The following is a great summary of a culturally responsive mathematics teacher I found in the thesis by Emily Peterek, pp. 156-158, 2009:
Culturally responsive teaching in the context of mathematics: A ground theory approach
Culturally responsive mathematics teachers know their students
These teachers take time to get to know student cultures at all levels, and use this information in their instructional planning and in the course of teaching. Specifically, these educators understand the community culture (e.g. communication patterns, shared values) in addition to what is commonly referred to as ―kid culture‖ (e.g. how 5th graders think and feel, where they are emotionally and intellectually) and relevant pop culture (e.g. what types of music students listen to, who are the big names in entertainment). This information comes from the students themselves, teacher involvement in the community, and a vested interest in students‘ ways of living. Further, learning about students is not an overnight process; it takes years of personal involvement to build relationships that will allow a teacher to access this type of knowledge, particularly if he or she does not live in the neighborhood surrounding the school.
Culturally responsive mathematics teachers are supported by a particular belief system
Effective teachers believe that their students, no matter what statistics say, have the ability to be talented and gifted. Their job is to work to find ways in which students can express their talents while accessing mainstream knowledge. These beliefs are fundamental in providing effective non-verbal communication and building relationships; as teachers we must realize that we are constantly communicating with students even if we don‘t realize that we are doing so. If a teacher does not truly hold positive beliefs about her population of students, on the other hand, she will communicate these nonverbally and will struggle to build relationships. Students can see straight through words to what is underneath, and that is what is most important. Lastly, effective teachers are aware of what they believe and continuously reflect and act on those beliefs.
Culturally responsive mathematics teachers do not ask students to abandon their home culture
As simple as this might sound, it is fundamental to the success of underrepresented students. Many times, these students are asked to learn from traditional, individualistic, lecture-type instruction, and are deemed disabled if this type of instruction does not provide them with a connection to the material. Culturally responsive teachers are able to teach content, even mainstream content, without asking students to live, act, or learn differently than they would at home. This creates cultural congruity for students, and greatly increases their chances for success. Further, it allows for racial and cultural identity development in the course of teaching, and provides a safe context from which they can learn about societal pressures and misconceptions. Such an environment provides a solid foundation from which students can achieve academic success within their own cultural norms.
Constant reflection and revision is necessary for culturally responsive mathematics teaching
Children need to be challenged and engaged in mathematics. In refusing to change particular aspects of instruction, a teacher is not attending to the needs of her students. Reflection allows an educator to see what it is that needs revision while encouraging innovation and change. This reflection-revision process is cyclical and should happen at the macro (i.e. reflecting on entire lessons, units, or ways of teaching) and the micro (i.e. in the course of teaching on a moment to moment basis) levels.
Culturally responsive mathematics teachers work beyond the classroom
Specifically, these teachers provide resources to the community in proportion to their personal expectations. For example, if a teacher expects her students to receive help at home, she recognizes that parents might not be familiar with the material, and provides a class that will help them to help their children. If a teacher expects a student to have supplies, she provides them with the necessary materials so that each child has the same opportunity. This type of commitment is a hallmark of successful teaching, and stems from a teacher‘s belief system, knowledge of students, and relationships.