## Imagine IT Phase 2: The Big Idea

I am a high school math teacher at Lindblom High School; I will be starting my 6th year of teaching and my 5th year at Lindblom. This year, I believe I will be teaching Geometry, AP Calculus, and KAM: Advanced Math. I have not yet taught Calculus, and the KAM: Advanced Math is a class that I am developing from scratch. I have a strong undergraduate math background, and I hope to use that to develop my class for advanced high school students.

The ultimate goal for this project will mirror my development of the KAM class. I have broad freedom to create this class, and I do not feel constrained by a “covering the standards” mindset. I want to prepare my students to be active creators of mathematics, not simply consumers of arithmetic. I want my students to realize that mathematics is organic: it is being created every day and they can contribute to that. I want my students to create mathematics together, to work against the stereotype of the solitary mathematician and bounce hunches off of each other.

The students in the KAM class are seniors who have already completed (or are concurrently taking) AP Calculus. In terms of content, I see this class as serving a bridge between high school math and rigorous, proof-based undergraduate level math classes. In terms of content, students that leave this class should be ready to succeed in the freshman-level math major classes at whatever college they go to in the country. In several ways, this class will be inspired by my own mathematical journey, since I did have the good fortune to take advanced math classes before college. I will start the proof journey with number theory, since I believe it has easy access since you can go into deep proofs with only a foundation of arithmetic. Then, we shall give Euclid’s geometry a thorough look, starting with his axioms, building up the foundation of traditional geometry. Perhaps if there is time we can look at what happens when we take out the parallel posulate! Finally, I thought I would finish with some graph theory. There is a rich connection here with 3-d figures as well as social networks.

I seek to create a class culture that will be very student-centered. I want students to play and explore with the mathematics; however, they must be provided a strong foundation so they can effectively write and express themselves mathematically. The performances of understanding will be as close as they possibly can to actual performances of mathematics. Students will write up proofs, reference previous problems they have solved and present their proofs to their peers up on the board. They will have a lot of flexibility in terms of solving problems since I will give them more problems that they can solve, but they will be expected to assemble a certain minimum of proofs in their portfolio. In addition, it would be fantastic if students can create videos of some of the mathematics they create. Students will also be given the opportunity to work closely with a partner so they can give and receive personalized feedback on their work from a neutral perspective.

In conclusion, I hope to teach the content of undergrad mathematics major classes in a lower stress high school environment. I stress that this class in unique on the South Side of Chicago. I hope to incorporate technology by having students create sharable videos about the mathematics. Maybe these videos can even be shown to underclassmen! I plan to expose my students to many puzzles and I will provide examples of proofs and answer clarifying questions, but my pedagogical approach will be less direct. Ideally, the only complete proofs that will be shown in the classroom will be done by my students, and they can continue to build off of each other’s knowledge.

The ultimate goal for this project will mirror my development of the KAM class. I have broad freedom to create this class, and I do not feel constrained by a “covering the standards” mindset. I want to prepare my students to be active creators of mathematics, not simply consumers of arithmetic. I want my students to realize that mathematics is organic: it is being created every day and they can contribute to that. I want my students to create mathematics together, to work against the stereotype of the solitary mathematician and bounce hunches off of each other.

The students in the KAM class are seniors who have already completed (or are concurrently taking) AP Calculus. In terms of content, I see this class as serving a bridge between high school math and rigorous, proof-based undergraduate level math classes. In terms of content, students that leave this class should be ready to succeed in the freshman-level math major classes at whatever college they go to in the country. In several ways, this class will be inspired by my own mathematical journey, since I did have the good fortune to take advanced math classes before college. I will start the proof journey with number theory, since I believe it has easy access since you can go into deep proofs with only a foundation of arithmetic. Then, we shall give Euclid’s geometry a thorough look, starting with his axioms, building up the foundation of traditional geometry. Perhaps if there is time we can look at what happens when we take out the parallel posulate! Finally, I thought I would finish with some graph theory. There is a rich connection here with 3-d figures as well as social networks.

I seek to create a class culture that will be very student-centered. I want students to play and explore with the mathematics; however, they must be provided a strong foundation so they can effectively write and express themselves mathematically. The performances of understanding will be as close as they possibly can to actual performances of mathematics. Students will write up proofs, reference previous problems they have solved and present their proofs to their peers up on the board. They will have a lot of flexibility in terms of solving problems since I will give them more problems that they can solve, but they will be expected to assemble a certain minimum of proofs in their portfolio. In addition, it would be fantastic if students can create videos of some of the mathematics they create. Students will also be given the opportunity to work closely with a partner so they can give and receive personalized feedback on their work from a neutral perspective.

In conclusion, I hope to teach the content of undergrad mathematics major classes in a lower stress high school environment. I stress that this class in unique on the South Side of Chicago. I hope to incorporate technology by having students create sharable videos about the mathematics. Maybe these videos can even be shown to underclassmen! I plan to expose my students to many puzzles and I will provide examples of proofs and answer clarifying questions, but my pedagogical approach will be less direct. Ideally, the only complete proofs that will be shown in the classroom will be done by my students, and they can continue to build off of each other’s knowledge.

## Links

My inspiration for doing a more constructive style of math comes from a class I took at the University of Chicago: Inquiry Based Learning Calculus . We didn't cover as much material as a traditional calculus class, but I remember it the most; I think it provided a much more rich understanding than other traditional lecture classes that I had. My class will not have the same exact curriculum, but it will have the same style: I give students a framework, and channeling my inner sketch improv facilitator, I will see what they are able to create.