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…

This paper describes an investigation looking at the underlying mathematics of poker machines. The aim of the investigation is for students to get an appreciation of how poker machines are designed to ensure that in the long-term players will inevitably lose when playing. The first part of this paper describes how students can model a simple poker…

In this paper, we present data from a study exploring the use of coding to promote mathematical thinking. A teaching experiment was undertaken with 40 Year 2 students participating in six 45-minute lessons of coding (one lesson per week for six weeks). All lessons were video-recorded and analysed to determine students' mathematical thinking.…

Having students address mathematical inquiry problems that are ill-structured and ambiguous offers potential for them to develop a focus on mathematical evidence and reasoning. However, students may not necessarily focus on these aspects when responding to such problems. Argument-Based Inquiry is one way to guide students in this direction. This…

Indigenous teacher assistants (ITAs) are often employed in schools to assist in addressing educational issues relating to Indigenous students. While, this practice has occurred for over 40 years in most Australian states, little has been written about their contribution in assisting Indigenous students to learn. This paper explores the influence…

The importance of actively engaging in mathematics discourse in order to learn mathematics is well recognized. In this paper, I use Basil Bernstein's concepts of pedagogic discourse to document and analyse academic learning time of students in Years 8 and 9 at a suburban lower secondary school: in particular, for what proportion of class time…

This paper considers the responses of 115 school students to two problems based on information provided in two-way tables. In each case the question asks if one of the variables involved depends on the other. Contextual knowledge might suggest a dependent relationship in both but in one problem the data show independence while in the other the…

Recent research findings indicate that using multiple metaphors in multimodal learning experiences are effective teaching approaches in early years mathematics. Using a social semiotic lens this paper reports on eight early years teachers' perceptions of this approach whilst engaging in a small collaborative professional learning group. This group…

An understanding of conditional probability is essential for students of inferential statistics as it is used in Null Hypothesis Tests. Conditional probability is also used in Bayes' theorem, in the interpretation of medical screening tests and in quality control procedures. This study examines the understanding of conditional probability of…

Developing pre-service teachers' (PSTs') knowledge of pedagogical practices can be particularly challenging within university classrooms. Teacher educators are well placed to provide PSTs with theoretical perspectives on pedagogical practices; what is particularly challenging, however, is linking theory with practice and developing PSTs' breadth…

Concept image is proposed by Vinner and Tall (1981) to differentiate the elements and relationships that a learner constructs about a concept from formal mathematical definition for the same concept. The answers of 119 University students to an examination question are analysed to establish the concept images they have for circle and ellipse. The…

The importance of mathematical visual images is indicated by the introductory paragraph in the Statistics and Probability content strand of the Australian Curriculum, which draws attention to the importance of learners developing skills to analyse and draw inferences from data and "represent, summarise and interpret data and undertake…

Australian and Singaporean students have been exposed to different forms of teaching due to cultural differences in education. In each country, varying degrees of importance has been placed on explicitly teaching problem-solving heuristics. This paper highlights the different strategies employed by students from each country when solving a word…

This paper reports on a design experiment regarding young children's concepts of mass measurement. 119 year one and two children were interviewed using a clinical interview both before and after the teaching period comprising five lessons that offered rich learning experiences regarding concepts of mass. The results of the interviews were that the…

This paper discusses upper primary school teachers' perspectives on changes to their knowledge and practice through participation in a design-based research project. It analyses their experiences using Clarke and Hollingsworth's (2002) empirically-founded model for professional growth to understand more about the mechanisms for change that might…