Inspired by Andy Rundquist, I did oral exams for the first time in my mathematics course for elementary education majors.
The format was a 20 minute one-on-one private interview in my office. Students signed up for appointments by using the Google Calendar Appointments feature. Students were told the questions ahead of time (“explain why you know that the standard algorithm for addition/subtraction/multiplication/division of integers is guaranteed to give you the correct answer to an addition/subtraction/multiplication/division question;” I did not ask the addition question). I gave students a worked-out multiplication problem (using the standard algorithm), but did not work out the solution to the subtraction and division problem.
Here are four things I learned:
- One-on-one oral exams take a lot of time. I have 32 students, which means that I had almost 11 hours of meetings over the course of three days. I cancelled two days of class to offset this, but it consumed my week (which was only a three-day week due to Easter).
- Google’s appoints feature can be buggy. A significant number of students viewed my appointment slot times as shifted by 12 hours, so some students signed up for meetings at 1 am. I am not sure why this happened, although students who used Firefox did not seem to have this problem (Safari and Explorer caused problems for some students, though).
- I learned of some incorrect reasoning on some of the algorithms that I would not have learned if I had just seen written work. In a problem like 203-87, there is a complex “borrowing” that needs to happen. Some students had written work that made sense, but they said (and meant) that you can borrow from the “0” (it just turns into a “9” after you borrow).
- I learned that my students have a really pretty good grasp of the details of why these algorithms work, but they cannot put the pieces together. I think that I have not done a good job of conveying the purpose of asking questions like “why does long division work?” I think that some students do not understand that the long division algorithm can be verified; they essentially still believe that division is defined to be “the long division algorithm” (in spite of the fact that they will give you a correct definition of division if you ask them).
In short, I found them extremely valuable (although tiring). Most students seemed to prefer them to written assessments, too (at least, the ones who spoke up when I asked the entire class about it). It definitely has influence how I will be teaching the next quarter of the semester: I will be focusing on the big picture.