The aim of this study is to examine the ability of pre-service mathematics teachers to detect errors made in solving questions about matrices. The study particularly focused on revealing the internalization of the teachings such as the meanings and relational dimensions of concepts and operations about matrix. The study was conducted with 26…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

We explore student performance on True-False assessments with statements in the conditional form "If P then Q" in order to better understand how students process conditional logic and to see whether logical misconceptions impede students' ability to demonstrate mathematical knowledge. We administered an online assessment to a population…

The article presents one of the possible ways of overcoming the misconception that is one of the myths about mathematics, which says that teaching mathematics is based only on the transfer of mathematical knowledge in the finished form -- often in the form of certain algorithms. The newly proposed method of access to mathematics teaching is…

To shed light on the value of the area model as a tool to elicit pre-service teachers' (PSTs') understanding of fractions and area, we explored their understanding of the fractional knowledge and geometric measurement knowledge incorporated in the area model by providing PSTs area models in an "atypical" way. We administered a written…

While it is widely believed that Specialized Content Knowledge (SCK) is essential to effective and quality mathematics teaching, the specific constructs that compose SCK remain underspecified. This paper describes the development and use of a new framework that extends the notion of SCK. The framework was trialled with a cohort of 90 first year…

A central understanding in mathematics is knowledge of "math equivalence," the relation indicating that 2 quantities are equal and interchangeable. Decades of research have documented elementary-school (ages 7 to 11) children's (mis)understanding of math equivalence, and recent work has developed a construct map and comprehensive…

Developing students' geometric reasoning skills is dependent on the quality of task designs and the role of the teacher. The purpose of this study was to apply Sfard's (2008) interpretive framework to analyse changes in students' mathematical discourse. This paper reports on the results of an investigation into the ways one class of Year 7…

Making sense of fractions is critical for building the mathematical competence of upper elementary students with and at-risk for a mathematics learning disability. The primary aim of this study was to investigate the effectiveness of teaching students with and at-risk for learning disabilities an intervention in which they learned to construct…

Teacher knowledge is a critical focus of educational research in light of the potential impact of teacher knowledge on student learning. The dearth of research exploring entry-level preservice teachers' geometric knowledge poses an onerous challenge for mathematics educators in initial teacher education (ITE) when designing experiences that…

This study has been aimed to propose a conceptual framework that helps researchers examine mathematics teachers' PCK in the context of supporting students' mathematical thinking. "Advancing Children's Thinking Framework" which is a pedagogical model developed by Fraivillig, Murphy and Fuson (1999) that supports the development of…

Instructional coaching has been a professional learning opportunity that many school districts have employed to support teacher practice. Pairing instructional coaching with on-going workshops is a relatively new approach to professional development. Participants for this study include fourteen middle school teachers that teach either mathematics…

This study investigated prospective elementary (PEMTs) and secondary (PSMTs) school mathematics teachers' statistical reasoning. The study began with the adaptation of the Statistical Reasoning Assessment (Garfield, 2003) test. Then, the test was administered to 82 PEMTs and 91 PSMTs in a metropolitan city of Turkey. Results showed that both…

This study aimed to document pre-service elementary teachers' (PSTs'), who are going to teach K-5, ability to construct as well as evaluate justifications varied in terms of levels of sophistication. Additionally, this study aimed to investigate how PSTs' knowledge of content in which they were being asked to prove influenced their ability to…

Many teachers experience the tension between using published curriculum materials and teaching in ways that are responsive to children. Teachers are often expected to use a particular mathematics curriculum series, but they still want to be able to build on and connect to children's multiple mathematical knowledge bases (MMKB).…