I typically write my own homework packets, rather than just selecting problems out of the book. I have several reasons for this:

- Students are forced to use the space that I provide. Since there is a bigger problem students not using enough white space, I can make most students’ assignments neater by forcing enough white space.
- Students cannot simply look up the solution in the solution manual; they need to figure it out or speak with someone about it (note: I still have the flexibility to assign these problems if I want them to be able to see the solutions, and I usually have some problems of this sort).
- I am not limited to the problems of a particular textbook: I can borrow/steal problems from other sources, and I can write my own.

Today I am going to focus on writing homework problems. Many of my problems are of the “Prove or disprove” variety, as opposed to the “Prove” variety. I think that this is important, since it forces the student to decide if the proposition is true. In a larger context, this forces students to think critically, since they are not told to blindly believe that the proposition is true. This is a habit I hope students build in my classes—to evaluate whether a statement is believable.

I have found a challenge in this, though: it is somewhat difficult for me to create “Prove or disprove” statements that the students are supposed to disprove. I create some based on common student misconceptions. For example, I would include a “Prove or disprove: (a+b)^{2}=a^{2}+b^{2} for all real numbers a and b” if I were teaching algebra. However, it is generally difficult to create statements that “look” true, but are actually false. With luck, I will be proficient at this by the end of the semester.

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Tags: abstract algebra, homework, math 331

This entry was posted on February 3, 2010 at 3:24 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed.
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February 5, 2010 at 10:33 pm |

Good luck! I’ll probably need to draw on your expertise on these “prove or disprove” problems when I teach logic next spring. Let me know if you learn any tricks as you practice this term.

(P.S. Nice to see you this morning! Thanks for listening to my ranting!)

February 10, 2010 at 8:26 pm |

Thanks, although I hope that you are not going to rely on me. I find that I tend to learn these things rather slowly.

I am excited that you get to teach logic!