Supporting Preservice Mathematics Teachers’ Culturally Responsive Teaching: A Focus on Teaching for Social Justice
Abstract
:1. Introduction
“leverage mathematical learning by expanding children’s mathematical thinking, building bridges between previous knowledge and new knowledge, supporting bilingualism and academic language development, fostering connections with cultural funds of knowledge and experiences, and cultivating critical mathematical knowledge that enables students to analyze and address authentic problems” (p. 168).
How do PSTs implement social justice contexts into their lesson design using the CRMT tool?
2. Literature Review
2.1. Lesson Design
2.2. Teacher Experiences with Teaching Mathematics for Social Justice (TMSJ)
3. Theoretical Framework
3.1. CRMT
3.2. Critical Mathematics/Teaching for Social Justice
 build on the knowledge that students bring with them from outside of school, and
 broaden their understanding of how mathematics can be used to interpret their world and act to rectify social injustices.
3.3. The CRMT Tool
4. Methods
4.1. Participants and Program
4.1.1. Previous Semester Activities
4.1.2. Spring 2021 Semester
4.2. Adaptation of the CRMT Tool
Explicit Subcategories in the Social Justice Element
4.3. Data Collection Procedures
4.4. Analysis Methods
4.4.1. Analysis 1 and 2
4.4.2. Analysis 3
5. Results
5.1. Cumulative Results of the Social Justice Element
5.2. Subcategory Results: Sustained Meaningful Social Justice Context & Integration of Social Justice and Mathematics
5.2.1. Sustained Meaningful Social Justice Context
5.2.2. Integration of Social Justice and Mathematics
5.3. Subcategory Results: Mathematizing, Handling Controversial Topics, and Student Agency
5.3.1. Mathematizing
Juliet: The discussion will start with the mathematical calculations. The students will discuss the proportion of class sizes, student population, teachers, etc. Then the class could begin talking about other proportions they found when comparing the schools such as resources, test results, etc. Then as a class we will discuss where they had consistent data and where there was inconsistency between groups. Discuss if the data could be misleading. The discussion should also lead to why the students’ thought schools in the same district varied or did not vary and how schools outside the district looked different. The teacher should ask the students to think about other comparisons they could make that could explain the differences/commonalities between schools. Students who used to attend other schools should get to talk about past experiences and how their experience changed from school to school.
Heidi: We will begin working through a guided practice on IQR and MAD. These topics are just being introduced to them and I am more focused on how proficient they are at computing mean, median, mode, and range at this point. We will have more time to practice MAD and IQR. I want the students to understand what IQR and MAD means for a data set and how we can use those values to compare between two data sets.
5.3.2. Handling Controversial Topics
Martha: For slide 2, students may have a large range of answers. Students may point out the difference between the ethnicity of women. This can bring up a sensitive issue for students as it may be upsetting to hear how their ethnicity is treated compared to a white male. Students could also discuss the undocumented pay percentage, which shows men who are undocumented still earn more than undocumented and us working women. For slide 3, students could discuss how this is a problem as women are not going to be given the same opportunities as men and therefore will struggle to become leaders in America. Females in the class may discuss their fears of this and how this is unfair if they are putting in the same work and effort as a male at a job.
Martha: If during the discussion, a controversial topic arises, such as someone stating how men work harder than women or are strong and can work fast pace compared to women, I could turn to talking about women figures who have had a large impact on the world or change the topic into discussing the mathematics content or talk about how men of other races may not earn the same amount as a white man. However, in my classroom I hope for a positive classroom culture, where a student would not try and put others down and remind the students of that during the discussion.
Jessie: What questions do they have? I expect that some students will be shocked by what they have just heard while others will already know about this particular case or one similar. I will facilitate this sensitive topic by first reminding students of the classroom norms. These norms include being respectful of their classmates, understanding that these are real people’s lives we are discussing and that there might be students in the class for who this topic is hard to discuss.
5.3.3. Transformative Student Action (Agency)
Otis: The role of the student in the discussion is to bring their conclusions about how minimum wage can be seen in linear equations so that they are “reading the world” through math. Then, after reading it they can form their own conclusions on how minimum wage should be reformed, abolished, or kept the same based on their findings.
Juliet: At the end of the discussion, students will return to their groups to brainstorm ways to improve equity between schools. They will summarize their reports by explaining their conclusions and their ideas about how to distribute resources more equitably.
6. Discussion and Conclusions
6.1. Overview of the Research Question and Key Results
6.2. Limitations
6.3. Adapted CRMT Tool
6.4. Implications for Teacher Preparation and Teacher Professional Development
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Analysis 2 Results
CRMT Codes  Code Description  #Codes  # PSTs  
1  Cognitive Demand  Encourages high level mathematical thinking and reasoning. Students are mathematically engaged.  5  3 
 Describes students as being potentially unable to complete the task and/or does the task for them.  3  1  
2  Depth of Knowledge and Student Understanding  Activity promotes deep understanding (probing/questioning to get at deeper understanding).  15  7 
3  Math Discourse and Communication  Develops collective understanding (not just sharing but engaging in collective discourse that enables everyone to understand what’s going on).  15  12 
4  Power and Participation  States something explicit about power relations and/or giving voice to historically marginalized students. Explicitly valuing students’ contributions over the teacher’s. Explicit recognition of power in the classroom.  20  9 
 Explicitly valuing students’ contributions over the teacher’s.  
 Explicitly valuing marginalized students’ contributions.  
5  Academic Language Support ELL  Academic language support for ELLs.  33  8 
6a  Culture/Community Funds of Knowledge  Connects mathematical activity/uses mathematics to explore experiences shared within a group/community/culture.  1  1 
6b  Social Justice  Connects mathematical activity/uses mathematics to explore issues of social justice.  0  0 
Other Codes  Code Description  Codes  Students  
Teacher Moves  Pedagogical moves that are made that are not explicitly connected to the mathematics. Note that there are moves that are made to enhance the student’s thinking that are not considered teaching moves.  36  11  
Caring  Affectively demonstrating consideration for students’ personal and mathematical emotions. Includes accommodating different types of students and valuing multiple ways of knowing.  15  9  
Deficit Thinking  Making an activity less rigorous because of perceived or anticipated student difficulties.  12  7  
Student Experiences  Making an aspect of the lesson more relatable to students through their individual experiences (not tied to cultural practices in the community).  13  7  
General Academic Language Support  Vocabulary support for understanding academic language in general.  24  9 
Appendix B. CRMTM Tools for PSTs
6b. Use of critical knowledge/social justice support How does the lesson support students’ use of mathematics to understand, critique, and change an important equity or social justice issue in their lives?
 
1  2  3 
[Superficial SJ context]  [Meaningful SJ context]  [Meaningful integration of Math/SJ context + student agency] 
Context: A social justice context is not used or is not relevant to the students in the class.  Context: A meaningful SJ context (An existing social injustice) is used that is relevant to the students but may not be sustained throughout the lesson.  Context: A meaningful SJ context (An existing social injustice) is used that is relevant to the students and is sustained throughout the lesson. 
Integration of SJ and math: The math is imposed and does not reveal anything new about the context. The PST could easily have switched the context without much change in the lesson.  Integration of SJ and math: The mathematics and SJ context are explored in such a way that:
 Integration of SJ and math: The mathematics and SJ context are simultaneously explored throughout the lesson in such a way that:

Mathematizing: The teacher sometimes/rarely probes the students to explore/interpret:
 Mathematizing: The teacher continuously probes students to explore/interpret:
 
Controversial topics: The teacher avoids anything controversial, including the context itself.  Controversial topics: Teacher does not anticipate (or plans to avoid) how they will manage controversial topics and discussions associated with the context.  Controversial topics: Teacher plans for how they will manage controversial topics and discussions associated with the context. (Ex: men working harder than women → gender pay gap; more crime in black communities → more police presence). 
Transformative student action: Do not believe that the students have any agency.  Transformative student action: students complete and discuss the lesson, but do not follow up the lesson with any sort of plan for action.  Transformative student action: Students are given opportunities to plan and/or make a meaningful attempt to transform the issue using mathematics as their justification (action plan, letter/email to policy makers, organization, etc.). 
6b. Use of critical knowledge/social justice support (Focus on integration of math/SJ/agency) How does the lesson support students’ use of mathematics to understand, critique, and change an important equity or social justice issue in their lives?
 
1  2  3 
[Superficial SJ context]  [Meaningful SJ context]  [Meaningful integration of Math/SJ context + student agency] 
Context: A social justice context is not used.  Context: A meaningful SJ context (An existing social injustice) is used, but may not be relevant to the students in the class, but may not be sustained throughout the lesson.  Context: A meaningful SJ context (An existing social injustice) is used that is relevant to the students and is sustained throughout the lesson. 
Integration of SJ and math: The math is imposed and does not reveal anything new about the context. The PST could easily have switched the context without much change in the lesson.  Integration of SJ and math: The mathematics and SJ context are explored in such a way that:
 Integration of SJ and math: The mathematics and SJ context are simultaneously explored throughout the lesson in such a way that:

Mathematizing: Students are not encouraged to mathematize the explored context (if there is one).  Mathematizing: The teacher sometimes/rarely probes the students to explore/interpret:
 Mathematizing: The teacher continuously probes students to explore/interpret:

Controversial topic: The teacher avoids anything controversial, including the context itself.  Controversial topics: The teacher discusses some controversial topics that are built into the lesson but avoids those brought up by the students.  Controversial topics: Controversial topics (which may be brought up by the students) are explored within the context of the lesson. The teacher does not shy away from such topics but handles them with intentionality and consideration for the experiences of their students. (Ex: men working harder than women → gender pay gap; more crime in black communities → more police presence). 
Transformative student action: Students are not encouraged to have any agency in the lesson.  Transformative student action: Students complete and discuss the lesson, but do not follow up the lesson with any sort of plan for action.  Transformative student action: Students are given opportunities to plan and/or make a meaningful attempt to transform the issue using mathematics as their justification (action plan, letter/email to policy makers, organization, etc.). 
Appendix C. Analysis 3
 red = level 1
 yellow = level 2
 green = level 3
 Meaningful social justice context = 2
 Integration of social justice and mathematics = 2
 Mathematizing = 1
 Handling controversial topics = 1
 Student agency = 1
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Semester  Activity  Pedagogical Goals  Analysis 

Fall 2020 
Ongoing Readings: How to Be an Antiracist by Kendi [50].  Develop a baseline understanding of PSTs’ understanding of CRMT and their lesson planning capabilities to guide instruction.  First round of analysis: develop a baseline. Second round of analysis: analyze PSTs’ understanding of the tool. 
Spring 2021 
Ongoing Readings: Reading and Writing the World with Mathematics by Gutstein [11]. 
 Third round of analysis:

Fall 2021 

 Fourth round of analysis:

Limitations of the CRMT Tool  Modifications (CRMTM) 

Too granular (five levels of attainment).  Reduced levels of attainment to three. 
Targeted toward a lesson observation as opposed to a lesson plan.  Developed two interconnected CRMT tools for lesson planning and lesson observation. 
Uses educational terminology that may not be familiar to PSTs.  Adjusted the language to accommodate the PSTs level of education and corresponding access to educational literature. 
Essential components of each element are unclear.  Identified essential components of each element and developed explicit subcategories drawn from the literature on critical pedagogy, critical mathematics, and realistic mathematics education (RME) [2,12,13,14,17,51]. 
Less emphasis on addressing the integration of mathematical and social justice goals.  Created a specific subcategory addressing the integration of mathematics and social justice goals in the social justice element. 
PST/Lesson Information  Social Justice Subcategories and PST Levels of Attainment  

Pseudonym  SJ Context  Math Topic  Sustained Meaningful SJ Context  Integration of SJ and Math  Mathematizing  Handling Controversial Topics  Student Agency  SJ Element Cumulative/Scaled PST Score 
Juliet  Student Representation in Schools  Ratios and Proportions  3  3  2  1  3  3 
Otis  Minimum wage  Linear functions  3  3  2  1  2  2 
Jessie  Incarceration rates  Probability  3  3  1  2  1  2 
Martha  Gender wage gap  Proportional reasoning  3  3  2  2  1  2 
Karen  Bias in media/ Racial represenatation  Measures of center and spread  3  2  1  1  1  2 
Allison  Minimum wage  Linear functions  3  2  2  1  1  2 
Elizabeth  Living wage/CEO salaries  Measures of center  2  2  2  1  1  2 
Heidi  Gender wage gap  Measures of center  2  1  1  1  1  1 
Joan  Access to services  Linear functions  1  1  1  1  1  1 
Rachel  No single context  Exponential functions  1  1  1  1  1  1 
Scaled Mean Score  2  2  2  1  1  2 
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Register, J.; Fernandes, A.; Pugalee, D. Supporting Preservice Mathematics Teachers’ Culturally Responsive Teaching: A Focus on Teaching for Social Justice. Mathematics 2022, 10, 896. https://doi.org/10.3390/math10060896
Register J, Fernandes A, Pugalee D. Supporting Preservice Mathematics Teachers’ Culturally Responsive Teaching: A Focus on Teaching for Social Justice. Mathematics. 2022; 10(6):896. https://doi.org/10.3390/math10060896
Chicago/Turabian StyleRegister, Jordan, Anthony Fernandes, and David Pugalee. 2022. "Supporting Preservice Mathematics Teachers’ Culturally Responsive Teaching: A Focus on Teaching for Social Justice" Mathematics 10, no. 6: 896. https://doi.org/10.3390/math10060896