Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely…

Children's multiplicative thinking as the recognition of equal group structures and the enumeration of the composite units was the subject of this research. In this paper, we provide an overview of the Multiplication and Division Investigations project. The results were obtained from a small sample of Australian children (n = 21) in their first…

This study aims to develop a conceptual framework regarding practitioner knowledge and describe how one mathematics teacher generates her practitioner knowledge based on the framework. The characteristic of this framework is a combination of static and dynamic aspects of knowledge based on the teacher's perception and interpretation. The research…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…

This paper describes results from a case study about how a primary pre-service teacher (PST) used curriculum materials (CMs) when planning for a mathematics lesson during her final practicum. The data is drawn from a doctoral study (in progress) and results show how the PST initiated an active process of searching for and sifting through CMs on a…

Building from the concept of verbing mathematics as a culturally consistent and enabling mathematics education practice for Mi'kmaw learners, the authors present an elementary multiplication lesson affectionately named "Sets of, Rows of, Jumps of". Through examination of this specific set of tasks emerging notions of structuring, play,…

The term numeracy is used widely in schools today and brings with it the expectation that students will be taught both how to do the mathematics, alongside an understanding of the concepts associated with the procedural application. One issue, which has arisen with the terminology 'numeracy classroom', is how to best support teachers to enhance…

In this article the authors describe a project during which they unpacked fraction standards, created rigorous tasks and lesson plans, and developed formative and summative assessments to analyze students' thinking about fraction multiplication. The purpose of this article is to (1) illustrate a process that can be replicated by educators…

Lesson study cultivates teachers' capacity for formative assessment by placing student thinking front and center throughout. Lesson study is a form of professional development in which a team of teachers determines a mathematical focus, collaboratively studies student thinking about the topic, designs a lesson about this content, implements the…

This paper focuses on selected findings from a study that explored the use of multiplication and division with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. The focus of instructional tasks was on working with groups of ten to support the understanding of place value. Findings from relevant assessment tasks…

This book contains a collection of multiplication lessons that support curriculum and instruction. It is expected that 3rd grade students will establish a firm foundation of understanding and skills in multiplication. The lessons in this book address a broader view of multiplication instruction and are aimed at building a strong foundation of…

This book contains a collection of multiplication lessons that support curriculum and instruction. The goals of the lessons are to give all students the chance to learn how to mentally multiply by 10, powers of 10, and multiples of 10; use the distributive property to calculate products; use paper and pencil to record thinking when solving…

Describes a mathematics lesson using digital sums that allows teachers to assess third grade students' understanding of reasoning, arithmetic, and geometry. (ASK)

Created by teachers for teachers, the Math Academy tools and activities included in this booklet were designed to create hands-on activities and a fun learning environment for the teaching of mathematics to the students. This booklet contains the "Math Academy--Let's Go to the Mall! Explorations in Combinatorics," which teachers can use to enhance…