Proportional reasoning is important to the field of mathematics education because it lies at the crossroads of additive reasoning in the elementary school and multiplicative reasoning needed for more advanced mathematics. This research reports on the representations used by pre-service teachers (PSTs) as they responded to tasks involving…

This study explored the relationship between technology use, tasks, and questions posed during mathematics lessons in three elementary school classrooms. Teachers were observed between 21 to 30 times per classroom during the year. Data was recorded about the types of technologies, mathematical tasks, and questions observed. Chi-square tests for…

The goals of problem-solving activities in the elementary grades often include making sense of story problems, developing a range of strategies, and reaching accurate solutions. These are important mathematical aims, but they do not fully address the demands of modeling with mathematics as described in the fourth of the Common Core's eight…

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…

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…

Surface area is consistently identified as a curriculum standard for K-12 students and it regularly appears on national and international assessments. Recently, many schools began acquiring digital fabrication and advanced manufacturing equipment. The growing use of digital fabrication in classrooms raises the question of whether or not this…

The focus of this study is the relationship between students' performance in mental calculation and the strategies they use when solving three-digit mental addition problems. The sample comprises 78 4th grade students (40 boys and 38 girls). Their mean age was 10 years and 4 months. The main novelties of the current research include (1)…

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…

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged…

Research findings have established that students often struggle with mathematical symbols including common misconceptions for literal symbolic representations of variables but provide little evidence of when or how these misconceptions arise. This article reports findings from a study of grade 4-6 students' conception(s) for various…

In this action research, first-graders were challenged to cope with a sequence of modelling tasks involving an analysis of given situations and choices of mathematical tools. In the course of the sequence, they underwent a change in the nature of their problem-solving processes and developed modelling competencies. Moreover, during the task…

The "Early Years Generalizing Project" ("EYGP") involves Australian years 1 to 4 (age 5 to 9) students and investigates how they grasp and express generalizations. This paper focuses on data collected from 6 Year 1 students in an exploratory study within a clinical interview setting that required students to identify function…

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…

This paper reports the findings of research into an educational intervention featuring open-ended mathematical problems situated in "real life" contexts and associated pedagogies. "Money and financial mathematics" is the topic in focus, with tasks termed "financial dilemmas" being trialled by 35 teachers in 16…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…