This paper draws on observation of a primary mathematics lesson prepared and taught by a second-year pre-service teacher who lacked mathematical content knowledge. A "knowledge quartet" (Rowland, Turner, Thwaites, & Huckstep, 2009) was used to investigate when and how a pre-service teacher drew on their knowledge of mathematics during primary…

This paper reports on early years teachers and how often they should devote planning time to anticipating student responses in advance of the lesson. Sixty-five Foundation to Year 2 teachers (students 5-8 years of age) completed questionnaires at the beginning and end of a year-long research-based professional development program. Participants…

Making accurate judgements and interpretations about student growth and progress in mathematics can be problematic when using open-ended assessments. This study reports on the development of a class-based assessment instrument and marking key designed to assess Year 2 students' mathematics competence to reflect their learning of mathematics…

The current study explores how teachers report using enabling and extending prompts when teaching with sequences of challenging mathematical tasks. Twenty-nine early years primary school teachers completed a questionnaire following their participation in a professional learning project. Findings suggest that teachers': view prompts as important…

This paper focuses on the time teachers take to adapt to a student-centred inquiry approach to teaching mathematics, the nature of those changes and the reasons for variations in both these aspects among teachers within and across schools. Five numeracy experts, who worked with 200 Foundation to Year 2 teachers to facilitate the implementation of…

Professional learning for school mathematics leaders is a key aspect of the Victorian Government's strategy for improving mathematics for Victorian students. This is because middle leaders in schools play a vital role in designing and leading school improvement. As part of the Numeracy Suite, four online courses were designed in 2020 to support…

Effective middle leading of mathematics is a complex task as it requires a focus on improving learning outcomes for students. This study gathered information about the activities of middle leaders of mathematics using a survey of primary and secondary mathematics leaders. Both primary and secondary mathematics leaders more often focussed on…

All students should have access to learning experiences that help them make sense of important mathematical concepts. This study highlights teacher actions for consolidating student learning during teacher-lead discussion in the early years. We report on a case study of a Year 1 teacher involving a lesson observation. Highlights of the lesson…

This paper reports on a mathematics leader who participated as a co-teacher alongside a teacher educator in a university classroom. The collaboration was designed to bring the profession into the university. Case study research design and qualitative methods were used to analyse written self-reflections, transcripts of interviews and the…

While spatial reasoning skills have been found to predict mathematical achievement, little is known about how primary students' conceptual understanding of three-dimensional objects develops. This paper reports insights into a Year 4 student's spatial reasoning when constructing and describing the properties of rectangular prisms, using Froebel's…

Differentiating students' learning needs in primary mathematics classrooms is an issue faced by many teachers. One technique designed to differentiate the level of challenge in mathematics tasks is the use of enabling prompts and extending prompts. We report on survey data pertaining to enabling and extending prompts, and teacher noticing of 37…

This paper provides historical insights and educational background of Froebel's Gifts, hands-on materials developed in the early 19th century. Based on an explorative study with 54 German children (aged 5 to 10) in 2016, we first took steps to explore how these materials meet the demands for early mathematics learning of primary children. Starting…

The following outlines the rationale and structure of a professional learning initiative that seeks to explore teachers' ways of engaging students more actively in building mathematical connections for themselves. An example of one of the suggested experiences is presented.

As part of a project exploring the use of challenging mathematical tasks, data from New Zealand teachers and their students were analysed to explore teachers' actions that encouraged students to persist. Rather than rescuing the students when they needed help, the teachers' actions included arranging for and encouraging students to work…

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…