In the mathematical literature on analytical geometry, various notions of the conics' eccentricity correspond to different approaches to these curves. After making a comparative analysis of well-known textbooks to determine coincidences and differences between the various concepts of eccentricity, as well as how the authors explain the…

This article reports and compares results from an interview study of early childhood teachers in the U.S. and Hong Kong, with a focus on the math outcomes that children may gain from play with unit blocks. Teachers were interviewed to obtain their ideas of the benefits of unit block play in three focal areas: geometry, measurement, and numeracy.…

"Mathematical knowledge for teaching" is a concept indicating the requirement for a specific kind of knowledge required to teach mathematics. Mathematical knowledge for teaching necessitates a more complex structure than what is required to carry out mathematical tasks and the knowledge to do that. The purpose of this study is to realize…

Teachers' content knowledge impacts on what they teach, how they teach and what their students learn. In order to check whether the prospective teachers in a rural South African university know the mathematics content they are expected to teach in the schools, at least at the same depth as their future students expected to attain, the research on…

Building on Shulman's (1986, 1987) construct of Pedagogical Content Knowledge (PCK), Ball and colleagues (Ball, Thames & Phelps, 2008) created a model of mathematical knowledge for teaching that differentiates between subject matter knowledge and PCK. The model categorises different types of knowledge within these two domains. In this research…

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…

This study investigated the relationship between prospective secondary mathematics teachers' perspectives and their mathematical knowledge for teaching in action. Data from two prospective teachers' practice-teachings, one in geometry and one in algebra, their lesson plans and self-reflections were analyzed with Teacher Perspectives and Knowledge…

Geometric experience, spatial representation, spatial visualization, understanding the world around us, and developing the ability of spatial reasoning are fundamental aims in the teaching of mathematics. (Freudenthal, 1972) Learning is a process which involves advancing from level to level. In primary school the focus is on the first two levels…

Teacher education has become an area of considerable interest among policymakers in many countries over recent years. Teacher's knowledge and skills in qualified teaching is of great importance. The main purpose was to study the level and depth of the school mathematics and related teaching knowledge attained by prospective Ukrainian secondary…

This study is about student teachers' conceptual understanding of shapes. While the National Curriculum Statement stipulates that by the time learners exit high school they should have grounded knowledge of basic geometry and know shapes such as polygons and polyhedrons and their properties, this study finds that the majority of student teachers…

Much of the work on teacher knowledge suggests that content knowledge shapes pedagogical content knowledge, and in fact is primary in the relationship between the two forms of knowledge. In this paper we challenge this view, arguing from a situated perspective on knowledge and learning, that pedagogical content knowledge strongly shapes content…

This study examines Indonesian primary teachers' mathematical knowledge for teaching geometry and what factors contribute to this knowledge. A translated and adapted version of the Learning Mathematics for Teaching measures and the Indonesian Educational Survey were used to gather information on teachers' knowledge for teaching geometry and their…

There are two basic guiding referents in the present investigation: the teaching and learning of school-level geometry (basic concepts of Euclidian geometry and measure) and the analysis of the conceptions of prospective primary teachers in Spain. The work assumes that such conceptions appear and develop during school years, and that consequently,…

A two year study investigating the state of pre-service teachers' (PTs') (n=224), teachers' (n=18) and students' knowledge (n=123) of Grade 7 geometry (using the van Hiele theory (1986) and acquisition scales of Gutierrez, Jaime & Fortuny (1991)) is reported. Results indicate that both teachers and PTs fail to reach the expected level of…

This document contains the proceedings of the 22nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education held October 7-10, 2000, in Tucson, Arizona. Selected papers include: (1) "Dealing with Complexity: New Paradigms for Research in Mathematics Education" (Richard Lesh); (2) "Algebra…