Eliciting and attending to students' thinking is an important component of teaching mathematics for understanding. Clinical interview protocols have shown the potential to support teachers in developing these skills. However, less is known about how to support teacher leaders' knowledge and development of these skills. Given that teacher leaders…

This qualitative study aimed to identify the changes in a prospective' conceptions about the nature of mathematical tasks and pedagogy in video cases and to investigate the characteristics of the prospective' professional knowledge and views during task design/modification. The study used the mathematical task demand engagement process, which…

Examining teachers' knowledge on a large scale involves addressing substantial measurement and logistical issues; thus, existing teacher knowledge assessments have mainly consisted of selected-response items because of their ease of scoring. Although open-ended responses could capture a more complex understanding of and provide further insights…

This paper compares and contrasts two approaches that are widely used in the English- and German-speaking discourse on mathematics teacher knowledge: 'mathematical knowledge for teaching' and 'mathematics didactic knowledge'. It is proposed that these constructs are based on distinct theoretical and conceptual positions and origins. Mathematical…

This study investigates what mathematicians, who teach academic mathematics courses to secondary school mathematics teachers, want to teach them about the discipline of mathematics. Data sources included interviews with five research mathematicians. The data analysis revealed that expanding teachers' knowledge about the discipline of mathematics…

This paper presents a discussion on a new focus area in mathematics teacher education, namely the mathematics teacher in shadow education (SE mathematics teacher). It addresses three issues pertaining to SE mathematics teachers: special knowledge and expertise they need to possess, teacher qualification and selection and SE mathematics teacher…

Teachers' knowledge of students' mathematical thinking is a growing area of research in mathematics education. The literature has reported plentiful evidence of the interplays between teachers' mathematical knowledge and their knowledge of students' mathematical thinking. The present study builds on this body of work to explain how such interplays…

Given the scarcity of studies explicitly exploring the often tacit assumption that teachers' content knowledge (CK) is pre-requisite of pedagogical content knowledge (PCK), in this study, we draw on Shulman's conceptualization of these notions to examine their relation by content-aligning the CK and PCK measures. Toward this end, we analyzed data…

The adequate preparation of future teachers of mathematics is critical, requiring sufficient opportunities to develop both pedagogical skill and content knowledge. Yet, despite new recommendations for mathematics teacher preparation, we know little about the landscape of course-based learning opportunities in US elementary teacher education…

Instruments designed to measure teachers' knowledge for teaching mathematics have been widely used to evaluate the impact of professional development and to investigate the role of teachers' knowledge in teaching and student learning. These instruments assess a mixture of content knowledge and pedagogical content knowledge. However, little…

Procedural fluency and strategic competence in operating and mathematizing with natural and rational numbers are based on a flexible and meaningful use of mental models, strategies, and procedures. The study to be presented in this paper pursued the question as to which subdomains or tasks relating to procedural fluency and strategic competence at…

Studies of facilitators of professional development (PD) for mathematics teachers have been increasing in order to improve their preparation for conducting PD. However, specifications of what facilitators should learn often lack a conceptualization that captures facilitators' expertise for different PD content. In this article, we provide a…

To anticipate and respond to the diverse ways of reasoning students with disabilities use to make sense in inclusive mathematics classrooms, special educators require a deep understanding of a diverse array of student thinking. Unfortunately, historic and contemporary data suggest that opportunities for special educators to develop this knowledge…

Proportional reasoning is foundational in school mathematics. Despite the importance of proportional reasoning, little has been written about the knowledge needed for teachers to teach proportional reasoning relative to its importance. In this paper, we present an initial definition for a robust understanding of proportional reasoning for teaching…

Given the prevalence of research in undergraduate mathematics education focused on student reasoning and the development of instructional innovations that leverage student reasoning, it is important to understand the ways undergraduate mathematics instructors make sense of these innovations. We characterize pedagogical reasoning about…