Two of the teachers' knowledge models most widely used in the literature are the Mathematical Knowledge for Teaching (MKT) and the Knowledge Quartet (KQ). We develop an analysis of the limitations of the knowledge required for teaching problem-solving published during 1990-2018 which includes these models. This analysis revealed that MKT takes…

This paper explores the optimization of teacher education programs to meet the evolving demands of 21st-century classrooms. It examines key strategies to enhance teacher preparation, such as the integration of technology, fostering critical thinking, promoting inclusivity, and preparing educators to address global challenges. The paper also…

This paper explores an innovative assessment framework for measuring children's formal and informal mathematical knowledge. Many existing standardized measures, such as the Early Grade Mathematics Assessment, measure children's performance in early primary grade skills that have been identified by researchers and policy makers as foundational and…

Key studies in history education (from France and the USA) are discussed and compared in order to explore their methodological issues in terms of the types of knowledge they can generate about teaching and learning. An epistemological framework that relates the history of historians as an inquiry to that of the classroom provides the criteria for…

In recent years, learning progressions (LPs) have captured the interest of educators and policy makers. There have been numerous efforts to develop LPs aligned to college and career readiness standards, to unpack these standards, and to provide more clarity on the pathways students follow to reach them. There is great variation, however, in the…

With science teachers facing comprehensive curriculum reform that will shape science education for decades to come, high school department chairs represent a critical resource for instructional leadership and teacher support. While the historical literature on the department chair indicates that chairs are in prime positions to provide…

The problem-based learning (PBL) literature presents the shift from teacher-directed transmission models of instruction to facilitation as a challenge for PBL tutors. This article reports an in-depth thematic analysis of reflective written responses on PBL of 63 teacher education students enrolled at an Australian university. Attitudes, skills and…

This paper documents the ways mathematical knowledge for teaching (MKT) and curriculum materials appear to contribute to the enactment of a 7th grade "Connected Mathematics Project" lesson on comparing ratios. Two teachers with widely differing MKT scores are compared teaching this lesson. The comparison of the teachers' lesson enactments suggests…

In this article, pre-service teachers' mathematics content knowledge is explored through the analysis of two items about ratio from a Mathematical Competency, Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors and misconceptions in their responses are presented and discussed. Of particular interest was the range…

The principal aim of this study is to consider the competencies of the modern teacher. To understand 21st-century instructional skills, we researched the following issues: students' skills; levels of teachers' professional growth; teachers' pedagogical culture; pedagogical innovations, and 21st-century teaching competencies. [For complete volume,…

This article analyzes the experiences of prospective secondary mathematics teachers during a teaching methods course, offered prior to their student teaching, but involving actual teaching and reflexive analysis of this teaching. The study focuses on the pedagogical difficulties that arose during their teaching, in which prospective teachers…

This paper reports on change in teachers' perceptions of important elements of their role as teachers of mathematics at the conclusion of a two-year professional learning project. Analyses of written responses to survey items indicated shifts in four categories describing important elements of their role: teaching skills, knowledge, concepts;…

We report the development of a multiple-choice instrument that measures the mathematical knowledge needed for teaching arithmetic with fractions, decimals, and proportions. In particular, the instrument emphasizes the knowledge needed to reason about such arithmetic when numbers are embedded in problem situations. We administered our instrument to…

This study examined ways in which expert and novice teachers mentally represent classroom problems in matters of instruction, assessment, and curriculum planning. A triad judgement task was administered to expert teachers (n=20) and novice teachers (n=98) to determine whether deep, structural features (i.e. the theoretical underpinnings associated…

This article presents our plans and initial work to explore how mathematics teacher education programs can prepare teachers for diverse middle grades classrooms. It describes the start-up of a five-year National Science Foundation project to design, develop, and test technology-enriched teacher preparation strategies to address equity in algebra…