This dissertation case study examines how teachers' levels of units coordination afford their ability to reason multiplicatively and fractionally, as well as use their mathematics knowledge for teaching to analyze student multiplicative and fractional reasoning, when a two-year intervention is put into place to evoke new mathematical reasoning.…

This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

Pedagogical content knowledge (PCK) was first introduced by Shulman in the 80s. It is defined as the integration or amalgamation of pedagogy and content which basically covers the "what" and "how" of teaching. PCK was considered as the missing paradigm in the study of teaching. This integration of knowledge was long searched by…

The purpose of this article is to sketch a conceptualization of a framework for Advanced Placement (AP) Statistics Teaching Knowledge. Recent research continues to problematize the lack of knowledge and preparation among secondary level statistics teachers. The College Board's AP Statistics course continues to grow and gain popularity, but is a…

The paper reports an investigation into how a group of elementary and middle school teachers collectively attempted to solve and understand a fraction division problem using an area model. Solving the word problem required that teachers determine how many two-thirds fit into three-fourths. The teachers struggled to conceptualise fraction division,…

This study describes the use of the double-slit thought experiment as a diagnostic tool for probing physics teachers' understanding. A total of 9 pre-service teachers and 18 in-service teachers with a variety of different experience in modern physics teaching at the upper secondary level responded in a paper-and-pencil test and three of these…

Technological pedagogical content knowledge TPACK refers to the knowledge set that teachers currently use to further improve the quality of their teaching and assist their students in learning. Several TPACK models have been proposed, either for discussing TPACK's possible composition or its practical applications. Considering that…

This paper examines contemporary issues in early childhood teacher education in Sweden. The aim of the study was to explore dimensions of the construct of preschool teachers' competence as reported by 810 students enrolled in early childhood teacher education at 15 Swedish universities. The results showed that students' definitions of preschool…

This study is the part of a larger study on investigating Hong Kong (HK) prospective teachers' (PTs) subject matter knowledge (SMK) and Pedagogical Content Knowledge (PCK). In this paper, five HK PTs' and PC on teaching one topic regarding square root were investigated. The results suggest that insufficient understanding on the concept of…

This article reports the investigation of change in preservice teachers' conceptions of effective history teaching across a secondary history methods course in a postgraduate diploma of education program. Using concept mapping to plot shifts in their expressed reflections, data were obtained that indicate personal constructs of effective history…

The need to design teacher preparation programs to ensure that pre-service teachers (PSTs) are prepared and equipped with knowledge, skills and practices to increase the chances that they will become effective novice mathematics teachers is of prime importance. Teacher educators are facing lingering challenges, since teacher education is…

Geometrical notions and properties occur in real-world problems, thus Geometry has an important place in school Mathematics curricula. Primary school curricula lays the foundation of Geometry knowledge, pupils learn Geometry notions and properties by exploring their environment. Thus it is very important that primary school teachers have a good…

Against the background of concerns around teaching and learning outcomes in primary school mathematics in South Africa, this article presents two studies conducted in American Samoa and seeks to draw implications for the teaching and learning of mathematics in South Africa. American Samoa has a very similar educational context to South Africa. The…

Effective professional development engages, rather than bypasses, teacher thinking. This article describes strategies to heighten teachers' awareness of the difference between procedural knowledge and conceptual understanding. (Contains 6 figures.)

Dividing by zero can be confusing for students at all levels. If teachers are to provide clear and understandable explanations of this topic, they must possess a strong conceptual understanding of it themselves. In this article, the authors present qualitative data on fourth- through eighth-grade teachers' perceptions of division by zero. They…