Search for: All records

Transitioning from a teacher education program to autonomous teaching is a complex process, fraught with challenges. This transition involves developing identities and teaching practices that allow novice teachers to reconcile the reformed teaching world of their teacher preparation program with the more traditional world of school teaching. In this paper, we follow the identity formation of one beginning teacher, Olive, by examining her narratives about her pedagogical actions as she transitions from being a pre-service teacher (PST) to being an intern (INT) to becoming a new teacher (NT). As PST, Olive’s narratives about her current and desired actions aligned with reform actions; as INT, a gap opened between her current traditional actions and desired reform actions; and as NT, the gap narrowed as she modified her desired narratives to more traditional ones. We discuss our findings and their scientific significance. 

Building on the theory of practical rationality, we explore how three beginning secondary mathematics teachers reconcile competing professional obligations, namely: disciplinary, individual, and institutional obligations. As these teachers transitioned from supervised teaching to teaching their own classrooms, they reconciled competing obligations and developed their own ideas about mathematics teaching and learning. The analysis revealed that it was only institutional obligation that conflicted with either disciplinary, or individual obligation, or with teachers’ own teaching preferences. No other two obligations appeared to clash. The conflict with institutional obligation was reconciled in favor of institutional obligation in less than 30% of instances. In the vast majority of cases, another obligation took precedence. 

Online learning and teaching, accelerated by the global pandemic and rapid advancement of digital technology, require novel conceptual and analytical tools to understand better the evolving nature of online teaching. Drawing on the classical model of the instructional triangle and previous attempts to extend it, we propose theInstructional Technology Tetrahedron(ITT)—a conceptual framework that integrates technology into the instructional triangle to represent the role of technology, as a learning tool and a mediator between teachers, students, and content. Combining the ITT framework with network visualization strategies allowed for representing the intensity of interactions within the tetrahedron. We illustrate the affordances of the ITT framework by analyzing reflective noticing patterns of three prospective secondary teachers (PSTs) who reflected on the video recordings of their own online teaching, with each PST teaching four online lessons to groups of high-school students. We demonstrate the utility of the ITT framework to characterize individual noticing patterns, in a particular lesson and across time, and to support a variety of cross-case comparisons. The discussion sheds light on the broader implications of the ITT framework. 

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. 

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.