A substantial body of research has documented that the types of knowledge that mathematics teachers draw upon during their practice often differs from the knowledge of individuals working in other fields. Drawing on the Mathematical Knowledge for Teaching (MKT) Framework and the School Mathematics Teaching Pedagogical Content Knowledge (SMTPCK)…

Previous studies have focused on negative physiological sensations and psychological emotions of mathematics anxiety experienced in real time. Similarly, prior research has noted that prospective elementary teachers (PSTs) may experience such feelings of distress while learning to teach mathematics in their teacher-preparation programs.…

This paper presents data from the first of three iterations of teaching experiments conducted with secondary teachers. The purpose of the experiments was to investigate how teachers' combinatorial reasoning could support their development of algebraic structure, specifically structural relationships between the roots and coefficients of…

Policy efforts in mathematics have focused on increasing teachers' mathematics content knowledge (MCK), with the goal of increasing teacher quality and in turn increasing student mathematics learning. An alternative approach to increasing student mathematics achievement is to investigate curricula that can be effectively used by teachers with a…

Isomorphism and homomorphism are topics central to abstract algebra, but research on mathematicians' views of these topics, especially with respect to sameness, remains limited. This study examines open response survey data from 197 mathematicians on how sameness could be helpful or harmful when studying isomorphism and homomorphism. Using…

Offering explanations is a central part of teaching mathematics, and understanding those explanations is a vital activity for learners. Given this, it is natural to ask what makes a good mathematical explanation. This question has received surprisingly little attention in the mathematics education literature, perhaps because the field has no…

Programming-based activities are becoming more widespread in curricula. Our theoretical and empirical investigation seeks to identify appropriate ways to connect computer programming and algorithmics to mathematical learning. We take the intermediate value theorem as our starting point, as it is covered by the French school curriculum, and because…

There is a growing attention around the preparation of pre-service teachers (PSTs) as both learners and teachers of mathematical modeling. Current literature focuses on preparing PSTs as learners of modeling, and we extend current work by examining how PSTs integrate their understanding of modeling into the work of teaching. This study follows two…

In agreement with the main tenets of the anthropological theory of the didactic (ATD), this study uncovers dependencies between what students can learn, the established curriculum and the current state of mathematicians' mathematics ('scholarly mathematics'). One main result is that the mathematics taught, too often taken for granted by curriculum…

Translation is a critical issue in international mathematics education studies but has seldom been carefully investigated. How can a theoretical approach be translated and subsequently used in different languages, and to what extent could the translation processes deepen the approach itself? This paper addresses such issues in the case of the…

The study involved 2,575 students selected through a combination of probability and non-probability sampling procedures. Explanatory sequential mixed methods design was used. Participants completed the FennemaSherman Mathematics Attitude Scales (FSMAS) to provide the quantitative data for the research. The qualitative data were gathered through…

This research article contributes to the growing literature highlighting the potential for innovation in mathematics education through design cycles that involve creative risk-taking and failure-based learning. Specifically, we explore how "failed" cycles of Story"Circles"--a practice-based professional development approach…

This case study inspected mathematical learning opportunities that employed the results from the participating preservice teachers' (n=75) original visual arts creation process. Data obtained during this study provided empirical evidence for the educational viability of employing original Mondrian-style rectangle sets as a context for generating…

Mathematicians frequently attend their peers' lectures to learn new mathematical content. The goal of this paper is to investigate what mathematicians learned from the lectures. Our research took place at a 2-week workshop on inner model theory, a topic of set theory, which was largely comprised of a series of lectures. We asked the six workshop…

In intervention studies, high rates of "implementation fidelity" are important markers of a study's success; however, the definition of implementation fidelity is both complex and dynamic. In this synthesis, we examined the dimensions of implementation fidelity measured and reported in 99 studies in which researchers utilized a…