The manuscript shares findings from a study engaging secondary mathematics preservice teachers using Artificial Intelligence (AI) chatbots to design mathematics lesson plans. Phenomenology was employed to investigate how six secondary preservice teachers used AI chatbots and navigated this new resource compared to their knowledge and experience in developing culturally responsive mathematics lesson plans that included mathematics and social justice goals. Our data analysis revealed that PSTs’ confidence in their Mathematical Content Knowledge and Pedagogical Content Knowledge allowed them to be critical of using AI-generated lesson plans. This finding contrasted with previous research on elementary education preservice teachers who gave away their decision-making agency to AI chatbots, especially about mathematics. The data suggests that the secondary PSTs had confidence in their Mathematical and Pedagogical Content Knowledge, making them more critical of the AI-generated lesson plans. The findings also indicate that AI tools can help teachers learn about Technological Pedagogical Knowledge (TPK). Overall, the data stressed the need to support PSTs in using AI chatbots critically. The implications of this study provide possible ways to help PSTs overcome their overconfidence in AI chatbots and imply that more professional development tools and programs must be constructed to help inservice teachers use AI tools.
more »
« less
Understanding Preservice Elementary Teachers as Mathematical Modelers and Their Perceptions of the Process
A growing consensus holds that preservice K–8 teachers (PSTs) need to experience the modeling process as learners to understand it and envision teaching modeling in their future classrooms. We examine this recommendation by exploring how PSTs construct models and how collaborative learning practices influence them in revising and refining their models. We also explore their reflections on modeling as a pedagogical experience. We introduce Modeling Decision Maps as a tool to examine how PSTs construct and refine mathematical models, and we draw on reflective journal entries to capture PSTs’ perspectives on the process. Our findings indicate that realistic modeling tasks provide opportunities to foster PSTs’ understanding of modeling, grow their mathematical modeling skills, and attune them to important pedagogical practices.
more »
« less
- PAR ID:
- 10544814
- Publisher / Repository:
- Journal for Research in Mathematics Education
- Date Published:
- Journal Name:
- Journal for Research in Mathematics Education
- Volume:
- 55
- Issue:
- 4
- ISSN:
- 0021-8251
- Page Range / eLocation ID:
- 182 to 209
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Christiansen, I (Ed.)Despite the importance of reasoning and proving in mathematics and mathematics education, little is known about how future teachers become proficient in integrating reasoning and proving in their teaching practices. In this article, we characterize this aspect of prospective secondary mathematics teachers’ (PSTs’) professional learning by drawing upon the commognitive theory. We offer a triple-layer conceptualization of (student)learning,teaching, andlearning to teachmathematics via reasoning and proving by focusing on the discourses students participate in (learning), the opportunities for reasoning and proving afforded to them (teaching), and how PSTs design and enrich such opportunities (learning to teach). We explore PSTs’ pedagogical discourse anchored in the lesson plans they designed, enacted, and modified as part of their participation in a university-based course:Mathematical Reasoning and Proving for Secondary Teachers. We identified four types of discursive modifications: structural, mathematical, reasoning-based, and logic-based. We describe how the potential opportunities for reasoning and proving afforded to students by these lesson plans changed as a result of these modifications. Based on our triple-layered conceptualization we illustrate how the lesson modifications and the resulting alterations to student learning opportunities can be used to characterize PSTs’ professional learning. We discuss the affordances of theorizing teacher practices with the same theoretical lens (grounded in commognition) to inquire student learning and teacher learning, and how lesson plans, as a proxy of teaching practices, can be used as a methodological tool to better understand PSTs’ professional learning.more » « less
-
Social justice mathematical modeling is powerful in helping teachers build awareness of social issues, critique existing systems, and engage in rich mathematical reasoning. In this article, we document a task in which 28 preservice teachers (PSTs) explored if teacher pay is fair and how to define “fair” mathematically. Through qualitative analysis of PSTs’ reflections, we studied the effectiveness of the task through the lens of critical consciousness. Twenty-six of the participants reported developing social and mathematical agency with respect to the task. Because the task related to PSTs’ lived experiences, it allowed them to examine their assumptions about teacher pay, empowered them to use mathematics to explore different perspectives, and helped them envision ways they could enact change.more » « less
-
Mathematics educators and researches have recommended that pre-service secondary mathematics teachers (PSTs) need opportunities both to engage in rich mathematical modeling and also to examine issues of social justice and equity. This poster describes a model-eliciting activity which aims to engage PSTs in mathematizing and modeling the social justice issue of gerrymandering. In the activity, PSTs are given a variety of data (including printed maps as well as the area and perimeter of congressional districts) and challenged to construct a mathematical model of “compactness.” PSTs must iteratively refine their model to rank congressional districts from most to least compact. This model-eliciting activity draws on geometric topics including a consideration of area, perimeter, scale, and attributes of shapes, while simultaneously provoking PSTs to reflect on the use of mathematics to inform public policy and positively transform our world.more » « less
-
Abstract Mathematics teacher education programs in the United States are charged with preparing prospective secondary teachers (PSTs) to teach reasoning and proving across grade levels and mathematical topics. Although most programs require a course on proof, PSTs often perceive it as disconnected from their future classroom practice. Our design research project developed a capstone courseMathematical Reasoning and Proving for Secondary Teachersand systematically studied its effect on PSTs’ content and pedagogical knowledge specific to proof. This paper focuses on one course module—Quantification and the Role of Examples in Proving,a topic which poses persistent difficulties to students and teachers alike. The analysis suggests that after the course, PSTs’ content and pedagogical knowledge of the role of examples in proving increased. We provide evidence from multiple data sources: pre-and post-questionnaires, PSTs’ responses to the in-class activities, their lesson plans, reflections on lesson enactment, and self-report. We discuss design principles that supported PSTs’ learning and their applicability beyond the study context.more » « less
An official website of the United States government

