We report on an effort to vet a list of 10 student learning objectives (SLOs) for geometry courses taken by prospective geometry teachers. Members of a faculty online learning community, including mathematicians and mathematics educators who teach college geometry courses taken by prospective secondary teachers developed this list in an effort to…

This paper reports on an ongoing project aimed at developing an inter-institutional system of professional support for the improvement of the Geometry for Teachers (GeT) courses that mathematics departments teach to preservice secondary teachers. In alignment with the literature on improvement science (see Bryk et al., 2015; Lewis, 2015), it is…

"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…

We show how we used a national distribution of responses from 416 practicing teachers to items of a test of mathematical knowledge for teaching geometry to estimate changes in knowledge by a group of 11 practicing teachers who participated in a 2-year practice-based professional development programme. To draw a reliable interpretation of the…

As a component of a course on geometry for preservice elementary teachers (PSTs), we derive area formulas for a variety of polygons including triangles, quadrilaterals, and both regular and irregular shapes whose areas can be measured empirically using decomposition. Decomposing a circle to justify why its area can be measured using the standard…

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 ways in which four middle grades teachers developed mathematical knowledge for teaching (MKT) geometry as they implemented dynamic geometry software in their classrooms with the assistance of a coach. Teachers developed various components of MKT by observing coaches teach, by dynamic discourse with students, which is…

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…

While recent national and international assessments have shown mathematical progress being made by US students, little to no gains are evident in the areas of geometry and measurement. These reports also suggest that practicing teachers have traditionally had few opportunities to engage in content learning around topics in geometry and…

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…

This article describes the development and validation of two forms of the Geometry Assessments for Secondary Teachers (GAST), which were designed to assess teachers' knowledge for teaching geometry. Both forms were developed by teams of mathematicians, mathematics educators, psychometricians, and secondary classroom geometry teachers. Predictive…

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…

In this study, we considered how four teachers reasoned about proportional situations involving geometry. We used pilot interviews conducted with in-service middle grades teachers around a set of proportional tasks. Analysis relied on a knowledge in pieces lens to uncover the resources that each teacher used in solving the tasks and which…