This article presents a case study of two Grade 5 boys' argumentation concerning addition and subtraction of negative numbers while using an interactive tablet-based application simulating positive and negative tiles. We examine the properties of integers they conjectured, and the kinds of evidence and arguments they used to support their…

Pre-service mathematics teachers' content knowledge is an important issue. Therefore, detailed studies are needed to be conducted on mathematical topics. The study examines preservice elementary mathematics teachers' (PEMTs) special content knowledge (SCK) of integer addition and subtraction in the context of using multiple representations,…

This article examines the importance of developing the notion of place value as a rate of ten. In exploring how to nurture this concept, the author looks at the role of the language of value, the problem types of multistep multiplication and addition along with measurement division, each with ten as an organizing unit, as well as strategically…

The "Reasoning Algebraically about Operations Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The thirty-four cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation into the…

In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…

While previous studies mainly focused on children's additive and multiplicative reasoning abilities, we studied third to sixth graders' "preference" for additive or multiplicative relations. This was investigated by means of schematic problems that were "open" to both types of relations, namely arrow schemes containing three…

In this case study with Devin (pseudonym), which was part of a larger, constructivist teaching experiment with students identified as having learning difficulties in mathematics, we examine how a fourth grader constructed a dual anticipation involved in monitoring when to start and when to stop the simultaneous count of composite units (numbers…

The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1,701 primary…

To better understand the role that ways of reasoning play in students' success on integer addition and subtraction problems, we examined the relationship between students' flexible use of ways of reasoning and their performance on integers open number sentences. Within groups of students in 3 participant groups--39 2nd and 4th graders who had…

The authors asked fifth-grade and eighth-grade students to pose stories for number sentences involving the addition and subtraction of integers. In this article, the authors look at eight stories from students. Which of these stories works for the given number sentence? What do they reveal about student thinking? When the authors examined these…

This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

This form rates childrens' grasp of basic mathematical concepts and procedures. See TM 001 111 for details of the program in which it is used. (DLG)