Professional learning that includes coaching is an effective method of supporting teachers to make changes to their teaching practice. This article provides an overview of the initial in-situ professional learning and coaching in a primary school in Western Sydney facilitated by a Mathematics Teaching Educator. In this article I present the…

Learning mathematics involves abstract thinking and the use of symbols. To be successful in a mathematics classroom, students must master what symbols mean and how they work. Much prior work has focused on the nature of the external representations used in mathematics instruction, including manipulatives and symbolic representations. In this work,…

For schools implementing Response-to-Intervention, it is important to understand how to efficiently intensify interventions. Treatment intensity, or intervention design, is a critical yet overlooked and understudied aspect in math. More frequent dosage results in greater student gains. However, questions remain regarding how teaching episodes…

The authors share the results of a research project involving the use of mathematics to develop students' Numeracy General Capabilities. The current article delves into an example of a teacher supporting 'good habits of mind' through focussing on the Critical Learning Disposition of accuracy.

Learning mathematical concepts and procedures typically requires extended cognitive effort, presenting a challenge for many children. People can make tracing actions with the index finger, as well as mimic another's movements, with little or no conscious effort. From the perspective of cognitive load theory, such biologically primary actions may…

Background/purpose: This article aims to identify and analyze the actions of a trainee teacher in orchestrating mathematical discussions in an Exploratory Teaching environment. Materials/methods: This qualitative study of an interpretative nature and case study design focuses on analyzing the content of four Multimodal Narratives. Results: The…

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…

The use of different registers to represent mathematical concepts enhances understanding. For example, rational numbers can assume pictorial, symbolic and natural language representations and this kind of change improves learning. Based on these assumptions, a teaching experiment for the learning of rational numbers by 2nd grade students was…

Assessing student learning traditionally involves determining whether students can solve a certain percentage of problems correctly, under the assumption that this achievement indicates they have the knowledge and understanding they need to progress to new topics. This article explores what teachers can learn from looking closely at student…

How people see the world, even how they research it, is influenced by beliefs. Some beliefs are conscious and the result of research, or at least amenable to research. Others are largely invisible. They may feel like "common knowledge" (though myth, not knowledge), unrecognized premises that are part of the surrounding culture. As we…

Elementary school students struggle in interpreting the equal sign as a symbol denoting equivalence. Although many have advocated using a pan-balance scale to help students develop this understanding, less is known about what features associated with this model support learning. To attempt to control and examine these features, the investigators…

In this study, we examined how curricular resources supported three expert teachers in their enactment of progressions. Using a video-stimulated interview process, we documented the multiple types of progressions identified, described, and enacted by the teachers. Results indicate that the teachers used four different types of…

Background: The sequencing of learning materials greatly influences the knowledge that learners construct. Recently, learning theorists have focused on the sequencing of instruction in relation to solving related problems. The general consensus suggests explicit instruction should be provided; however, when to provide instruction remains unclear.…

Early elementary school students are expected to solve twelve distinct types of word problems. A math researcher and two teachers pose a structure for thinking about one problem type that has not been studied as closely as the other eleven. In this article, the authors share some of their discoveries with regard to the variety of…

The reference contexts that accompany the "realistic" problems chosen for teaching mathematical concepts in the first school grades play a major educational role. However, choosing "realistic" problems in teaching is a complex process that must take into account various pedagogical, sociological and psychological parameters.…