The revised Australian curriculum presents a new emphasis in primary schools on the process of Mathematical Modelling. A modelling focus brings close attention to confidence and capability with a potentially new problem-solving process, associated language, and pedagogical processes. This paper presents a Year 4 classroom modelling experience that…

Mathematical thinking is a complex, multi-faceted process that has been described as messy and difficult but can also show growth and insights into conceptual understanding and knowing. This paper explores the application of Edward de Bono's practical thinking, in particular, the occurrence of porridge words to examine the mathematical thinking of…

This study reports on the capabilities of 53 Year 4 students as they completed the final stages of their first complete statistical investigation. In the context of becoming acquainted with students in a sister school in another city, students in both schools wrote and refined questions, which were answered by all students in an on-line survey.…

Although an understanding of time is crucial in our society, curriculum documents have an undue emphasis on reading time and little emphasis on core underlying ideas. Given this context, a one-to-one assessment interview, based on a new framework, was developed and administered to investigate students' understanding of core ideas undergirding the…

This study explored the potential of a rich assessment task to reveal students' multiplicative thinking in respect to a hypothetical learning trajectory. Thirty pairs of students in grades 5 and 6 attempted the task. Twenty-two pairs applied multiplicative structure to find the number of items in arrays. However counting and computational errors…

As part of ongoing design-based research exploring financial literacy teaching and learning, ten tasks termed "financial dilemmas" were trialled by 14 teachers and more than 300 Year 5 and 6 students in 4 government primary schools in urban Darwin. Drawing on data related to two tasks--"Catching the bus" and "Buying…

Research that has explored students' interpretations of graphical representations has not extended to include how students apply understanding of particular statistical concepts related to one graphical representation to interpret different representations. This paper reports on the way in which students' understanding of covariation, evidenced…

This paper outlines a framework to explain the early development of place-value understanding based on an analysis of data from 84 five- to seven-year-old children from diverse cultural and linguistic backgrounds. The children were assessed individually on number knowledge tasks (recalled facts, subitizing, counting, place-value understanding) and…

This paper explores the group dynamics among three groups of students involved in collaborative learning in mathematical modelling activities. It reports how group dynamics were established and their influence on the students' mathematical problem-solving endeavours. Through video analyses, discourse structures were identified to suggest the…

This paper focuses on children's number fact knowledge from a study that explored the impact of using multiplication and division contexts for developing number understanding with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children's knowledge of number facts, including…

This paper presents a preliminary study of three six year-old children's use of functional language when engaging collaboratively on a mathematics task. The analysis is presented as an illustration of young children's authority and agency in mathematics as evidenced in their discourse. Modality, as a function of language, was seen to indicate…

Guided by the principles of lesson study as applied to microteaching, this paper discusses the results and conclusions of a series of activities done by some graduate students of De La Salle University, Philippines, in an attempt to test the applicability of the lesson--Sequence and Patterns--to facilitate the transition of seventh graders from…

This paper presents findings as part of a wider study that investigated the professional knowledge of teachers when teaching mathematics for numeracy in the primary school classroom. This paper focuses on teachers in action as they taught two lessons on multiplication. It outlines the specific pedagogical categories the teachers used and the…

With the advancement of new technologies, this author has in 2010 started to engineer an online learning environment for investigating the nature and development of spatial abilities, and the teaching and learning of geometry. This paper documents how this new digital learning environment can afford the opportunity to integrate the learning about…

In recent years there has been an increased emphasis on algebraic reasoning in primary school classrooms. This includes introducing students to the mathematical practices of making conjectures, justifying and generalising. Drawing on findings from a classroom-based study, this paper explores one teacher's journey in shifting her task design and…