Eva Thanheiser

Episode 41: Centering Professional Development Around the Instructional Quality Assessment Rubrics

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.

Episode 40: Conversation with MTE editors: Vision, Submission Advice, Etc.

March 11th, 2022  |  Season 9  |  33 mins 20 secs

In this conversation Michael Steele and Kate Johnson share their vision as the new editor team for MTE. They share their vision and give advice for submissions.

Episode 39: Developing Skills for Exploring Children’s Thinking From Extensive One-on-One Work With Students

February 8th, 2022  |  Season 9  |  34 mins 7 secs

preservice teacher education; field experiences; exploring student thinking; practice-based teaching skill

In this article, we share results from a field experience model in which junior-year methods classes were held in an elementary school and preservice teachers (PSTs) worked with a single student (a “Math Buddy”) on mathematics for 30 minutes per day. We focus on the development of PSTs’ skills for exploring children’s thinking and the structures and tools that we used to support this development. Data sources include screencast recordings of interactions with Math Buddies and written reflections completed by PSTs. Although the responsiveness of interactions varied across individuals and interactions, in general, PSTs showed improvements in exploring children’s thinking. We share implications of these findings for similar field experience models and for practice-based approaches to teacher education generally.

Episode 37: Supporting Preservice Teachers’ Growth in Eliciting and Using Evidence of Student Thinking: Show-Me Narrative

February 8th, 2022  |  Season 9  |  35 mins 34 secs

Episode 38: Support and Enrichment Experiences in Mathematics (SEE Math): Using Case Studies to Improve Mathematics Teacher Education

February 8th, 2022  |  Season 9  |  31 mins 17 secs

mathematics teacher education; field experiences; community engagement

This article describes an innovation in an elementary mathematics education course called SEE Math (Support and Enrichment Experiences in Mathematics), which aims to support teacher candidates (TCs) as they learn to teach mathematics through problem solving while promoting equity during multiple experiences with a child. During this 8-week program, TCs craft and implement tasks that promote problem solving in the context of a case study of a child’s thinking while collecting and analyzing student data to support future instructional decisions. The program culminates in a mock parent– teacher conference. Data samples show how SEE Math offers TCs an opportunity to focus
on the nuances of children’s strengths rather than traditional measures of achievement
and skill.

Episode 36: Supporting Prospective Teachers in Problem Solving: Incorporating Mindset Messaging to Overcome Math Anxiety

February 8th, 2022  |  Season 9  |  29 mins 39 secs

mathematical mindset; math anxiety; elementary prospective teachers; growth mindset; problem solving

Prospective and practicing elementary teachers have historically demonstrated anxiety about mathematics, which can affect their mathematics teaching and their students’ math anxiety. Yet, developing productive dispositions prior to teacher preparation programs is rarely addressed in the research. We propose mindset messaging in mathematics courses as an intervention to influence prospective teachers’ (PSTs’) self-reported mathematical mindsets and math anxiety.

Survey results indicated shifts toward growth mindsets and decreases in math anxiety. Further analysis of PSTs’ written responses suggests that mindset messaging may support
PSTs in overcoming math anxiety, and that perseverance during problem solving is critical for PSTs’ mathematical improvement. Additionally, some PSTs connected course experiences to future mathematics teaching practices. Results propose MTEs might consider explicitly offering mindset messaging in mathematics courses.

Episode 35: If the World Were a Village: Learning Mathematics While Learning About the World

December 15th, 2021  |  Season 8  |  39 mins 39 secs

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.

Episode 34: Mathematics Teachers’ Understanding of Privilege and Oppression

December 15th, 2021  |  Season 8  |  31 mins 9 secs

The Access, Allies, and Agency in Mathematical Systems project team designed
a professional development for mathematics teachers positioning equity at the systemic level and activities aimed at supporting mathematics teachers in considering the influence of privilege and oppression on mathematics teaching and learning (Scroggins, 2017). Here, we examine the levels of oppression activity, aimed at supporting mathematics teachers in understanding that oppression operates at multiple levels (i.e., as a system) and that these levels exist and operate in/on mathematics education. Such understanding can support mathematics teachers in disrupting inequities, and how mathematics teachers engage in this activity can support mathematics teacher educators in preparing teachers to do such work. Specifically, we explore the question: How does this activity support mathematics teachers’ understanding of levels of oppression?

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

December 15th, 2021  |  Season 8  |  41 mins 18 secs

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.

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

December 15th, 2021  |  Season 8  |  33 mins 37 secs

equity and diversity; learning trajectories (or progressions); teacher education—in-service/professional development; geometry and geometrical and spatial thinking

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.

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

June 1st, 2021  |  Season 7  |  23 mins 1 sec

cognitively demanding tasks; noticing; pedagogies of practice; practice-based teacher education; secondary methods course; task launch

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.

Episode 30: Student Argumentation Work Sample Sorting Task and Teachers’ Evaluations of Arguments

May 25th, 2021  |  Season 7  |  30 mins 11 secs

professional development; pk–12 teachers; argumentation

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

Episode 29: Double Demonstration Lessons: Authentically Participating in an Inquiry Stance

May 18th, 2021  |  Season 7  |  28 mins 32 secs

professional development; grades 3–5

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.

Episode 28: Supporting Preservice Secondary Mathematics Teachers’ Professional Judgment Around Digital Technology Use

May 11th, 2021  |  Season 7  |  30 mins 12 secs

mathematics methods course; grades 6–12; use appropriate tools strategically; technology

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.

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

May 4th, 2021  |  Season 7  |  18 mins 23 secs

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.

Episode 23: Exploring Real Numbers as Rational Number Sequences With Prospective Mathematics Teachers

January 4th, 2021  |  Season 6  |  35 mins 22 secs

prospective mathematics teachers; quantitative reasoning; real numbers

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.