Pedagogy

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. This study examined the qualitative differences in written feedback of secondary teachers, undergraduate mathematics and computer science majors, and pre-service teachers participating in a capstone course focused on mathematical reasoning and proving.

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. This study provides insight into the importance of expertise in teacher noticing for whole-class discussions while also illustrating the mathematical and pedagogical richness of the details of children’s mathematical thinking.

Efforts towards providing inclusive science and mathematics education for marginalized students are increasingly found in literature advocating for equity-oriented instruction through supporting students’ critical consciousness. Despite a growing body of research centering on teachers’ development of culturally relevant pedagogies, studies examining how teachers support students’ critical consciousness development are scarce in the context of science and mathematics education. Thus, this systematic review uses empirical literature on critical consciousness to explore teachers’ experiences integrating sociopolitical issues into their science and mathematics classrooms.

Socioscientific issues (SSI) are problems involving the deliberate use of scientific topics that require students to engage in dialogue, discussion, and debate. The purpose of this project is to utilize issues that are personally meaningful and engaging to students, require the use of evidence-based reasoning, and provide a context for scientific information. This study highlights the value of integrating SSI in science education to engage students with social justice.

Computational modeling tools present unique opportunities and challenges for student learning. Each tool has a representational system that impacts the kinds of explorations students engage in. Inquiry aligned with a tool’s representational system can support more productive engagement toward target learning goals. However, little research has examined how teachers can make visible the ways students’ ideas about a phenomenon can be expressed and explored within a tool’s representational system. In this paper, we elaborate on the construct of ontological alignment—that is, identifying and leveraging points of resonance between students’ existing ideas and the representational system of a tool.

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.

Learning trajectories in early mathematics instruction have received increasing attention from policymakers, educators, curriculum developers, and researchers. They are generally deemed useful for guiding curriculum standards, instructional planning, and assessment. However, the specific contributions of learning trajectories to education and children’s learning are unclear. We review research over the last five years to describe what is known and what still needs to be learned about methods of development, refinement, and validation of the goals, developmental progressions, and instruction of learning trajectories in early mathematics and possible advantages and disadvantages in the educational application of learning trajectories.

Learning trajectories in early mathematics instruction have received increasing attention from policymakers, educators, curriculum developers, and researchers. They are generally deemed useful for guiding curriculum standards, instructional planning, and assessment. However, the specific contributions of learning trajectories to education and children’s learning are unclear. We review research over the last five years to describe what is known and what still needs to be learned about methods of development, refinement, and validation of the goals, developmental progressions, and instruction of learning trajectories in early mathematics and possible advantages and disadvantages in the educational application of learning trajectories.

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. We utilize a semiotic framework, expanding systemic functional linguistics to encompass non-linguistic elements, to identify aspects of what we call navigational expertise—which supports PTs in engaging both as practitioners and students of the practice.

Children who live in under-resourced communities and attend under-resourced schools deserve access to high-quality teachers and educational opportunities to support their success and well-being. This study emerged from a professional development (PD) for urban teachers working in such schools, to expand educational opportunities for elementary students through outdoor science teaching.