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Student Assumptions

September 26, 2013

My mentor here at HCC gives students a homework format handout in his classes. Actually, it isn’t really a format but more a list of steps that he wants students to follow when solving problems. Things like drawing a diagram, checking units, etc. I’ve never required students to follow a specific format before but I was intrigued so I decided to use the idea in my classes this semester.

Each week I assign a handful a problems for students to work on as homework. They turn these problems in and I grade them not based on correctness but based on the extent to which they follow the format (to the extent that each step is applicable to a given problem). I frame the format requirement by telling students that 1) these are good habits to develop that will help them on exams and in future classes and 2) following the format helps ensure that students are showing me enough of their thought process that I can give them useful feedback. So far it seems to be working pretty well.

One of the steps that I put in my homework format is for students to explicitly state any assumptions they make while solving a problem. I was mainly thinking about “Fermi problems” when I added this requirement and even added a note in the handout telling students that not every problem will involve assumptions. (Well, at least not assumptions that the students are making themselves.) However, I’m finding that students list some interesting things under assumptions for various problems. I’m noticing three general categories of “assumptions”:

  1. True assumptions – Things like assuming a reasonable value for temperature or assuming that the system is isolated from the environment.
  2. Facts – Things like 1 L = 0.001 m^3 or v = d/t
  3. Invalid assumptions – Things like assuming there is 1 mole of gas when in fact the students needs to solve for the number of moles.

This has given me some interesting things to think about. Looking at the first two categories of “assumptions” makes me think that I need to do a better job of helping students to understand the process of modeling and the role of assumptions. At the moment, I can’t really tell if some students think facts and assumptions are the same thing or if they are simply listing facts because they think they have to list something as an assumption to get full credit. “Assumptions” in the 3rd category have been very helpful in allowing me to understand the students’ thinking. I don’t have to wonder how a student came up with 1 mole because the student tells me it is an assumption.

If I didn’t use the homework format, then some students in the 3rd category would likely have found how to correctly solve for the quantity they need. If I didn’t present making assumptions as a possible step in constructing a solution then it likely wouldn’t occur to some students to ever make an assumption. However, I want students to think about assumptions and know that making an assumption might be a necessary step in solving a given problem. Once students leave my class they are going to find themselves working on problems that involve both assumptions and deductions. It seems that the homework format is helping students to practice this skill and opening up opportunities for discussion that wouldn’t otherwise happen.

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