What Precal Students Can’t Do

I am the fortunate (perhaps?) position of teaching Chemistry simultaneously with Precalculus, and so often times I will come across an equation and wonder “can my Precalculus students do this?”  Today’s equation I “simplified” (read: took away the decimals and made into integers [1]) into this:

\frac{1}{x} = \frac{3}{2}

At first it depressed me that my students didn’t intuitively know what to do and where to go, in addition to the fact that they were not at all confident in their answer.  Soon after, I became more depressed by the fact that some couldn’t solve it on their own.

Our Alg II teacher told me that they were done a little early with their curriculum, and asked if there was anything that he wanted me for the upcoming Precal students to work on.  I told him that I wanted them to be able to solve the above problem.

I wonder if my frustration is increased because of the fact that there are about half a dozen different ways to do this problem.  Of course, about half of those involve stupid little tricks, which I don’t like because they don’t increase understanding, but there are more than a few legitimate ways of solving this without resorting to “cross multiplication” and “cancelling” (ugh, bad words).

After school, I had a few Chemistry students who were talking about solving that kind of equation (well, I brought it up), some of whom are Alg II students and others whom are Precal students. Some of the Alg II students could do the problem and others couldn’t, and likewise some of the Precal students could do the problem and others couldn’t.  I used to think that students forgot how to do this kind of thing because they had a whole summer to forget how to do it, but now I’m realizing that students forget how to do this kind of thing because they have an entire school year to forget how to do it.

[1] As another teacher pointed out, it is really sad that making an equation have decimals rather than integers increases the complexity for students.

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9 responses to “What Precal Students Can’t Do

  1. Pingback: How Could You Solve This? | Productive Struggle

  2. Thanks for linking Nix the Tricks! I linked back to this post from Productive Struggle: http://productivestruggle.wordpress.com/2013/05/06/how-could-you-solve-this/

    • Awesome! Yeah, I had to dig deep in my “edited Google documents” to find it, but it’s something that I’d like to keep in the forefront of my teaching because all of those are awesome suggestions.

      I’d also like to share “Nix the Tricks!” with my colleagues, but am worried it would come off very arrogant and very “you’re-teaching-all-this-wrong-do-this-instead”. Thoughts? (Perhaps that could be part of a foreword for Nix the Tricks?)

      • I added your suggestion of a foreword to the editors planning document- thanks! In the meantime you could ask your coworkers if they think anything is missing or have ideas for the project and how it fits into your school. Or you could join the editors and write the foreword so it would be ready now!

      • Hmm, I’ll try to introduce it to my colleagues and see how it goes over. If I’m successful, I’ll gladly write a foreword on how to do it (or not to if it is unsuccessful!).

  3. You’re right about a number of things here (In MY opinion, at least)
    1. Decimals make things harder – fractions SHOULD make them seem easier but as this whole post attests, they do not
    2. You’re on to something about the whole school year being a time for forgetting. It’s not just the summer where ideas lay fallow, it is during the busy school year when we don’t mention some idea once we have ‘mastered’ that idea

    I once taught at a small enough school that the physics teacher (the only one!) was down the hall from me – and I was the only Precalc teacher. On any number of occasions when his students told him that they did not know how to solve some equation, he’d say “Do I need to go get Mr Dardy and have him remind you?” At that point, most kids would reluctantly remember. I think that this is just an aspect of human nature. I think that little reminders get them back on track quickly as long as we are using similar little reminders. This points out the importance of having some communication time between teachers in different – but related – disciplines. If we know how we talk about these things, then it is easier to structure a supportive conversation for our kids.

    • Yes, you reminded me of something that just happened yesterday! In Chemistry, a student saw something like:
      35.5 = [OH] (20.4)
      And even though I explained that [OH] was just one variable, the student asked “so to solve for [OH], do I subtract 20.4?” To which I replied “replace [OH] with x, and pretend you’re in math class”; “oh, so I should divide!”

      Why does such a simple little switch make it clear to students? And why can’t they see that on their own? This happens so often in my science classes, and like your colleague, I find myself telling them “pretend you’re in math class”. Except that I’m that math teacher, too…

      • One thing that I witnessed that works REALLY well is to intentionally align the vocabulary we use. With you filling two roles, that should be easy, right? In general, the more careful we can be to use a common vocabulary, the more likely our students will be able to draw connections. They have been so drilled into little cubby holes for their knowledge that the idea of drawing connections does not seem like a natural part of their job. As with most shortcomings in education, we all share the blame. I struggle even with simple things like radian preference in calculus and degree preference in physics. Similarly, we struggle with unit preferences for measurement. The more we seem to be in line with each other as educators, the more possible it is for students to see their daily task as a manageable and meaningful one.

  4. Pingback: Math Teachers at Play #62 | Let's Play Math!

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