Pedagogical Content Knowledge

Fostering student engagement with mathematical reasoning and proving requires a special kind of teacher knowledge – Mathematical Knowledge for Teaching Proof (MKT-P). One important component of MKT-P is Knowledge of Content and Teaching specific to Proof (KCT-P), which is knowledge of pedagogical practices for supporting student learning of proof. Providing effective feedback on students' mathematical arguments is one of the key aspects of KCT-P.

We extend research that connects teacher noticing expertise and instructional quality by providing rich illustrations of these connections at three levels of noticing expertise. Grounded in a vision of teaching that is responsive to children’s mathematical thinking, we investigated connections between teachers’ expertise in noticing children’s thinking and their centering of children’s thinking in whole-class discussions. We showcase three upper elementary school teachers as focal teachers, each with a different level of noticing expertise.

In this article, we present a framework of culturally relevant science and mathematics pedagogy (CRSMP), which is grounded in the tenets of culturally relevant pedagogy. It delineates practices ranging from the most accessible and easy-to-implement, to the most challenging and often contentious ways to teach mathematics and science. We provide examples of CRSMP that re-position marginalized learners in relation to science and mathematics.

Critical elements of the expertise of mathematics teacher educators (MTE) can be identified in the artifacts they design for working with prospective teachers (PT), specifically for engaging PT in the double role of practitioners and students of practice. While MTE are increasingly utilizing designed multimodal representations of practice (such as storyboards), theoretical frameworks and methods for analyzing these pedagogical artifacts and the meanings they support are still in early development.

Educative curriculum materials (ECM) have been shown to support K-12 teacher learning, but little is known about teacher educators’ use of ECM. In this study, we report on enactments of ECM designed to support the development of preservice elementary teachers’ content knowledge for teaching about matter in two different courses to understand how teacher educators use ECM. Participants were two full professors teaching science content and science methods courses for elementary preservice teachers at a public university in the Pacific Northwest.

Educative curriculum materials (ECM) have been shown to support K-12 teacher learning, but little is known about teacher educators’ use of ECM. In this study, we report on enactments of ECM designed to support the development of preservice elementary teachers’ content knowledge for teaching about matter in two different courses to understand how teacher educators use ECM. Participants were two full professors teaching science content and science methods courses for elementary preservice teachers at a public university in the Pacific Northwest.

Proportional reasoning is an important but challenging skill for students and teachers. This article, presents findings from two studies investigating whether four categories of reasoning identified by Copur-Gencturk et al. (2022, A Closer Look at Teachers’ Proportional Reasoning. International Journal of Science and Mathematics Education, 21(1), 113–129) apply to a national sample of U.S. middle school mathematics teachers (N = 1,320) and can be captured consistently by similar tasks.

Mathematical knowledge for teaching (MKT) is a professional knowledge crucial for effective mathematics instruction, encompassing both content knowledge (CK) and pedagogical content knowledge (PCK). The purpose of this study is to investigate the hierarchical structure of PCK for fractions by seeking further evidence for the PCK-Fractions assessment. The PCK-Fractions measure is designed to examine the effectiveness of teacher education program and field experiences in facilitating preservice teachers’ (PSTs) PCK for children’s fraction reasoning in grades 4–6.

In a traditional lecturing environment, students possess limited agency in accepting or rejecting information provided by teachers. A higher level of student agency involves opportunities and actively identifying uncertainties and collaborating with peers to deepen understanding within the classroom community. Teachers play a crucial role in guiding students through sensemaking by addressing uncertainties and assisting in solution development. Student uncertainty is recognized as a pedagogical resource, engaging them in sensemaking and enhancing agency levels.

Extended reality (XR) is increasingly used to support preservice and inservice teacher training. Its use in teacher education has shown promise in improving future educators’ engagement, self-confidence, and noticing skills. Despite this evidence, the field lacks innovative measures to assess outcomes such as those offered through biometric data collection. This article addresses this gap by presenting the findings of a study involving 18 PSTs, who watched a 360 video of an elementary classroom while their heart rate data was gathered.