Park City Mathematics Institute High School Teacher Program Helping Students Understand Proof - James Stallworth

To help students understand proof, I have used two videos to allow students to become detectives. The students understand that as the detective, they have to find the evidence and explain why it is important. The first movie that I show is "Laura" (1944) starring Gene Tierney (NR). This is a classic film noir. The movie opens with the detective at the scene of a murder of a beautiful model, who was shot in the face with a shotgun. He is looking for evidence that will help to discover who has killed her. As the movie progresses he finds out that Laura is actually alive. So now he has a new question to answer, "Who was the woman killed, and why was she wearing Laura's robe?" At the point where the Laura is revealed, I stop the video and point out to the students that just because the person has changed, the evidence has not. The students evaluate any notes that they had taken up to this point and then resume watching the movie. I stop the movie before the end, and allow the students to hypothesis who they think killed her and why. We finish the movie and discuss the arguments. Once we know everything that has happened, as a class we evaluate the argument and place it in two-column form.

Once we have finished this activity the students are starting to have a more positive experience with proof. But I then allow the students to reach a bit farther. I present the next film with the same information. The students will know the expectations from the first time, but there is a twist. This time the movie is "Clue" (1985) starring Tim Curry (PG). This is a slapstick comedy, but holds the same premise as "Laura." The twist is that the movie has three endings. So the students can watch the movie, collect the evidence, write up a proof, have a different answer from their neighbor, and still be correct. This shows that they students can find evidence but use it differently depending on what they want to prove.

Teachers, who are strapped for time or unable to show movies in class, can allow their students to participate in a similar activity using some of the Encyclopedia Brown stories or Two-minute mysteries by Donald Sobol. The books should be below the reading level of the students, but it will allow the students to concentrate on the logic and the mystery involved.

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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
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