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=a2+b2 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.