Pre-Service Mathematics Teachers’ Learning About Equity: Methods and Early Results of Our Study

By: Rebecca McGraw, Ph.D., Associate Professor, Mathematics, University of Arizona
Anthony Fernandes, Ph.D., Associate Professor, Mathematics Education, University of North Carolina, Charlotte
Aubrey Neihaus, Doctoral Student, University of Arizona
Jennifer A. Wolfe, Ph.D., Associate Professor, Mathematics Education, University of Arizona

Peggy Brookins, CEO, National Board for Professional Teaching Standards, talks with Noyce scholars and alumni at the 2019 Noyce Summit.

Through our Noyce Track 4 research project, we are exploring middle and high school mathematics teacher development related to equity beginning during the students’ preparation programs and extending into their first two years of teaching. Improving our efforts to support future teachers’ learning about equity is important because “the prevailing ideological preference [among both preservice teachers (PTs) and inservice teachers] continues to be claims of colorblindness, denial of widespread educational and societal inequalities, and the pre-eminence of de-contextualized individuality” (Gay, 2015, p. 440). In addition, because mathematics is widely (and inaccurately) perceived to be objective and free of bias, issues of equity may be less salient to the prospective mathematics teacher.

This project involves five teacher preparation programs across three states, and research subjects include both Noyce and non-Noyce teacher candidates. Our research questions are:

• How do future teachers’ courses and fieldwork impact the development of their knowledge and beliefs about equity?
• How are future teachers’ knowledge and beliefs about equity expressed in their emerging teacher practice?
• Which Noyce program elements are associated with the development of one or more aspects of equitable practice?

Our theoretical framing combines culturally responsive teaching (Gay, 2002; 2010), equity literacy (Gorski, 2014; Gorski & Swalwell, 2015), and self-determination theory (Ryan & Deci, 2000), and we collect data from surveys, student work, interviews, and videos of instruction. We are currently in year 2 of 5 and, thus far, have been focused on recruiting participants, collecting initial survey and interview data, and further developing our efforts to engage future teachers in thinking about equity and equitable teacher practices in our preparation programs.

Initial Survey and Results

For the initial survey, which has been administered to 32 (out of an expected 60) research subjects to date, we used a combination of two instruments:

• Teacher Multicultural Attitude Survey (TMAS) (Ponterotto, Baluch, Greig, & Rivera, 1998), which measures multicultural awareness and sensitivity, and
• Culturally Responsive Teaching Outcome Expectancy (CRTOE) (Siwatu, 2007; 2011), which measures beliefs about outcomes of using a culturally responsive teaching approach.

These surveys were selected because of their focus on multiculturalism and culturally responsive teaching. Also, the instruments had been demonstrated to have adequate internal consistency, validity, and/or reliability.

The results from our administration of TMAS show that the future teachers believe that they can learn from their students who are from culturally different backgrounds, that teaching these students will be rewarding, and that it is important for them to be aware of the cultural backgrounds of their students. In addition, they believe that it is important to get multicultural training, and do not agree that teaching students about cultural diversity will create conflict in the classroom. In some cases, however, the future teachers remained undecided, and indicated the need for more experience. For example, they were unsure if the curriculum gave undue importance to multiculturalism and diversity, and if communicational styles of bilingual students were interpreted by teachers as behavioral problems.

With respect to the CRTOE, the future teachers tended to believe that building relationships with students; building on their prior knowledge, interests, cultural backgrounds; and providing appropriate resources would help motivate the students to learn and develop in the classroom. The future teachers were less sure about the influence of the students’ home culture on discipline, or the role of native languages in the class in maintaining students’ cultural identities.

Our survey data suggest that the future teachers’ beliefs may be consistent with those found by other researchers. Namely, researchers have found that future teachers tend to be “receptive, or at least tolerant, of broad, general ideas about . . . awareness, sensitivity, and appreciation of cultural difference” (Gay, 2015, p. 445). However, when the discourse shifts toward empowerment and activism, resistance begins to occur (Gay, 2010; Howard, 2010; Kitchen, 2005; Lee, 2005). Research on efforts to challenge this resistance suggests that future teachers need meaningful, sustained experiences working with emerging multilingual students and other non-dominant student populations, as well as critical self-examination of personal perspectives and biases (Lucas, Villegas, & Martin, 2015; Milner, 2006).

Interview Protocol

In our study, at four of the five sites, we conduct initial interviews of research participants at the end of their coursework but prior to their one-semester student teaching experiences. One of the five sites is a post-baccalaureate program in which students are already teaching full-time in classrooms. In this case, we conduct initial interviews at the end of the post-bac program. The goal of the initial interviews is to engage future teachers in reflecting on equity-related learning in their preparation programs, in order to support us in making reasoned interpretations about the impacts of program components on knowledge and beliefs about equity. We did not adopt an existing interview protocol but rather developed our own. We cannot report yet, except anecdotally, about results from administration of the initial interviews. However, we can describe some key aspects of the protocol development process, which may be useful to others engaged in similar work.

As we considered various formats and structures for the interview, we were cognizant of the need to disrupt the power structure of researcher and subject, so that the subjects are able to act as teachers or storytellers in sharing their beliefs and perspectives with the researchers. With this in mind, our interview protocol development process involved making decisions about framing, terminology, and artifacts. With regard to framing, we considered whether to mention equity at the onset or to first engage the future teachers in reflecting more broadly about their experiences in their preparation programs. We decided on the latter in order to see whether course experiences related to equity would surface without our probing specifically for them. We settled on this initial question: “So, tell me about your teacher preparation program. What would you say are some of the things that have been especially helpful to you?” We created several follow up prompts, none of which mention equity, in order to draw out how the experiences that future teachers described had affected their thinking about teaching and about students.

After the initial question and follow-up prompts, we do ask the future teachers specifically about equity. In protocol development, this required a decision on our part about what term to use and whether to define it. We worried about the potential use of different terms across sites and across courses within sites, and we worried about imposing a definition on the interviewees that might impact the scope of their responses. In the end, we decided that we could assume the future teachers would have some familiarity with the term “equity” and that we would attempt to draw out their implicit definitions rather than imposing one. We wrote the following questions, each of which includes several follow-up prompts.

• What, if any, instruction or experiences related to equity have you had?
• What have you learned about equity through your teacher education program?
• How do you feel personally about equity?
• What actions should mathematics teachers take to promote equity?
• What do you wonder about, or what questions do you have, about equity and mathematics teaching?

Taken together, our interview protocol questions are intended to act as a funnel which allows students to bring forth and describe experiences that are important to them while also drawing out their thinking about equity.

We did not ask the future teachers to bring any artifacts (e.g., portfolios) to the interview. One reason for this was that we wanted to focus on the “residue” or “take-aways” from their preparation programs, rather than focusing their attention on the intended learning of particular assignments. However, after asking the questions listed above, we included time in the interviews for different research sites to include questions particular to their programs. These questions could include reflections on particular assignments, although it was still not the case that the future teachers would necessarily have the assignments themselves on hand. Looking ahead to our second set of interviews, which will occur after the research subjects’ first full year of independent teaching, we are considering whether to include prepared examples of different views of equity to use towards the ends of the interviews. (This was a suggestion from our advisory board members.)

Program Development

Our efforts to support future teachers in developing their understanding of equity are multi-faceted, focusing on uncovering and critically examining biases, experiencing mathematics (as learner or teacher) in ways that are deeply connected to issues of equity and social justice, and learning and practicing strategies for promoting equity (via courses and via engagement with non-dominant student populations in local area classrooms). As one example, some participants at one site engaged in an activity to determine if there was any police bias in traffic stops conducted in the city using a recent dataset of 68,488 stops. The participants were guided in the use of Excel PivotTables© to analyze their conjectures as they sought to justify their reasoning using the data. In addition to learning how to handle a large dataset and discussing statistical ideas, the participants shared their personal views about traffic stops and understood other viewpoints that were shared. Grounding the discussions in the data helped mitigate preservice teachers’ resistance to discussing controversial topics.

Our preliminary analysis of interview data give us some insight into how students view and engage with equity-oriented learning activities such as the police bias activity. Of the three research participants present for this activity who have been subsequently interviewed, all three mentioned the activity without direct prompting. This demonstrated that this activity was salient for all three in their learning about equity. In addition, each of the three participants had a different view of the activity, taking it up or resisting it in various ways. This illustrates that this social justice context for data analysis was provocative, surfacing the range of ways a prospective teacher may respond to this type of activity in their learning about equity and mathematics. Moving forward in our research, we will be interested to determine the extent to which such social justice activities are connected to by the students themselves when they are engaged in teaching.

Implications

While we are in the early stages of this study, we can offer some implications for stakeholders engaged in preservice teacher education and/or researching teacher education:

• Engaging in investigation of teaching and equity improves one’s own practice.  As in teacher action research projects, our research involves a component of “action” as we implement equity-focused lessons with our preservice teachers and collect data on their learning trajectories. These cycles of implementation and cross-pollination of ideas across research sites has already led to improvements in our programs.
• Combining existing instruments with instrument development allows for both structure and flexibility.  Existing, previously validated survey instruments are efficient to use and will allow us to make comparisons with results from prior studies; however, the instruments do not perfectly match our study’s framing and focus. By developing our own interview protocols, we create opportunities to ask targeted questions across sites and site-specific questions as well.
• Gaining meaningful feedback from preservice teachers about preparation program experiences informs future efforts to prepare successful teachers. By allowing the research subjects to identify which program components were particularly useful to them, we are gaining valuable information about what is most memorable to students and perhaps which experiences will impact their own practices as teachers.

As we continue with this research, we will be collecting video data of beginning teachers’ instruction and reflections on practice. We will also continue to administer surveys and conduct interviews periodically. These data should support us in addressing a pressing question in our field, namely “How do beginning teachers attempt to promote equity in their mathematics classrooms?” And we look forward to hopefully sharing our findings in a future blog.

This work was funded by the National Science Foundation (NSF) under Grant No. .  The views expressed here are those of the author and do not necessarily reflect those of NSF. 

Rebecca McGraw, Ph.D., Associate Professor, Mathematics, University of Arizona
rmcgraw@arizona.edu

Rebecca McGraw is an associate professor in the Department of Mathematics at the University of Arizona. Her research focuses on secondary mathematics teacher preparation and classroom practice, particularly foundational concepts for Algebra 2 and beyond, and teacher preparation for equitable mathematics instruction. Dr. McGraw currently leads the Teacher Education for Equitable Mathematics Instruction (TEEM) Noyce Track 4 grant.

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Anthony Fernandes, Ph.D., Associate Professor, Mathematics Education, University of North Carolina, Charlotte
anthony.fernandes@uncc.edu

Anthony Fernandes is an associate professor of mathematics education in the Department of Mathematics and Statistics at the University of North Carolina Charlotte. His research focuses on the intersection of language and mathematics, especially the use of cultural and multimodal resources by emerging bilingual students. He draws on this research to prepare future mathematics teachers to work with emerging bilingual students. He currently leads the Noyce Track 1 program, UNC Charlotte CResT.

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Aubrey Neihaus, Doctoral Student, University of Arizona
aneihaus@math.arizona.edu

Aubrey Neihaus is currently a doctoral student at the University of Arizona, and will be joining the faculty at Wichita State University in fall 2020. Her research focuses on teacher learning, particularly the development of teachers’ identities related to equity, social justice, and mathematics. Ms. Neihaus is also an experienced teacher professional development provider and national program leader.

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Jennifer A. Wolfe, Ph.D., Associate Professor, Mathematics Education, University of Arizona
jwolfe628@math.arizona.edu

Jennifer A. Wolfe is an Associate Professor of Mathematics Education at the University of Arizona (UA). She has taught a variety of courses, facilitated professional development workshops for K–12 prospective and in-service teachers, and most recently co-developed a middle/secondary summer lab school with a local school district where teachers could observe the modeling of equitable teaching practices.  She is also the UA AAU Undergraduate STEM Teaching Excellence Award winner for her efforts to effectively implement research-based equitable teaching practices for engaging students in challenging mathematics through collaborative group work, and currently is a Fellow of The Center for Inquiry and Equity in Mathematics.