With the aim of strengthening mathematics teaching | learning, classroom video is increasingly used as a tool for teachers to reflect on their practice. In the first phase of a two-phase design-based study, a group of primary teachers selected, viewed and discussed video excerpts from mathematics lessons. Engaging with and working to reconcile…

In the context of a professional learning research project we investigated the nature of support offered to classroom teachers and school mathematics leaders to facilitate teachers' implementation of sequences of challenging tasks. End of year questionnaire data were collected from 70 Foundation to Year 2 teachers and ten numeracy leaders who…

An awareness of pattern and structure (AMPS) is critical in young children's mathematical development (Mulligan & Mitchelmore, 2009). AMPS is formally assessed in the early years of school (K-3), in structured conditions using predetermined materials, requiring verbal and written responses. However, children also express mathematical thinking…

Our qualitative case study explored the nature of pre-service teacher (PST) reflections when analysing video-based lessons aimed at developing their reflective practice. 14 PSTs participated in the study. Data were collected through lesson observation and individual PSTs' written reflections. The initial data show that PSTs find lesson reflection…

This paper presents findings from classroom observations of one teacher (Beth). It focusses on the development of conceptual understanding of fractions with her students, articulated in Kieren's sub-constructs (Kieren, 1980,1988), and Hansen's progressions (Hansen, 2005). The study covers three lessons within a six week unit. Findings from this…

Mathematical reasoning features in curriculum documents around the world, but is understood and enacted poorly by teachers in classrooms. We explore teachers' noticing of reasoning during observed lessons. Two teams of primary teachers in Canada and Australia worked to plan, deliver, and observe lessons intended to include reasoning. They observed…

Pedagogical content knowledge is widely considered an essential and complex facet of mathematics teacher knowledge, but little research has focused on PCK at the senior secondary level. This study explores some of the complexities of PCK in a teacher's lesson for senior secondary students by analysing data from lesson observation, the teacher's…

Highly capable mathematics students are not usually considered strugglers. This paper reports on a case study of a Year 6 student, Debbie, her response to a lesson, and her learning involving a challenging mathematical task. Debbie, usually a highly capable student, struggled to complete a challenging mathematical task by herself, but as the…

This paper explores young children's drawings (6 years old) in early number and addition activities in Malaysia. Observation, informal interviews and analysis of drawings revealed two types of drawing, and gave insight into the transitional process required for children to utilise drawings in problem solving. We argue the importance of valuing and…

Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic…

This study investigated a group of six junior primary school teachers' learning as they collaboratively inquired into teaching practice they observed together. The focus of the study was on understanding how teachers collaborated around observed teaching practice to improve their pedagogy. The design involved four iterative stages of co-planning,…

An empirical study was conducted with the aim to develop teachers' confidence and proficiency with teaching mathematics through inquiry. The study followed 41 primary teachers and compared a regular mathematics lesson to a lesson taught using an inquiry approach; 19 of these teachers were also followed over three years. Lessons were coded on the…

Much is known about preschool children's mathematics learning and the role of play in that learning. Many early childhood educators are quite adept at observing and documenting the mathematics learning of the children in their settings. These teachers "notice" the children's mathematics but they are not the only ones to…

Teacher knowledge, including Pedagogical Content Knowledge (PCK), continues to be the focus of research, with the general consensus being that PCK impacts upon teaching and learning. Much of the current research has focused on pre-service teachers and practicing primary teachers, with few studies focused on studying senior secondary teachers' PCK.…

This paper promotes the importance of noticing young children's mathematical strengths. It draws on the philosophical positions of children's rights and competence to propose a shift in the ways in which all involved might notice the mathematical engagement, understandings, experiences and practices of young children. Noticing children's…