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Math 17: An Introduction to Exploration, Conjecture, and

Proof in Mathematics

Reflection on Instructional Change:

The focus of Math 17 is for students to in the process of doing mathematics by exploring enticing scenarios, games, or questions that allow them to play with ideas and generate conjectures based on their explorations. Using their experiences and data, students then construct convincing arguments for why their claims are valid. The instructor's role is to provide sufficient challenge and support while allowing students to own the mathematics. The course is highly interactive and driven by students' responses and questions, so the exact content of each class meeting varies among classes.

Students' reactions to synchronous online class meetings during the last half of Spring Semester, led me to adjust the pacing of the course, revise homework assignments, and adapt assessments. Based on activities and discussions in the STEM Sidecar, I adjusted the pacing of class meetings to allow for more time, the nature of assignments, the focus and weighting of quizzes. In the first few class meetings students spent more time in small groups (breakouts) discussing course expectations. Our initial investigation was one that did not require any hands-on materials or handouts. During class meetings students discussed their most recent findings and in several breakout groups. Providing specific discussion prompts and sufficient interaction time helped make the breakouts more comfortable and productive. The students appreciated the chance to talk with each other in a safer space than the whole class setting. As a result, many formed study groups and became more comfortable having their cameras on during whole class discussions.

I feel that the ways I try to promote a safe learning environment for all students helps promote equity in the course. Each synchronous class meeting is recorded so students have opportunities view a class they have missed, or want to view again, and can pause the recording to facilitate note-taking. However, the first few minutes of each class are not recorded. I open the meeting early so I can greet each student as they join, students can greet each other, and we can warm up with an informal conversation. The recording starts when we start our mathematical discussions. Similarly, we finish our mathematics before the end of class and stop the recording so students can say good-bye to each other. The first few homework assignments mainly focused on having students reflect on their learning processes. The assignments were graded on following the Homework Guidelines and thoughtful completion, which relieved anxiety about getting the "right answer" for the mathematical reasoning. The first two of our six quizzes also focused on students' reflections on their learning. To make quizzes less stressful, and remove incentive for cheating, each quiz is only worth ten points (the same as one homework assignment), and the lowest two scores are dropped.

ideas from groups Section 1

Ideas generated in small group discussions in Section 1

ideas from groups Section 2 Ideas generated in small group discussions in Section 2

Student work for HW #4

Student responses for HW #4 Student's Assignment #4

Grazing Goats Game at Home

Quiz #2 response 1

Quiz #2 response 2

Quiz #2 response 3

Quiz #2 response 4

Sample responses to the last question on Quiz #2

Post Side Car - Syllabus and Schedule

Pre Side Car - Syllabus and Schedule

Faculty Biography

photo of Elaine Kasimatis

I am a long-time member of the Department of Mathematics & Statistics with special interests in mathematical pedagogy and curriculum development, the mathematical preparation of teachers, and the on-going professional development of teachers. My mathematical interests center on questions in geometry dealing with the dissection of objects and the filling of space with copies of certain star bodies.

I love asking questions and believe that doing mathematics is a three-part process that involves
    playing (aka - exploring a situation or question to collect information or data),
    looking for patterns in the data (aka - making conjectures based on the data), and
    proving that the conjectures are true (aka - forming correct, complete and comprehensible explanations).

"I imagine good teaching as a circle of earnest people sitting down to ask each other meaningful questions.

I don’t see it as handing down answers."

Alice Walker (Meridian, 1976)

This work was supported by the National Science Foundation NSF Hispanic Serving Institution Award 1832335. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.