Today I was reflecting on my past life experiences and my interactions with people at different stages of life among varied communities; I noticed that every activity is governed by some salient rules that are non-negotiable. These largely depend on the belief systems and underlying ideologies of such communities. These rules fashion out the social patterns and cultural practices of the community. They act as rating scales for what is acceptable or not acceptable; Shabtay and Heyd-Metzuyanim (2019) refer to these as figured identities. I have attempted to view this in the humanistic approaches to mathematics learning lens to center my mathematics classroom in a community woven by social practices, cultural beliefs, and ideological perspectives. I concur with Yackel & Cobb (1996) and Yackel et al. (2001) that we cannot separate an individual's thinking and sense-making from their social experiences, culture, and ideology. It spells out individuals' identities. I would therefore imagine the diversity in identity students and teachers bring to mathematics classrooms. As a teacher, one should account for the various figured identities presented in their classes. The teacher should therefore be well equipped with pedagogical content knowledge, content knowledge, and discourse pedagogy knowledge (Shulman, 1986) to position them as agents of facilitating math thinking and sense-making.
My challenge is to establish how students' and teachers' figured identities impact classroom discourse. I trail the humanists, social constructivists, symbolic interactionists, and ethnomethodologists to fetch, frame, and define a reflective math classroom discourse. To quantify the effects of figured identities on classroom discourse, I would explore teachers' in-moment moves, professional noticing, valuing student strategies, and organizing and orchestrating classroom discourse. I would also evaluate differences in these traits between classes facilitated by deliberately in-service trained and non-trained teachers as they try to overcome the effects of geospatial factors in orchestrating classroom discourse.
How far any player in this field goes would be determined by the social engagement rules, community beliefs, culture, and ideologies besides the geographical landscape.