Mathematics Teacher Educator Podcast

Latest Episodes:

Episode 35: If the World Were a Village: Learning Mathematics While Learning About the World Dec 15, 2021

Show notes

Long-standing and ongoing calls exist for making mathematics meaningful, relevant,
and applicable outside the classroom. Major mathematics education organizations (National Council of Teachers of Mathematics [NCTM], National Council of Supervisors of Mathematics [NCSM], Association of Mathematics Teacher Educators [AMTE], TODOS: Mathematics for ALL) have called for mathematics to be seen as a tool for understanding and critiquing the world. To prepare students and teachers to do this, we must go beyond “everyday” contexts and include analysis of social justice issues into our courses. We share an activity designed to address these calls while also addressing the mathematics goals of the course. We share data showing that prospective teachers learned mathematics while also learning about their world and reframing their view of mathematics as a tool to make sense of the world.

Special Guest: Courtney Koestler.

Episode 33: Exploring Power and Oppression: An Examination of Mathematics Teacher Educators’ Professional Growth Dec 15, 2021

Show notes

The preparation of mathematics teacher educators (MTEs) varies widely, with little
guidance regarding the essential skills and knowledge necessary to tackle the field’s
looming challenges. Equitable access to, and engagement with, mathematics has
surfaced as an elusive goal of mathematics education organizations. MTEs, therefore, ought to identify and engage with resources that help them comprehend and confront systemic oppression and inequities. We present the process and reflections from an examination of MTEs’ professional growth through engagement in a collaborative interrogation of critical texts outside of mathematics education. Participation in this series of structured readings and dialogue led MTEs to develop a deeper understanding of the historical movements and events that created today’s local and global status quos. Furthermore, MTEs could more readily make connections between macrocontexts of colonialism, violence, and oppression, and the micromanifestations of power and marginalization within mathematics education. Implications for future development of MTEs are discussed.

Special Guests: Craig Joseph Willey, Jill Newton, Michael R. Lolkus, and Troy Bell.

Episode 32: Developing an Asset-Based View of Students’ Mathematical Competencies Through Learning Trajectory-Based Lesson Study Dec 15, 2021

Show notes

This article details the design and implementation of a professional development model called Learning Trajectory-Based Lesson Study focused on issues of equity, identity, and agency. We developed the Vertical Articulation to Unpack the Learning Trajectory (VAULT) tool to orient teachers’ instructional planning toward an asset-based view of students’ mathematics competencies. We examined teachers’ use of the VAULT to plan, implement, and debrief on student strategies for one spatial reasoning task in elementary, middle, and high school classrooms. The VAULT facilitated intentional planning for a progression of anticipated strategies and equitable access to instruction. Teachers demonstrated an asset-based view of all student thinking independent of grade-level expectations.

Special Guests: Jennifer Suh and Sara Birkhead.

Episode 31: Learning to Launch Cognitively Demanding Tasks: A Practice-Based Unit for Secondary Methods Jun 01, 2021

Show notes

Cognitively demanding tasks provide important opportunities for students to develop an understanding of mathematics; however, they are challenging to launch and implement. The authors designed a secondary methods unit on launching tasks. Participants in the study were enrolled in five different methods courses. Using a noticing framework, findings suggest that by engaging in the unit, preservice teachers developed a greater understanding of the four aspects of an effective task launch. When viewing video examples, preservice teachers were able to talk about the four aspects of a task launch with increased specificity. Additionally, they began to identify ways of developing common language without reducing cognitive demand. We discuss implications of this work and offer suggestions for future teacher education research.

Special Guests: Christopher W. Parrish, Mark A. Creager, and Rachel B. Snider.

Episode 30: Student Argumentation Work Sample Sorting Task and Teachers’ Evaluations of Arguments May 25, 2021

Show notes

To support teachers in implementing ambitious reform efforts, professional developers and teacher educators need to know more about teachers’ thinking about argumentation. Specifically, there is a need to understand more about teachers’ views and evaluations of students’ mathematical arguments as they play out in practice. In this article, we share a tool developed to elicit teachers’ pre- and post evaluations of students’ mathematical arguments on a problem-solving task. We discuss the design of the tool and provide evidence of its utility. Our findings indicate that the tool can be used to (a) identify changes in teachers’ evaluations of student mathematical arguments over time and (b) inform the design of professional learning experiences

Special Guests: Jillian Cavanna, and Megan Staples.

Episode 29: Double Demonstration Lessons: Authentically Participating in an Inquiry Stance May 18, 2021

Show notes

Research has shown that the ways in which teachers engage in professional development activities vary widely. Farmer et al. (2003) identified three levels of teacher appropriation within professional development, with their inquiry stance indicative of teachers engaging in self-sustaining practices. In our project, we modified the demonstration lesson format so that teachers took an active role in changing an observed lesson and then viewing the impact of those changes as a second lesson was taught. We share evidence that this modified structure provided opportunities for teachers to engage in an inquiry stance on teaching and discuss implications for professional development providers in structuring activities to foster an inquiry stance.

Special Guests: Angela T. Barlow and Natasha Gerstenschlager.

Episode 28: Supporting Preservice Secondary Mathematics Teachers’ Professional Judgment Around Digital Technology Use May 11, 2021

Show notes

The pervasiveness of digital technology creates an imperative for mathematics teacher educators to prepare preservice teachers (PSTs) to select technology to support students’ mathematical development. We report on research conducted on an assignment created for and implemented in secondary mathematics methods courses
requiring PSTs to select and evaluate digital mathematics tools. We found that PSTs primarily focused on pedagogical fidelity (ease of use), did not consider mathematical fidelity (accuracy), and at times superficially attended to cognitive fidelity (how well the tool reflects students’ mathematical thinking processes) operationalized as the CCSS for Mathematical Practice and Five Strands of Mathematical Proficiency. We discuss implications for implementing the assignment and suggestions for addressing PSTs’ challenges with identifying the mathematical practices and five strands.

Special Guests: Charmaine Mangram and Kathy Liu Sun.

Episode 27: Editorial February 2021: Considering Connections Across Research Questions, Data, Methods, and Claims May 04, 2021

Show notes

A key component of a Mathematics Teacher Educator (MTE) journal article is a description of the innovation or tool that was used with teachers and a report of the details of the research on that innovation/tool. In our September editorial we highlighted the innovation. In this editorial, we will focus on the importance of aligning research questions, data, and claims with existing research and theories to present a strong and coherent argument about the contribution the innovation/tool makes to mathematics teacher education.

Special Guests: Heather West and Karen Hollebrands,.

Episode 23: Exploring Real Numbers as Rational Number Sequences With Prospective Mathematics Teachers Jan 04, 2021

Show notes

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students’ understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real numbers as rational number sequences. We found that the instructional sequence enhanced prospective teachers’ understanding of real numbers by considering them as quantities and explaining them by using rational number sequences. In particular, results showed that prospective teachers reasoned about fractions and decimal representations of rational numbers using long division, the division algorithm, and diagrams. This further prompted their reasoning with decimal representations of rational and irrational numbers as rational number sequences, which leads to authentic construction of real numbers. Enacting the instructional sequence provides lenses for mathematics teacher educators to notice and eliminate difficulties of their students while developing relationships among multiple representations of real numbers.

Special Guests: Gülseren Karagöz Akar and Mervenur Belin.

Episode 25: Creating a Third Space for Learning to Design Technology-Based Mathematics Tasks Jan 04, 2021

Show notes

In this article, we examine the ways in which the creation of a third space can bridge the divide between coursework and practice for preservice secondary mathematics teachers (PSTs) taking a technology, pedagogy, and content course. A university-based instructor partnered with two high school teachers to create a space in which PSTs draw upon and use both academic and practitioner knowledge while creating technologybased tasks for high school students to use. Our results revealed increased focus on pedagogical decisions in areas such as technology-task design and questioning techniques. The data also indicate that the success of this collaboration was connected to fair distribution of work, feeling valued, and personal benefit and challenges centered on maintaining rejection of hierarchy.

Special Guest: Allison W. McCulloch.