Right before I graduated from University of Illinois at Urbana Champaign, I was required to write a Teaching Philosophy. This was what I wrote in Spring of 2013: College Teaching Philosophy in 2013

Reflecting on whether much has changed on my teaching philosophy, I recognize there are foundational beliefs that I feel very strongly about. When I stated “I aspire to create a community of active learners,” I truly meant that. I do not believe that students can learn meaningfully through merely taking notes and listening to a teacher lecture for an extended period of time. I find myself very lucky to be in a supportive school district that coincides with a lot of my beliefs in teaching. We use the Connected Mathematics Program (CMP3) which allows students to explore and to think about mathematics deeply through a Launch, Explore, Summary model. Furthermore, I get to teach students for 80 minutes everyday so that they have time to explore and process new mathematical ideas.

**Then**: From my education, I experienced a lot of direct instruction. I remember going home with 20 practice problems to complete every night; skill and drill was the approach. I recall memorizing the Pythagorean Theorem and the Quadratic formula in 8th grade without really understanding what those equations meant. Math was a lot of rote memorization for me as a child, and I sadly, I was good at memorizing. It was not until I was a college student majoring in mathematics when I started making more connections and thought about mathematics more deeply. Struggling through Abstract Algebra and Abstract Linear Algebra and writing proofs, I began to making deeper connections in foundational mathematics at the secondary level. I made a vow to myself that once I understood the concepts that one day when I teach it to my students, I will not ask them to memorize but to help them understand WHY the mathematical concept works.

**Now**: As we are wrapping up our unit on finding the shortest distances, students had the opportunity to explore how to find the exact distances and formulated the Pythagorean Theorem through their investigations. I did not start the unit telling them to memorize a^2+b^2=c^2 and it is incredible to see how deeply students understand. Below are some student activities that helped them explore the Pythagorean Theorem.