but the verbs.

Oh, the verbs, they are killing me.

Here's an example of the toxicity of mathematical babytalk.

In the math lab at lunch time, I listen in on the students trying to answer tutors' or teachers' questions. "Um, you times it by two...?" or "You minus one." or "You put three."

Which makes me say to myself, You WHAT?

What bothers me even more is hearing how other teachers respond to this. Most of them don't. They simply cringe and try to ignore it, as if overlooking the use of babytalk will improve the doing of the mathematics on paper and in the mind.

And I have not noticed magical thinking to be an especially effective intervention in the classroom.

I started listening in with regularity and I noticed two related correlations:
  • When students sound ignorant, they tend to be treated with subtle (or not-so-subtle) contempt.
  • When students sound knowledgeable, they tend to be treated treated with respect.
This gave me pause. It also made me wonder if I am doing this too. Which naturally gives rise to worry.

So since the only way I know to address this kind of blind spot is head-on, I've decided to address it head-on. No shame, no blame. Just another couple skills for students to master on the skills checklist.

I want to set my students up to sound knowledgeable and be taken seriously as math learners. And that means I have to encourage their courage by means equipping them with the language skills (both oral and written) to get themselves taken seriously in the math classroom as well as in the world outside.

So I'm adding two mathematical language skills to the skills checklist this year -- both for Algebra 1 and for Algebra 2.
  1. Use the appropriate mathematical names for arithmetic operations (noun forms) when answering short-response questions
  2. Use the appropriate verb forms of basic arithmetic operations when answering short-response questions
Same SBG rules as ever: Just show me you can do it twice perfectly and you'll be off the hook for those questions in the future — forever.

But secretly, in my heart of hearts, I'll be hoping that by that point, they will already have internalized a better set of language habits.


  1. I agree with this sentiment. I think in general though it's better to embed this kind of thing into particular standards because content vocabulary is so dependent on content knowledge. So if you're talking about graphing inequalities, then use of the appropriate vocab is tied to mastery of that particular standard versus something separate. The way I picture it as you've written the skill, students would get it (check) and then learn something new and not get it (uncheck) and then get it again (check) and so forth.

  2. @Jason- I think your characterization is much clearer than mine, as that is not what I had intended. The language tasks of each skill should be embedded in what is considered mastery of that skill on the checklist.

    On additional thing I have noticed is that mastery of the language tasks in a skill definitely seem to enhance conceptual understanding of that skill and its concepts. While it's theoretically (or actually) possible for a student to fake his or her way through some symbolic manipulation on paper, it is not at all possible to fake one's way through a written account of the work and its concept.

    Isn't this what is so powerful about Sam Shah's e-mail form for requesting an opportunity to reassess?