Student Work Samples

"A mathematician is a machine for turning coffee into theorems."--Paul Erdös

Quiz #3

Homework quizzes are given to students who elect not to turn in the homework (or who turn in patently incomplete homework, the criterion being "do what you think will convince me that you tried"). As negotiated with students earlier in the year as a means of increasing homework return rates, it replaces the homework score and provides (in theory) a way for students who "get" the material to show their knowledge.

Thus, these quizzes are graded the same way as homework is, out of 10 points. The system is based more on completion than correctness, since I consider homework an arena for students to practice newly-gained knowledge or review rusty old knowledge, and earlier in the year I was concerned that students would often not attempt a problem at all if they thought they would get a wrong answer anyway. 10/10 is a "perfect paper." 9/10 is a paper in which everything has been attempted, if not correctly, but the basic idea behind the questions is addressed. After that the score is based on the proportion of work that has been attempted, including the amount of work shown indicating an understanding of what the problem was asking for. A paper with responses to everything but no work shown, if applicable, gets 8/10 so students get the benefit of the doubt. If they copied without understanding and I didn't catch them, it'll show up elsewhere in any case.

Scoring is not precise, and I would actually prefer to return homework (for example) solely with comments, a grade for completion, and a requirement that it be revised and handed in later. I don't, however, know how time-consuming that would be, and as my master teacher has established some framework for grading I have stuck with it for consistency's sake.

Student #1's work (GIF image) on this quiz shows confusion between Cartesian-to-polar (which was asked) and polar-to-Cartesian (which he attempted).

Student #2's work (GIF image) on this quiz shows that she has figured out how to plot the point and use the formulas involved. I gave her a perfect score as I was grading too hastily and didn't notice that she had not included an estimate of the coordinate; I would probably take off a point for that. Also, she did not write the answers in coordinate form, but she has the idea.

Cartesian-to-Polar Warmup

This was a brief conversion exercise intended to get students used to handling angles when the points are in quadrant II or III. I graded it out of 5 points, mainly on completion. As I had been walking around the class to see what students were actually doing and they checked their answers with each other, I gave them the benefit of the doubt if they didn't show all their work.

Student #1's work (GIF image) shows estimates, including the auxiliary lines used to plot the Cartesian points, and correct answers. Though no work is shown, he copied the relevant formulae from the whiteboard for reference.

Student #2's work (GIF image) shows near-complete work and solutions, though they are somewhat disorganized (it is not immediately evident how she derived the final angle values). I'm not sure whether her notation for arctangent is simply a notation glitch or whether it reflects a deeper uncertainty about arctangent as a function. However, most of the class has a shaky understanding of functions and inverses, so this would not be unusual either way.

Distance Warmups

I gave this warmup on May 16 to give students another opportunity to practice working with distances. Like most warmups, it was graded out of 5 points on completion and some demonstration of relevant reasoning.

Student #1, like most of the class, forgot to hand this in.

Student #2's work is complete, shows all work, and indicates to me that she has "got it" either from listening to and participating in discussions, or on her own. Later, she was one of two students who demonstrated understanding of "angular distance" on HOMEWORK #5.

Letter to Zap #1

Students wrote LETTER TO ZAP #1 in pairs to explain a Cartesian-to-polar or polar-to-Cartesian coordinate conversion. It was graded based on a group grade out of 10 points for the accuracy of the letter and their assessment of another student's work, and an individual grade of 5 points based on their grading feedback.

Student #1's portion of the letter attempts to explain polar coordinates. It's not immediately clear what "pay attention to the zero" signifies in this context; they were to "convert" the origin but offered no computations or explanation for why computation would be redundant. The pair ended up receiving a 7/10 because they missed the conversion, a comment on the usefulness of conversions, and an example of a related real-life situation. On the other hand, Student #1 and his partner are able to carry out conversions with some reminders of formulae (which are not the focus anyway) in previous assignments, and the main point of writing the letter was to practice communicating math. In that sense, Student #1 showed a measure of success.

Student #1's feedback (JPEG scan) on the grade report (JPEG scan) is straightforward and shows acknowledgement that "we didn't spend a whole lot of time." His answers generally show that he read the feedback for its major features. He scored a 5/5.

Student #2's written contribution (JPEG scan) to the letter is evident in the middle section detailing computations. (Due to an odd number of students in the class, she was in a group of three.) She was carrying out correct computations, but her "grammatical" confusion in writing out the steps of solving the equation were foreshadowed in her earlier work. Notice particularly the notational confusion over x and y and solving for the variable. In other words, she contributed her knowledge of the process, but continued to have difficulty communicating it using standard mathematical symbolism.

"What Did I Learn about Grading?"

After GRADING LETTER TO ZAP #1, I asked students to each write one of their thoughts on "What did I learn about grading?" on a large sheet of butcher paper. Not every student got around to doing this, but the class' thoughts follow, in no particular order. Student #1 wrote "Show No Mercy!" which is consistent with his offbeat, humorous approach to life. Student #2 chose not to answer, or didn't have the time to do so.

• I learned that it is hard to grade papers.
  
• Don't grade friends.
  
• I learned it's easier than doing the work!
  
• I learned that you have to be picky but at the same time fair.
  
• I learned that grading isn't as easy as it seems. And you have to be fair.
  
• If was kind of hard because you have to look for different things to grade on.
  
• It's fun, [sic] only when it's fair to both sides/groups. And it's easier than doing the work!
  
• It is easier than doing work but you fill [sic] bad for taking points.
  
• Show No Mercy!
  
• Grading is easy if you know how to follow directions!
  
• It isn't as easy as it looks because what you think is fair someone else might not.
  
• There is a lot to think about.
  
• That it's not easy to do. You have to be fair.
  
• Its [sic] not easy to grade other people's work!
  
• Just Be Honest! 100% TRUTH.
  
• You need to explain and have [a] good reason for giving out that grade.
  
• Grading is a lot more difficult than I expected. You have to make accurate and excellent decisions on what you grade.
  

Copyright © 2002 Yoon Ha Lee <requiescat@cityofveils.com>
Last updated on 8 June 2002