One traditional way of assessment in a College class is in the form of mid-term or final exams. How does this fit in with an Inquiry-Based approach to learning mathematics? Our group has played with different approaches:
No exams :)
Using a Learning Contract, we convince our students to work really hard on all other assignments. In return they don't have to pass exams. To make sure that the semester doesn't just end a week early, we make sure that there is a significant amount of work due in the exam week.
Different Final Exams
- New material exam: We give the students a problem that doesn't rely on any of the covered material. The purpose is for us to assess whether they can independently do mathematics.
- Notebook exam: This exam builds on the material covered during the semester, but students are allowed to use their notebooks. This way students don't have to memorize material but have an incentive to look through, review, and organize all the materials they created throughout the semester. We usually ask one question they have answered before and one new question.
- Pyramid Exam: The students can first work in groups and then independently on the problems. This helps reduce anxiety and assesses how well the students work in groups.
Sample Final Exams
To give you a sense of what a final exam might look like, here are two examples. In both cases, the students had worked on other combinatorial explorations in class, but the particular question and context were new to them. The focus is on their skills in exploring patterns, collecting data, making conjectures, and explaining their reasoning.