Investigating Preservice Teachers’ Conceptualizations of Mathematical Knowledge for Teaching Through Video Analysis

Mathematics Preservice Teachers’ (M-PSTs) conceptions of Mathematical Knowledge for Teaching (MKT) enhance their reflective skills because they utilize such conceptions to reflect on how to contextualize content knowledge during secondary mathematics teaching. While previous studies suggested M-PSTs develop MKT, including pedagogical content knowledge by analyzing teaching in video lessons, how M-PSTs enhance their conceptions of MKT through such analysis is underexplored. I used a collective case study approach to investigate how four secondary M-PSTs conceptualized MKT when they analyzed and discussed teaching represented in a video lesson using the MKT framework. The findings indicated that the M-PSTs often described teacher knowledge either as purely pedagogical or solely content knowledge in their initial analyses of the video lesson. After engaging in a discussion that introduced the MKT framework, the M-PSTs began to illustrate how a teacher’s content knowledge influenced her instructional decisions and actions. Through this discussion, M-PSTs began identifying MKT as professional content knowledge unique to teaching and, thus, distinguished MKT from generic pedagogical or content knowledge. I argue that the language and concepts offered through the framework enhanced the M-PSTs’ conceptions of MKT and suggest that the instructional activities from this study contribute to developing M-PSTs as reflective practitioners

Assessing Concepts, Procedures, and Cognitive Demand of ChatGPT-generated Mathematical Tasks

In November 2022, ChatGPT, an Artificial Intelligence (AI) large language model (LLM) capable of generating human-like responses, was launched. ChatGPT has a variety of promising applications in education, such as using it as thought-partner in generating curricular resources. However, scholars also recognize that the use of ChatGPT raises concerns, such as outputs that are inaccurate, nonsensical, or vague. We, two mathematics teacher educators, engaged in a collaborative self-study using qualitative descriptive approaches to investigate the procedures, concepts, and cognitive demand of ChatGPT-generated mathematical tasks focused on fraction multiplication using the area model approach. We found that the ChatGPT-generated tasks were mostly procedural and not cognitively demanding. Moreover, despite ten variations of input prompts, ChatGPT did not produce any tasks that used the area model approach for fraction multiplication. Rather, it generated tasks focused on procedural approaches. Alarmingly, some tasks were conceptually and/or procedurally inaccurate and vague. We suggest that educators cannot fully rely on ChatGPT to generate cognitively demanding fraction multiplication tasks using the area model. We offer recommendations for educators’ strategic use of ChatGPT to generate cognitively demanding mathematical tasks

Elementary Mathematics Curriculum: State Policy, COVID-19, and Teachers’ Control

In the U.S., state guidance to schools in response to the COVID-19 pandemic was politicized. We used state-level political affiliation to explore whether access to curricular resources differed pre-pandemic or during pandemic remote teaching and teachers\u27 reported control over curricular resources during pandemic teaching. We found that pre-pandemic the percentage of teachers in Republican states reported higher levels of resources overall, and use of core and teacher-created curricular resources in particular. They also reported having greater control over their curricular decision-making during the pandemic. There were no state-level differences in teachers’ level of preparation for pandemic teaching, but teachers in Democrat states reported a greater proportion of their students had sufficient resources for online learning. We discuss the implications of these findings in terms of teacher control and state policies

Girls Excelling in Math and Science (GEMS): Stories of the Original GEMS Girls

Girls Excelling in Math and Science (GEMS) is an afterschool club started in 1994 by a parent, Laura Reasoner Jones, who was dismayed to hear her 10-year old daughter Julie opt herself out of attending a magnet school because “Math is hard.” Julie’s math performance had been good in school, therefore Laura wondered what else might be causing her self doubt. Laura decided to address the issue. Collaborating with Julie’s teacher, she started the first GEMS club for Julie and her friends in fifth and sixth grade. During the following 25 years, GEMS clubs have operated globally to provide resources to support leaders to implement community-based, single-sex learning environments with over 200 hands-on STEM activities. Through the website library, GEMS provides free, equal access to these activities for students, parents, and educators. The mission of GEMS is to cultivate curiosity and confidence in STEM for girls in elementary and secondary school

Final Report: Conceptualizing Ethics, Authenticity, and Efficacy of Simulations in Teacher Education

This working group was a continuation of working groups in 2019 and 2021 that initially aimed to focus on equity in simulations of practice in mathematics teacher education. We began by discussing our conceptualizations of simulations and equity. Next, we reflected on the lack of work that currently exists at the intersection of simulations and equity as well as our limited collective expertise in this space. We proposed the following areas of potential research: Access, Design, Affective Domains, Teaching Practices, Assessment, Critical Conversations. Attendees self-selected into focus groups and met to discuss their current work and how future work could focus more on equity and access. At the conclusion of our time together we developed a plan for achieving our key goal of disseminating a book that documents the landscape of the field

Conceptualizing Ethics, Authenticity, and Efficacy of Simulations in Teacher Education

This working group was a continuation of working groups in 2019 and 2021 that initially aimed to focus on equity in simulations of practice in mathematics teacher education. We began by discussing our conceptualizations of simulations and equity. Next, we reflected on the lack of work that currently exists at the intersection of simulations and equity as well as our limited collective expertise in this space. We proposed the following areas of potential research: Access,Design, Affective Domains, Teaching Practices, Assessment, Critical Conversations. Attendees self-selected into focus groups and met to discuss their current work and how future work could focus more on equity and access. At the conclusion of our time together we developed a plan for achieving our key goal of disseminating a book that documents the landscape of the field

Exploring International Educators\u27 Learning About Local and Global Social Justice in a Virtual Community of Practice

In this chapter, the authors report themes that emerged when a cross-cultural team of researchers involved in a virtual international community of practice (Global Social Justice in Education-GSJE) investigated reflections on activities focused on social justice in local and global contexts. The findings suggested that the activities elicited GSJE community members\u27 understandings of the complexities of social justice associated with naming practices, privilege, and the arts within their own and across contexts. The authors discuss implications of the activities to advance diverse educators\u27 understanding of social justice in global and local contexts. They also unpack the opportunities and challenges that resulted from the collaborative research process and the writing of this chapter completed by the international author team comprised of 11 education scholars from seven countries

Figured Worlds of Women Mathematics Education Scholars

Drawing on the concept of figured worlds (Holland et al., 1998), this project focuses on addressing, responding to, and understanding the self within the figured world of the mathematics education community. Specifically, we examine a group of women with diverse backgrounds in terms of race, class, and cultural contexts, who are engaged in various roles as mathematics education scholars, including teachers, teacher educators, and researchers. Using a dialogical self approach, we facilitate both internal and external discourses, exploring personal histories, narratives, and the development of evolving identities. Our findings reveal that culture and social positions, such as gender, class, and race, inform our positionalities within the mathematics education community. The understanding of the roots of our identities serves as a foundation for constructing a more inclusive figured world of mathematics education

PRESERVICE TEACHERS’ MATHEMATICAL KNOWLEDGE FOR TEACHING: FOCUS ON LESSON PLANNING, PEER TEACHING, AND REFLECTION

   Mathematics teacher educators have suggested that approximations of practice provide preservice mathematics teachers (PMTs) with opportunities to engage with, develop, and demonstrate subdomains of Mathematical Knowledge for Teaching ([MKT], Ball et al., 2008) because MKT provides a way for PMTs to understand how to contextualize their discipline-specific content knowledge for effective mathematics teaching and learning. However, the affordances and limitations of commonly used forms of approximations of practice (i.e., lesson planning and peer teaching) coupled with reflective practices to engage PMTs in subdomains of MKT are still being explored. In this study, I investigated how lesson planning, peer teaching, and associated reflections individually and collectively afforded opportunities for PMTs to demonstrate and develop the MKT subdomains. Eleven PMTs enrolled in a secondary mathematics methods course at a large Midwestern University participated in the study. My dissertation comprises three sub-studies (Sub-study “1”, “2”, and “3”), and I produced three manuscripts to individually report findings from those sub-studies. I investigated how lesson planning, peer teaching, and reflections afforded opportunities for PMTs to demonstrate and describe MKT subdomains in Sub-studies 1, 2, and 3, respectively. The findings across the sub-studies suggested that several MKT subdomains (e.g., Knowledge of Content and Teaching, Knowledge of Content and Students) were evidenced in the PMTs’ planned teacher and student actions (e.g., selecting mathematical tasks, formulating and sequencing questions), and in-the-moment actions and decisions (e.g., mathematically representing students’ responses, implementing mathematical tasks). Several aspects of MKT subdomains (e.g., evaluate the diagnostic potential of tasks) were strongly evidenced only in the PMTs’ lesson plans whereas other aspects (e.g., modifying tasks based on students’ responses) were evidenced only in peer teaching. These findings suggested that various forms of approximations of practice (planned and enacted actions) created unique opportunities for the PMTs to engage with and demonstrate MKT. I also found that the PMTs reflected on some subdomains of MKT that were not evidenced in their approximated practices, indicating that how PMTs describe the MKT subdomains is not entirely a result of what subdomains they engage in during approximations of practice. My findings also revealed limitations of using approximations of practice to engage PMTs with MKT subdomains. The MKT subdomains that required the PMTs to think about students’ alternative mathematical concepts, big mathematical ideas, and non-standard mathematics problem-solving strategies were least evidenced across the approximations of practice and reflections. These findings have two primary implications for mathematics teacher educators. First, I invite mathematics teacher educators to engage PMTs in multiple forms of approximations of practice to optimize their opportunities to engage with, demonstrate, and develop the MKT subdomains. Second, I suggest potential instructional activities (e.g., inviting PMTs to reflect on their roles as students and teachers during peer teaching) that could be incorporated into approximations of practice to address the existing limitations. Broadly, I invite mathematics teacher educators to design instructional activities at the intersection of mathematics content and pedagogy, collaborating with colleagues to enhance these opportunities across programs.   </p

Preservice teachers\u27 mathematical knowledge for teaching: Focus on lesson planning and reflection

Mathematics teacher educators have suggested preservice mathematics teachers\u27 (PMTs\u27) practices provide evidence of their mathematical knowledge for teaching (MKT). PMTs engage in approximations of practice to rehearse teaching. To explore connections between MKT and PMTs’ practices, we operationalized six MKT subdomains in terms of approximations of practice. We used that operationalization to investigate, which subdomains were evidenced in PMTs’ lesson plans and their lesson plan reflections. Eleven secondary PMTs participated in our study. Using a qualitative content analysis method, we found Knowledge of Content and Teaching most evidenced, suggesting that the PMTs demonstrated MKT when they described mathematical tasks and associated instructional activities. Also, the PMTs demonstrated Knowledge of Content and Students when they described how their students would engage with proposed mathematical tasks. However, the PMTs struggled to plan for activities by building on students’ potential mathematical thinking and reasoning. Only limited instances of Horizon Content Knowledge suggest that the PMTs had limited opportunities to demonstrate how their advanced mathematical knowledge connected with their mathematics teaching in the approximations of practice provided. We propose alternative forms of approximations of practice to optimize PMTs’ opportunities to demonstrate and develop MKT