Curriculum decisions about what mathematics should be taught to students with Down syndrome in secondary school are often based on utilitarian goals and assessments of current attainment. We report in this paper on the effect of an alternative approach - adjusting the standard mathematics curriculum for the year level - on students' affective…

Rowland's Knowledge Quartet (KQ) model can provide illuminating insights into teacher practice in mathematics classrooms. This paper explores a framework developed for pedagogical technology knowledge (TPACK) to consider teacher practice in integrated technology classrooms alongside the KQ model. Observations of a Year 11 class in an Australian…

This study examined the shared beliefs among mathematics teachers in one secondary school in the United Kingdom across the first term of a school year and almost 4 years subsequently. Leximancer software was used to analyse the language used as teachers responded to questions concerning their beliefs about mathematics, mathematics teaching,…

This paper presents the findings of a small-scale study that investigated the issues and challenges of teaching and learning about quantitative reasoning (QR) within a project-based learning (PjBL) context. Students and teachers were surveyed and interviewed about their experiences of learning and teaching QR in that context in contrast to…

The benefits of rich tasks, project-based learning, and other inquiry-based approaches in terms of student understanding and engagement with mathematics are well documented. Such pedagogies are consistent with the development of mathematical proficiencies as described in the "Australian Curriculum: Mathematics" (Australian Curriculum…

Proportional reasoning has been recognised as a crucial focus of mathematics in the middle years and also as a frequent source of difficulty for students (Lamon, 2007). Proportional reasoning concerns the equivalence of pairs of quantities that are related multiplicatively; that is, equivalent ratios including those expressed as fractions and…

This paper presents a framework for examining the Pedagogical Content Knowledge (PCK) required of mathematics teacher "educators" as they endeavour to build the PCK for teaching mathematics that is required of the pre-service teachers with whom they work. The framework builds on existing research into PCK, and provides a series of…

In this article, we report on the use of a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning programme. The instrument was designed to assess the aspects of teachers' knowledge identified by Shulman ("1987") refined by Ball et al. ("2008") and extended to include teachers' confidence to use…

There is broad acceptance that mathematics teachers' beliefs about the nature of mathematics influence the ways in which they teach the subject. It is also recognised that mathematics as practised in typical school classrooms is different from the mathematical activity of mathematicians. This paper presents case studies of two secondary…

The introduction of negative numbers should mean that mathematics can be twice as much fun, but unfortunately they are a source of confusion for many students. Difficulties occur in moving from intuitive understandings to formal mathematical representations of operations with negative and positive integers. This paper describes a series of…

This paper reports the findings of a study that sought to identify particular centrally held beliefs of secondary mathematics teachers that underpinned the establishment of classroom environments that were consistent with the principles of constructivism. The nine crucial beliefs identified were held by one or other of two teachers and emerged…

The findings of a study that examined the connection between the beliefs of secondary mathematics teachers and their classroom practices are reported in this article. Classroom practice was defined in terms of the extent to which classroom environments could be characterised as constructivist. Cluster analysis was used to group teachers according…

This paper reports on one aspect of a larger study and comprises an analysis of the beliefs concerning mathematics, its teaching and its learning, and the classroom practice of one secondary mathematics teacher. It focuses on the question, "What specific teacher beliefs about students are relevant to teachers' classroom practice in various…