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…

Several previous researches showed that students had difficulty in understanding the basic concept of multiplication. Students are more likely to be introduced by using formula without involving the concept itself. This underlies the researcher to design a learning trajectory of learning multiplication using Permainan Tradisional Tepuk Bergambar…

This study compared one lesson across four U.S. "traditional" textbook series, two U.S. reform-based textbook series, and one Chinese mathematics textbook series in teaching the connection between multiplication and division. The results showed the differences across U.S. and Chinese lessons in both the teaching and the practice parts of…

The "Census in Schools Educator Update" is sent to educators and educational organizations periodically to keep them informed about current and upcoming census data and to provide ideas about how to use data in the classroom. This issue of the "Census in Schools Educator Update" newsletter focuses on the following topics: (1) Census in Schools is…

A description is given of a lesson on two digit multiplication with nine-year olds that utilizes trial and error and partitioning of the problem in a discovery type approach. (MN)

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…