In describing the core of my teaching philosophy and motivators behind excellence in teaching, I borrow these thoughts from Federico Ardila:
Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
Everyone can have joyful, meaningful, and empowering mathematical experiences.
Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
Every student deserves to be treated with dignity and respect.
In every decision I make in regards to my teaching, classroom materials, and course content, I always keep my students in mind. These four thoughts are behind the way I interact with and encourage my students. In addition, I take effort to convey to my students the “Rights of the learner” from C. Kalinec-Craig:
You Have the Right to Be Confused
You Have the Right to Claim a Mistake
You Have the Right to Speak, Listen and be Heard (e.g., Engage in Conversations, Ask Questions, Share Ideas, and Listen to the Thinking of Others)
You Have the Right to Write, Do, and Represent Only What Makes Sense to You
I might replace "I expect you" with "you have the right" in these rights, or maybe include both as "you have the right and I will expect you", in order to make clear that being confused and making mistakes is not only viewed as not something bad (having the right) but also something that should expected to happen.
To promote equity in the mathematics classroom, I allow my students to take more explicit ownership of their learning, both in writing and in oral communication. I aim to create a course climate that is welcoming, encouraging, and serves everyone. I believe the only way to learn mathematics is to do mathematics. As long as a student puts in the effort, I am confident they will be rewarded with growth, and I want to help them along that path.
I would like to point out that very little of my teaching methods, techniques, materials, etc., happen in a vacuum. I would not be able to achieve my teaching goals without the valuable conversations and exchanging of ideas I have had with my colleagues. In return, I always try to support and share information, advice, and ideas whenever possible.