There is a quote by Paul Halmos that I admire for both its truthfulness and simplicity: "The only way to learn mathematics is to do mathematics." It corroborates my stance that math is an action verb and emphasizes my belief that worthwhile learning is rooted in doing. As an instructor, my goal is to facilitate an environment where I am only responsible for part of the 'doing' of mathematics that is happening at any given time. The aim of my teaching is not merely to impart information to students, but to aid in the establishing of new schemata that allow them to learn independently, think critically about the course content, and to sharpen problem solving skills both inside and beyond the classroom.
I believe any instructional method must have student learning as its primary goal. Too often, instructors focus the bulk of their energy on imparting knowledge, and less attention is paid on whether that transmittance leads to new knowledge in students. Of course once objectives are established, the most important component, undoubtedly, is the how. Personally, I love to teach with games, with colorful lectures featuring Hagoromo chalk (you haven't lived until you've tried it), instructional videos, and inquiry based learning activities.
I believe that the foundation of any approach to diversity should be rooted in intersectionality. Rather than subscribing to the rigid classifications that dominate how we contextualize students, black or white, male or female, rich or poor, etc, it is more important to focus on how the intersection of multiple identities, and the priviliges and marginalizations associated with each, play a vital role in any student's experience in academia before they ever set a foot inside our classrooms. We must create learning environments influenced by such considerations so that all students have the opportunity to thrive.
As indicated in the statement above, I approach diversity through an intersectional lense. I believe this is the best way that I can approach the issue of all learners having access to success in my classroom. It can be tempting to take a stance on diversity that states all learners be treated equally regardless of their differences, but I implore that these differences must be considered, both humanistically and pedagogically, so that all students are treated equitably. For this to happen, a critical look must be taken at how the lived experiences of intersectional groups shape their attitudes and exposure to mathematics, and how course design rooted in accessibility can help sure the success of diverse learners.