Questions, Answers, and Mathematical Discourse

Technology has often been accused of just giving students answers without the students knowing why. In this talk, we examine problems in which this is a very good thing. Specifically, we discuss problems in which technology provides the answer very quickly. At that point, the initial conditions are changed-but the answer remains the same! As a result, the answer becomes less important than figuring out why the answer is not changing as conditions change. What will emerge from this pattern is that these problems require students to focus on proof and reasoning, and engage in mathematical discourse.