This has been my stated teaching philosophy for some time now. I am working to expand on it in my own words, adding contrubutions from new perspectives I am adopting as a result of doctoral study.

Accomplished mathematics teachers […] confront issues of diversity proactively to promote academic and social equity. They actively and positively challenge sexist, racist, and other biased behaviors and stereotypical perspectives, including those directed toward various ethnic groups, regardless of the source. They are keenly aware of the historical perspectives and biases that have created social and academic barriers for students, and they work to remove these obstacles. They maintain high expectations for all learners regardless of gender, race, socioeconomic class, [sexuality], or previous experience. They ensure that their students receive equal opportunities to learn and advance in mathematics, and they act to dispel the notion that not all students are capable of learning mathematics. They consistently communicate their respect for all students and their belief that all students can learn. By example and guidance, they help students learn to treat one another as valued members of the learning community.

National Board for Professional Teaching Standards’ Statement on Equity, Diversity, and Fairness

The teacher and student characteristics below are taken from Wikipedia’s entry on Inquiry Education. I think they are generally okay, but could be expounded on.

Student characteristics

• Self-confidence in their learning ability
• Pleasure in problem solving
• A keen sense of relevance
• Reliance on their own judgment over other people’s or society’s
• No fear of being wrong
• No haste in answering
• Flexibility in point of view
• Respect for facts, and the ability to distinguish between fact and opinion
• No need for final answers to all questions, and comfort in not knowing an answer to difficult questions rather than settling for a simplistic answer

Teacher characteristics

• They avoid telling students what they “ought to know”.
• They talk to students mostly by questioning, and especially by asking divergent questions.
• They do not accept short, simple answers to questions.
• They encourage students to interact directly with one another, and avoid judging what is said in student interactions.
• They do not summarize students’ discussion.
• They do not plan the exact direction of their lessons in advance, and allow it to develop in response to students’ interests.
• Their lessons pose problems to students.
• They gauge their success by change in students’ inquiry behaviors (with the above characteristics of “good learners” as a goal).