Developing an analytical tool for radical socially-just teacher educator action research about language diverse mathematics classrooms

Figures & data

Table 1. The LATACME framework (from Lange & Meaney, 2019, p. 2).

	Responsibilities
Roles	Facilitating the exploring and learning of mathematics	Facilitating the exploring and learning about the world through mathematics
Teacher	Knowing how mathematical topics and mathematical argumentation can be developed where languages are considered a resource.	Knowing how to develop connections between critical mathematics education and argumentation.
Learner	Learning from multilingual students about their understanding of mathematical topics and argumentation.	Learning about critical mathematics education issues of interest and importance to multilingual students and their communities.
Advocate	Knowing how to provide input about mathematics education, including argumentation, to (multilingual) parents, school communities and government.	Knowing how to advocate that students need to use mathematical arguments in order to explore the world.

Figure 1. The integration of the frameworks into the analytical tool.

Figure 2. Flowchart for responsiveness – short version (Pierson, 2008, p. 69).

Figure 3. Flowchart for intellectual work – short version (Pierson, 2008, p. 81).

Table 2. Adapted description and example of responsiveness high-I level.

Pierson’s (2008) description	Our adapted description	Transcript
Follow-up that is responsive to S(tudent) idea, question, or perceived misconception. The teacher’s thinking is on display, but in response to the student’s idea. This includes answering student questions and responding to student misunderstandings. T can expand on S comment but takes over S’s idea and puts his/her thinking as focus (p. 77)	Genuine attempt to respond to PTs’ ideas or questions – clarifying directions/ instructions, where the TE’s thinking is on display.	Extract 1 PT: How would you go about it if you’re the only one speaking your language? Would that be possible? TE: No, if you’ve got someone in your class, where there’s no one else to talk about it, then that is where it’s absolutely essential that you have a language teacher, a mother tongue language teacher alongside. That’s where your role as a teacher advocate for the student has to come into play.

Table 3. Adapted and extended description and examples of high demand intellectual work.

Description	Examples	Transcript	LATACME framework
Request to evaluate what PTs experienced in the tasks they were asked to do, and to connect it to what they knew about themselves as a teacher or learner and to ask questions from that evaluation	(1) PTs are asked to reflect on their own language use in learning about mathematics education in English.	Extract 2 TE: And while you’re looking at it, think about how learning about mathematics education research in English. Does your first language mean that you have a problem doing that? Or do you think of it as a resource?	(1) Role: Learner Responsibility: Exploring and learning of mathematics
	(2) Questions about the teacher’s role of being an advocate for multilingual students.	Extract 3 TE: So, one of the interesting things with this video is that it says there’s a role for advocacy. There’s a role for parents to have discussions with teachers, but also for children in classes to say, “you are not giving me enough interesting work to do”. Now I wonder, just how well received a child would be if they told their teacher that their schooling was not appropriate?	(2) Role: Advocate Responsibility: Exploring and learning of mathematics

Figure 4. Adapted flowchart for responsiveness.

Figure 5. Adapted flowchart for intellectual work.

Lange, T., & Meaney, T. (2019). Discussing mathematics teacher education for language diversity. In J. Subramanian (Ed.), Proceedings of the tenth international mathematics education and society conference. MES10. https://www.mescommunity.info/proceedings/MES10.pdf

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Pierson, J. L. (2008). The relationship between patterns of classroom discourse and mathematics learning [Doctoral dissertation, University of Texas at Austin]. Faculty of the Graduate School. http://www.jstor.org/stable/teaceducquar.42.4.83

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