Lorraine Day and Derek Hurrell provide a convincing argument for using arrays to promote students' understandings of mental computation strategies for multiplication. They also provide a range of different examples that illustrate the benefits of arrays in the primary classroom.

This paper presents the analysis of two teaching experiments carried out in the context of the mathematics laboratory in a primary school (grades 3 and 4) with the use of the pascaline Zero + 1, an arithmetical machine. The teaching experiments are analysed by coordinating two theoretical frameworks, i.e. the instrumental approach and the Theory…

This study investigated how fifth-grade children's concept images of the unit fractions represented by the symbols 1/2, 1/3/ and 1/4 changed as a result of their participation in an instructional intervention based on multiple embodiments of fraction concepts. The participants' concept images were examined through pre- and post-teaching written…

Classroom culture is established through both conversations and practices. Traditionally in mathematics class, the focus is primarily on the latter; that is, students are shown what "doing mathematics" looks like, and then asked that they try it themselves. This article discusses three mathematical conversations that help bring…

This article presents effective strategies for educators of young children to promote children's mathematical communications, which include think-aloud during individual work time, utilizing reasoning and proof questions, and questioning back to children.

This article provides an overview of effective instructional strategies and interventions for kindergarten and first-grade students at risk in mathematics. The article reviews instructional strategies and interventions within a multitier instructional model in order to provide a framework for teachers and schools looking to increase the…

Counting all and counting on are distinct counting strategies that can be used to compute such quantities as the total number of objects in two sets (Wright, Martland, and Stafford 2010). Given five objects and three more objects, for example, children who use counting all to determine quantity will count both collections; that is, they count…

A "tessellation" is a pattern of geometric shapes that fulfills three conditions: (1) No gaps exist between the shapes; (2) The shapes do not overlap; and (3) The pattern can go on forever in all directions. Tilings (such as tiling a floor) are familiar to children and provide a rich resource at all grade levels for learning many…

The primary goal of the study was to explore first-grade children's reasoning about plane and solid shapes across various kinds of geometric representations. Children were individually interviewed while completing a shape-matching task developed for this study. This task required children to compose and decompose geometric figures to identify…

The present study attempts to report a collaborative cycle of professional development in teaching elementary school mathematics through lesson study. It explores a practice of lesson study conducted by teachers aiming to improve their knowledge of pedagogy. The study adopts an ethnographic approach to examine how collaborative teaching within an…

Integrating curriculum provides rich opportunities for students to focus on relevant applications to the real world and make meaningful connections across different disciplines. This article attempts to go beyond common discourse and platitudes by offering specific examples, showing we--an ethnomusicologist and a mathematics educator--attempted to…

In this paper we report on two assessment tasks extracted from a larger study. The tasks involved number-line placements on two different number lines (0-to-10 and 0-to-20) and place-value understanding. Participants were 119 children from four different classes (Years 1-3). Children's placements were more accurate on the 0-to-20 than the 0-to-10…

Developing mathematical inquiry practices requires that teachers are explicit about classroom norms that support these practices. In this study, we asked: "How can a teacher scaffold the development of norms and practices in mathematical inquiry over time?" Analysis of classroom video over a year showed that the teacher constantly…

This case study narrative reports on the journey of *Sammy as her mindset as a learner of mathematics is challenged. Often students who are mathematically highly capable are viewed as being privileged, they are rarely placed with the cohort of struggling students. Children like Sammy who are mathematically highly capable or gifted, however, are…

We often understand something only after we've had to teach or explain it to someone else. Learning-by-teaching (LBT) systems exploit this phenomenon by playing the role of "tutee." BELLA, our sixth-grade mathematics LBT systems, departs from other LTB systems in several ways: (1) It was built not from scratch but by very slightly…