Background: The sophistication of young children's arithmetic problem-solving strategies can be influenced through experience and instructional intervention. One potential pathway is through encountering story problems where the location of the unknown quantity varies. Aims: The goal of the present study is to characterize how arithmetic…

Previous research has shown the importance of conducting early interventions in mathematics in disadvantaged children. Solving arithmetical word problems is a field in which children particularly fail. In this study, preschoolers from disadvantaged French public schools (n = 101; M[subscript age] = 5-6) were taught strategies for using fingers to…

The hundreds chart is a valuable tool for teachers in elementary mathematics classrooms. The present study investigated the effects of spatial configurations of virtual hundreds charts on children's knowledge of base-ten concepts. Kindergarten and first-grade students were assigned to three instructional conditions in which they worked with a…

In this article, we present research on eight kindergarten and eight first-grade students' understandings of the arithmetic properties of commutativity, additive identity, and additive inverse during a classroom teaching experiment, selected from a larger study that included 88 students. In this study, we explore the students' types of…

Investigators often rely on the proportion of correct responses in an assessment when describing the impact of early mathematics interventions on child outcomes. Here, we propose a shift in focus to the relative sophistication of problem-solving strategies and offer methodological guidance to researchers interested in working with strategies. We…

In this article, the authors share frameworks for problem types and students' reasoning about integers. The authors found that all ways of reasoning (WoRs) were used across grade levels and that specific problem types tended to evoke particular WoRs. Specifically, students were more likely to use analogy-based reasoning on all-negatives problems…

It has become increasingly clear that the early use of decomposition for addition is associated with later mathematical achievement. This study examined how younger children execute a base-10 decomposition strategy to solve complex arithmetic (e.g. two-digit addition). 24 addition problems in two modalities (WA: Written Arithmetic; OA: Oral…

What constitutes effective teaching of arithmetical skills in early school years is still uncertain. Finger use could play a crucial role in this acquisition, but some children do not use them spontaneously and studies would be necessary to know if it is possible to teach them. This research assesses the impact of a teacher-implemented…

This study investigated income group differences in kindergartners' and first graders' (N = 161) arithmetic by examining the link between accuracy and strategy use on simple and complex addition problems. Low-income children were substantially less accurate than high-income children, in terms of both percentage of correctly solved problems and the…

Arithmetic word-problem solving is an important component of elementary mathematics curricula that links school mathematics to real-life problem solving. The present 3-year longitudinal study examined children's arithmetic word-problem solving through understanding its 2 component processes: number-sentence construction and computation. Chinese…

The aim of this paper is to investigate the role that auxiliary means (manipulatives such as cubes and representations such as number line) play for kindergartners in working out mathematical tasks. Our assumption was that manipulatives such as cubes would be used by kindergartners easily and successfully whereas the number line would be used by…

"Number Talks" is: (1) A five- to fifteen-minute classroom conversation around purposefully crafted computation problems that are solved mentally; and (2) The best part of a teacher's day. Whether you want to implement number talks but are unsure of how to begin or have experience but want more guidance in crafting purposeful problems, this…

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…

"Focus in Grade 1: Teaching with Curriculum Focal Points" describes and illustrates learning paths for the mathematical concepts and skills of each grade 1 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate…

Students struggling with mathematics may benefit from early interventions aimed at improving their mathematics ability and ultimately preventing subsequent failure. This guide provides eight specific recommendations intended to help teachers, principals, and school administrators use Response to Intervention (RtI) to identify students who need…