Observations from the calculus classes

It’s been a few days since the last article, because I’m already digging out from grading, prep work, committee stuff, engineering stuff… But I just finished grading the first semi-major homework set from the calculus classes, and I’m seeing some things (possibly for the umpteenth time):

(1) It’s pretty clear that most of the students in the class have never been asked or expected to justify their reasoning and have never been held accountable for anything but the parity (right/wrong) of their answers. I insist that students give thorough, detailed explanations of their solutions on everything, or else they suffer grave grade deductions. They are giving a good-faith effort to do so, most of them, but often it’s like reading the first few paragraphs written by somebody who just learned English — really unpolished, pretty obvious that this kind of thing is brand new to them. What exactly goes on in those high school math classes, anyway?

(2) Maybe the approach I have been taking to the first 2–2.5 weeks of a calculus course — namely, to go through a meticulous and thorough review of precalculus concepts with the big ideas of calculus (slopes, rates of change) woven in — needs to be changed. There are some students who are really not in the right place, and should be either in our precalculus course or else in a different major that doesn’t require calculus. The slow and lengthy precalculus review might be providing nothing more than a false sense of security; the students who are going to do OK in the course could all go at twice the speed, and for the students who are not going to be OK it doesn’t matter how slow I go. Perhaps I should just plan on getting the precalculus stuff done in a week and go as fast as I need to in order to accomplish that. That would give the at-risk students a realistic sense of what the course is going to be like, and not bore the others.

(3) Just two weeks into the semester and already I have four potential academic dishonesty cases on my hands, all from calculus and all from a 5-point problem on a homework set. That’s smal potatoes, but I’ve made a commitment to seek out and destroy academic dishonesty down to the roots this semester, so if these students broke the rules then they’re going to get hammered grade-wise — 0 on the assignment, the letter grade for the course dropped one letter, and potential dismissal if there’s a second violation — and all for 5 measley points that they could very well just have done without (maximum points for the course = 700). That’s just stupid.

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Filed under Calculus, Education, High school, Teaching

8 responses to “Observations from the calculus classes

  1. Eric

    Have any students chosen to embed within their assignment a poorly written criticism of the need for homework in a college level math course? Just curious.

  2. Strangely enough, no. That’s only happened once in my entire career. 🙂

  3. I think that students don’t understand that academic dishonesty is dishonesty. But I could be naive. When I give 0s on my students’ papers because of plagiarism, they are always shocked. “I didn’t meant to do anything wrong.” But even when I explain beforehand what is academic dishonesty, they still don’t understand.

  4. Just another liberal professor

    Holy crap…you take *two weeks* for a pre-calc review in Calc I? I usually take
    2 days for a pre-calc review (well, really about one and a half days…the last
    half of the second day is taken up by a diagnostic precalculus quiz).

  5. JALP: Here’s the roadmap for the first 12 days of class:

    Day 1: Syllabus/intro to the course stuff
    Day 2: Introduce the main ideas and questions of calculus
    Day 3: Functions — basic notation and terminology; functions as graphs and tables of data
    Day 4: Functions as formulas and algebraic manipulation
    Day 5: Problem-solving techniques, and building functions from information in a word problem
    Day 6: Tutorial on computer algebra system software
    Day 7: Linear, power, and polynomial functions plus intro to Excel
    Day 8: Function composition; rules for translation and stretching/shifting functions
    Day 9: Exponential functions
    Day 10: Inverse functions and logarithms
    Day 11: More logarithms
    Day 12: Comprehensive practice session and open question time.

    Anything involving algebra leads to near disaster most of the time, hence the focus on reviewing and practicing it. A good portion of my students tell me that they were actually not taught logarithms in high school, and when we follow up we find that it’s because their teachers actually didn’t understand logarithms.

    Still, as I said, I am wondering if being this thorough is really changing the outcomes of the students.

  6. We’re harsh. We have 0 review of pre-calc. And we start Calc 1 with parametric equations.

    With the exception of “projects” in Discrete Math, no one graded any of my math homework from 8th grade to 12th grade. Odds are that things aren’t much different in many of your students’ backgrounds.

  7. Dan

    As a high school teacher, it’s often hard to know exactly what to demand of students. The standards and the high-stakes tests focus on procedures and techniques, but there is next to no explanation/justification/reasoning/proof required. You’re right – students don’t know how to justify their work at all. I have been trying to teach students how to apply the basic properties (associative, distributive, commutative, identity, inverse) to justify their steps in simplifying a simple algebraic expression, and most of them have a lot of difficulty with this. I’ve also been trying more error analysis types of problems, where students must identify where an error is, explain what the error was, and correct it.

    If you have the time, it would be great if you could post something on what you expect a student prepared to succeed in a freshman calculus course to be able to do day one. Maybe an example problem that you assign, along with the type of solution/explanation you expect.
    I would like to think about how to work it into our algebra / pre-calc curriculum. This is something that would need to be scaffolded out over the years to really be effective.

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