The Mathematics Teacher Educator Podcast accompanies the Mathematics Teacher Educator Journal and co-sponsored by the Association of Mathematics Teacher Educators and the National Council of Teachers of Mathematics
Episode 57: Dilemmas and Design Principles in Planning for Justice-Oriented Community-Based Mathematical Modeling Lessons
October 24th, 2023 | Season 14 | 34 mins 36 secs
This article details the development of design principles to support teachers in planning for a Community-Based Mathematical Modeling task with a focus on social justice in the elementary grades. By reflecting on the dilemmas we encountered in the design and enactment of the tasks, we developed five design principles that allowed us to address issues of social justice as well as attend to powerful mathematical ideas to bring awareness and take action around a local problem. Through our article, we hope to share with mathematics teacher educators
design principles to help plan for tasks with pre- and in-service teachers that prioritize connecting mathematics to social issues and empower both teachers and students to take action to make a positive impact in the community.
Episode 56: Are We Preparing Agents of Change or Instruments of Inequity? Teaching Toward Antiracist Mathematics Teacher Education
October 11th, 2023 | Season 14 | 34 mins 13 secs
equity; social justice; teaching & learning instruction; preservice teacher training; math methods course
The authors began this work with the understandings that (a) there is no “neutral” when it comes to the teaching of mathematics, and (b) mathematics teacher educators need to do something to help produce teachers of mathematics that develop students’ relationships with mathematics and push against the inequities that exist both within and outside of the classrooms in which they will teach. In response, the authors created, deployed, and studied a learning module in an attempt to enact antiracist mathematics teacher education. The learning module activities, the findings about the learning from the prospective teachers who engaged in the module, and messages for mathematics teacher educators who want to engage in this work are shared.
Episode 54: “Rahul is a Math Nerd” and “Mia Can Be a Drama Queen”: How Mixed-Reality Simulations Can Perpetuate Racist and Sexist Stereotypes
September 12th, 2023 | Season 14 | 36 mins 55 secs
mixed-reality simulation; discourse analysis; equity; stereotype
This article focuses on using simulations of practice in teacher education. We studied preservice teachers’ engagement with a popular simulations platform, which creates mixed-reality simulations of five digital avatars controlled by a single live interactor. Because simulations are only an approximation of real practice, our overarching goal was to understand how mathematical stereotypes might arise in simulated spaces. We used Discourse analysis to classify the stereotypes present and the EQUIP observation tool to understand how PTs made participation opportunities available. We found that the simulations might have perpetuated
overtly racist and sexist stereotypes and that negatively stereotyped students were afforded lower-quality opportunities to participate. We discuss how to mitigate potential harm caused and offer guidance for redesigning more equitable and antiracist simulations. Our goal is to raise critical questions for our field around the use of simulations of practice.
Episode 55: When Only White Students Talk: EQUIP-ing Prospective Teachers to Notice Inequitable Participation
September 12th, 2023 | Season 14 | 21 mins 25 secs
noticing; race; gender; equity; number talk
We introduce a teacher learning practice called EQUIP-ing, which aims to foster sociopolitical noticing by leveraging EQUIP, an equity-oriented classroom observation tool. We detail our iterations of EQUIP-ing to a field-based Number Talk experience in a secondary mathematics methods course with 25 White prospective teachers (PTs). We offer empirical accounts of how EQUIP-ing empowered PTs to connect their teaching practices with racialized and gendered patterns of student participation; as a result, PTs began to reconsider taken-for-granted practices. However, we also found that PTs demonstrated potentially detrimental ways of attributing marginalizing patterns to minoritized students without actionable plans to redress the inequity. We conclude by inviting mathematics teacher educators to apply EQUIP-ing while emphasizing purposeful support for asset-based noticing.
Episode 53: Building Mathematics Professional Development With an Explicit Attention to Concepts and Student Opportunities to Struggle Framework
August 31st, 2023 | Season 13 | 35 mins 38 secs
teacher professional development; instructional practice; productive struggle; conceptual understanding
Two broad categories of instructional practices, (a) explicitly attending to concepts and (b) fostering students’ opportunities to struggle, have been consistently linked to improving students’ mathematical learning and achievement. In this article, we describe an effort to build these practices into a framework that is useful for a diverse set of professional development (PD) offerings. We describe three examples of how the framework is used to support teacher learning and classroom instructional practice: a state-mandated course, lesson studies, and a large-scale teacher–researcher alliance. Initial findings suggest that consistently emphasizing this framework provides both content and structural guidance during PD development and gives coherence and focus to teachers’ PD experiences.
Episode 48: Design Principles That Support Course Design Innovation for Elementary Mathematics Methods Courses
June 1st, 2023 | Season 12 | 33 mins 56 secs
preservice teacher education; mathematics teacher education; self-study
Learning to teach mathematics is a complex endeavor, requiring sustained focus and time. Yet time is especially scarce in elementary teacher education programs, where preservice teachers (PSTs) learn all content areas. Through a collaborative self-study, five teacher educators identified three time-related tensions in elementary mathematics methods courses: (a) teaching mathematics content and pedagogy; (b) connecting theory and practice; and (c) promoting social contexts in teaching mathematics. To address these tensions, we offer three design principles and illustrative examples: (a) addressing multiple goals for each course component; (b) developing PSTs’ dispositions over time; and (c) building on PSTs’ strengths to develop understanding of mathematics. We present a reflection tool to assist mathematics teacher educators in designing their courses to maximize their instructional time.
Episode 51: Promoting Equitable PST Participation in Mathematical Discourse: Rough Drafts on an Asynchronous Discussion Board
June 1st, 2023 | Season 13 | 30 mins 40 secs
preservice teachers; equity; rough-draft thinking; online discussions; number theory
Issues of equity in mathematics classrooms existed prior to COVID-19. For many students, however, meaningful participation in mathematical discussions became nearly impossible in online settings during the pandemic. In this study, we note the diversity in and nature of participation in mathematical discourse in an online course for preservice teachers (PSTs). We investigate the influence of implementing two support strategies for discussion: (a) establishing a “rough-draft/ revision” orientation to mathematical tasks; and (b) providing time and structure (tasks and prompts) in an online discussion board for PSTs to post their initial thoughts, react to peers’ solutions, and collectively revise their ideas. In this article, we highlight several benefits of these support strategies to equitable PST participation in a unit on number theory. For example, as compared with oral discussions where only a few PSTs offered their ideas, the written discussion format encouraged every PST to post their ideas. Using a rough-draft/revision stance in the prompts fostered sharing and revealed diverse mathematical approaches, perspectives, and ideas. We argue that giving students opportunities to interact with one another and the mathematics in a variety of ways promotes equitable participation.
Episode 49: Filling a “Void”: The Mathematical Quality in Planning Protocol for Mathematics Teacher Educators
June 1st, 2023 | Season 13 | 18 mins 14 secs
mathematical knowledge for teaching; lesson planning; teacher preparation; secondary mathematics; mathematical content knowledge; mathematics teacher educators
This article explores one novice mathematics teacher educator’s initial use of the Mathematical Quality in Planning Protocol, an innovative tool that was developed to assist in providing feedback on the mathematical quality of novice mathematics teachers’ lesson plans. The protocol was devised to help mathematics teacher educators bridge the gap between prospective teachers’ mathematical content knowledge and their mathematical content knowledge for teaching. Results of our analysis on an initial use of the protocol point to its potential as a tool to help mathematics teacher educators direct their feedback from being overly focused on the pedagogical aspects of the lesson (e.g., timing, planned activities) to the mathematical content prospective teachers are attempting to teach (e.g., anticipated student solutions, problem-solving strategies).
June 1st, 2023 | Season 13 | 19 mins 20 secs
This Perspectives on Practice manuscript focuses on an innovation associated with “Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task” from Volume 7, Issue 2 of MTE. The Flint Water Task has shown great promise in achieving the dual goals of exploring mathematical modeling while building awareness of social justice issues. This Perspectives on Practice article focuses on two adaptations of the task—gallery walks and What I Know, What I Wonder, What I Learned (KWL) charts—that we have found to enhance these learning opportunities. We found that the inclusion of a gallery walk supported our students in the development of their mathematical modeling skills by enhancing both the mathematical analyses of the models and the unpacking of assumptions. The KWL chart helps students document their increase in knowledge of the social justice issues surrounding the water crisis. Using the mathematical modeling cycle to explore social justice issues allows instructors to bring humanity into the mathematics classroom.
June 1st, 2023 | Season 12 | 34 mins 41 secs
space; place; spatial justice; mathematics teacher education
The spaces we inhabit and the physical communities in which we learn all affect how we come to experience the world, construct what mathematics is to us, and develop how we teach mathematics. In this theory-to-practice article, we discuss why explicitly considering spatial ways of knowing is important in mathematics teacher education. We begin by providing theoretical arguments for the importance of considering space in mathematics education. We then present a rationale for why considering space is so important in mathematics teacher education, specifically discussing links to the practice of teaching mathematics. Examples of how to consider tasks related to spatial justice are provided to help reimagine what an mathematics teacher education task can look like.
Episode 46: Developing Equity Literacy and Critical Statistical Literacy in Secondary Mathematics Preservice Teachers
May 22nd, 2023 | Season 12 | 27 mins 35 secs
preservice teacher education; equity; statistics
There is a lack of teacher education materials that develop equity literacy in content courses for preservice secondary mathematics teachers. In response, we created teacher education curriculum materials for introductory statistics that include an integrated focus on developing equity literacy and critical statistical literacy. In this article, we provide an overview of our materials’ design along with a detailed look at one activity regarding racial demographics and tracking in high school STEM courses. We present evidence regarding the positive impact of these materials on the teacher candidates’ competency, value, and likelihood of applying their equity literacy and critical statistical literacy. Implications for mathematics teacher educators working to develop equity literacy together with content knowledge are discussed.
Episode 50: Engaging Teachers in the Combination of Statistical Investigation and Social Justice: Fairness in School Funding
May 15th, 2023 | Season 13 | 22 mins 37 secs
This Perspectives on Practice manuscript focuses on an innovation associated with “Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task” from Volume 7, Issue 2 of MTE. We built on Aguirre et al.’s (2019) integration of mathematical modeling and social justice issues in mathematics teacher education to similarly integrate statistical investigations with social justice issues
October 19th, 2022 | Season 10 | 27 mins 40 secs
A group of mathematics teacher educators (MTEs) began a lesson study to develop a research-based lesson to engage elementary preservice teachers with professional teacher noticing within the context of multidigit multiplication. Afterward, MTEs continued teaching and revising the lesson, developing an integrated process that combined lesson study with the continuous improvement model. This article introduces the continuous improvement lesson study process, shares an example of how the process was used, and discusses how the process serves as a collaborative professional development model for MTEs across institutions.
Episode 45: From Argumentation to Truth-Telling: Critical Race Theory in Mathematics Teacher Education
October 19th, 2022 | Season 11 | 37 mins 30 secs
critical race theory; mathematics education; teacher education
Critical Race Theory (CRT) has entered into public discourse at an accelerated rate. Instead of using CRT as a basis to produce a more racially conscious populace, the latest hysteria, unfortunately, has centered on ban- ning CRT. Governmental actions have been instituted
to establish executive orders to forbid CRT training. Administrators and educators have been written up, sus- pended, and even terminated for teaching about race. The current landscape around CRT is about censoring race-related discussions and obstructing any advance- ments in service to racial equity and justice. In the edu- cational arena, more than 20 states have banned CRT from being taught in our nation’s public school class- rooms. A new report from the Institute for Democracy, Education, and Access found that 35% of all students in U.S. K–12 schools have been affected somehow by local anti-CRT efforts (Pollock & Rogers, 2022). CRT proper
is not taught in K–12 schools, so these efforts clearly demonstrate that those who are championing them are ill-informed about where CRT is taught in the first place.
October 19th, 2022 | Season 10 | 37 mins 25 secs
teachers; area model; visual representations
Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.
October 3rd, 2022 | Season 11 | 31 mins 48 secs
instructional quality; teacher reflection; teacher’s perspectives; professional development; mathematics education; classroom observation; instructional tasks
In this article we detail a research study using the Instructional Quality Assessment (IQA) Rubrics (Boston, 2012) as the frame for a professional development with mathematics teachers in grades 3-8. We wanted to create a professional development around a tool that was typically used in research as a way to observe teachers,
as a tool to use with teachers on their reflection of instruction. In this study we share both the researchers’ and teachers’ perspectives of affordances and constraints of the professional development and observational rubrics.