The aim of this article is to carry out a work of networking theories which combines two perspectives on the mathematical activity involved in a modelling process, in order to answer the following question: To what extent does the application of the onto-semiotic tools complement the analysis from a cognitive perspective of a mathematical…

This paper attempts to deepen our understanding of teachers' selection and modification of mathematical tasks for their classroom instruction. In this paper, we focus on teachers' orientations and resources that subtly influence teachers' choices during their routine undertaking of task selection and modification. Interviews using stimulus…

Habermas' construct of rationality is a tool adapted from social sciences into mathematics education to identify the difficulties in the proving process and to plan the teaching of proof for reducing these difficulties. According to Habermas, people engaged in an activity/action are considered to "act rationally" if they choose and use…

The purpose of this study is to observe the changes on pre-service teachers' cognitive (i.e. fluency, flexibility, and originality) and affective outcomes (e.g. perceptions towards creativity-directed tasks, beliefs about the nature of mathematics) related to mathematical creativity after they participated in a creativity-focused mathematics…

In this study, we aim to explain choices that groups of preservice teachers made to implement modelling tasks in primary school. We found that the preservice teachers decided to facilitate everyday-inspired contexts for the tasks and that this could be explained by their reasoning that modelling is supposed to be an activity close to reality.…

In this paper, we investigate the mathematical, social and affective nature of children's engagement with "TouchCounts," a multitouch application for counting and doing arithmetic. In order to study these dimensions of engagement in a way that recognizes their fundamental intertwinement, we use rhythm as a primary unit of analysis.…

Proportional reasoning is important to students' future success in mathematics and science endeavors. More specifically, students' fluent and flexible use of scalar and functional relationships to solve problems is critical to their ability to reason proportionally. The purpose of this study is to investigate the influence of systematically…

Narratives that capture children's learning as they go about their day-to-day activities are promoted as a powerful assessment tool within early childhood settings. However, in the New Zealand context, there is increasing concern that learning stories--the preferred form of narrative assessment--currently downplay domain knowledge. In this paper,…

Word problems about motion contain various conjugated verb forms. As students and teachers grapple with such word problems, they jointly operationalize diagrams, gestures, and language. Drawing on findings from a 3-year research project examining the social semiotics of classroom interaction, we show how teachers and students use gesture and…

This research was designed to investigate the conceptualisations and thinking strategies Indigenous Australian students use in counting tasks. Eighteen Aboriginal students, in years 1 to 11 at a remote community school, were interviewed using standard counting tasks and a "counting" task that involved fetching "maku" (witchetty…

This is the report of an investigation in partnership with a team of junior secondary classroom teachers of the potential of posing more challenging tasks to their students. A range of data sources are used to represent the experience of teachers and students in a unit of work that incorporated a range of challenging tasks. Students learned the…

The goal of Indigenous education is that it should be approached on the basis of the Indigenous language and culture; this is also the case with Sami education. The Sami School Board has stated that all teaching in Sami schools should be culturally based, despite the fact that Sami culture-based teaching is not specifically defined. Therefore,…

In this paper, we discuss our experiences with an after-school program in which we engaged middle-school students with low socioeconomic status from an urban community in mathematical problem solving. We document that these students participated in many aspects of problem solving, including the posing of problems, constructing justifications,…

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…

In this article results from an examination of beliefs about teaching and learning primary mathematics are reported. Commencing and graduating pre-service teachers completed written surveys and interviews. Common to many pre-service teachers were memories of mathematics lessons with teacher demonstrations, completing set exercises, using…