This article focuses on how two mathematics teachers (Amy and Beth -- pseudonyms) cope with the changes of meanings in multiplication due to the changes of contexts. It highlights the qualitative similarities and differences between these two teachers in the sense-making process of multiplication. A potentially useful framework of supportive and…

The article reports an empirical study on the introduction of elementary probabilistic concepts in school, focusing on tasks related to the psychological tradition of heuristics and biases. The concepts involved were studied using an extensional natural frequencies approach. We describe the school intervention conducted in an interaction across…

Patterns pervade our everyday life and are natural and familiar to children. Exciting new research in the field of Early Algebra describes the development of young children's algebraic thinking through the meaningful study of patterns. This paper contributes to this research by reporting on a case study of two primary schools in South Africa and…

The purpose of this analysis was to assess whether effects of first-grade mathematics intervention apply across the range of at-risk learners' initial skill levels. Students were randomly assigned to control (n = 213) and two variants of intervention (n = 385) designed to improve arithmetic. Of each 30-minute intervention session (48 over 16…

Mathematics-related affect comprises an individual's attitudes, beliefs, emotions and motivations towards mathematics. These affective constructs have been widely studied in mathematics education and cognitive psychology and have been shown to be related to cognitive outcomes such as performance on a range of mathematical tasks. However, it is not…

Pirie & Kieren (1994b) states that conceptual understanding in human beings is divided into eight levels. This qualitative and descriptive research study aims to identify the layers of conceptual understanding of fractions through three representations, namely of circles, rectangles, and number lines. The subjects of this research are three…

The question of teaching a standard written algorithm for the four arithmetical operations in the first years of elementary school is increasingly raised as a consequence of the possibility of using calculators, tablets, and computers. This article first presents arguments both against and for maintaining this teaching in the first school years.…

In this study, the variety in quality of instruction in fraction lessons at Grade 5 in Dutch primary schools was investigated. Twenty-four teachers participated in the study. To examine the quality of instruction of fraction lessons, Hill's mathematical quality of instruction framework and general pedagogical instruction strategies (seen to…

The purposes of this study were (a) to test the efficacy of whole-class equal-sign instruction, (b) to contrast the effects of symbolic and nonsymbolic instructional representation, (c) to determine whether visual representation compensated for language deficits, and (d) to evaluate maintenance of intervention. We randomly assigned 195 children…

The advent of a democratically-elected government in South Africa in 1994 disrupted the erstwhile synchrony between the schooling system, teacher education system, curriculum and pedagogy. Yet many South African teachers continue to express their teacher identities much like they did prior to 1994. The explanations posited for why this is the case…

This paper offers a new methodology for researching children's identifications in the early primary phase that makes visible the 'seeds' of academic dis-/identities, which typically flower later in adolescence. It focuses on the 'case' of mathematical identifications (MI) to exemplify how children come to dis/identify from the academic curriculum…

Whole-half-quarter are important mathematical concepts that form the basis of fractions and should be well understood for advancing mathematical topics. The aim of this study is to determine the primary school students' abstraction levels of whole-half-quarter concepts according to RBC theory. The participants of the study are six students (8 age…

This study investigated the performance of 790 fourth graders from Taiwan for judging the reasonableness of a computational result by using corresponding methods pertaining to whole numbers. A number-sense web-based two-tier diagnostic test was used to assess the number-sense performance of the fourth graders who participated in this study. The…

Students in the elementary grades often experience difficulty setting up and solving word problems. Using an equation to represent the structure of the problem serves as an effective tool for solving word problems, but students may require specific pre-algebraic reasoning instruction about the equal sign as a relational symbol to set up and solve…

The process of planning to teach mathematics is complex and idiosyncratic and is gaining increased attention in educational research. In this paper, I propose a framework for conceptualising the critical factors that influence teachers' mathematics planning decisions. The framework is informed by the analysis of teacher survey data (n=114) and two…