Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…

Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…

The labels used to describe patterns and relations can influence children's relational reasoning. In this study, 62 preschoolers (M[subscript age] = 4.4 years) solved and described eight pattern abstraction problems (i.e., recreated the relation in a model pattern using novel materials). Some children were exposed to concrete labels (e.g.,…

Decades of research have emphasized the need for engaging, accessible ways to help students learn fundamental mathematical concepts. Research also shows that teacher beliefs about teaching and learning have an outsized influence on the quality and effectiveness of curricular interventions. This article reports results of an independent evaluation…

This paper discusses the implementation and evaluation of an innovative professional development program that supported 8th grade mathematics teachers in designing learning activities that assisted students in developing a conceptual understanding of mathematics. Funded by an Investing in Innovation (i3) grant from the U.S. Department of…

The main purposes of this study were to test the effects of teaching at-risk 4th graders to provide explanations for their mathematics work and examine whether those effects occur by compensating for limitations in cognitive processes. We randomly assigned 212 children to 3 conditions: a control group and 2 variants of a multicomponent fraction…

Educators often use manipulatives when teaching mathematics because manipulatives are assumed to promote learning. However, research indicates that instructional variables impact the effectiveness of manipulatives. In this article, the authors consider the relations between two instructional characteristics: (a) level of instructional guidance and…

In a series of two in vivo experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly assigned…

The purpose of this study was to examine the hypothesis that helping preschoolers learn words through categorization may enhance their ability to retain words and their conceptual properties, acting as a bootstrap for self-learning. We examined this hypothesis by investigating the effects of the World of Words instructional program, a supplemental…

Researchers in both cognitive science and mathematics education emphasize the importance of comparison for learning and transfer. However, surprisingly little is known about the advantages and disadvantages of what types of things are being compared. In this experimental study, 162 seventh- and eighth-grade students learned to solve equations (a)…

This study examined the effects of an intensive shared book-reading intervention on the vocabulary development of preschool children who were at risk for vocabulary delay. The participants were 125 children, who the researchers stratified by classroom and randomly assigned to one of two shared book-reading conditions (i.e., the experimental, Words…

Encouraging students to share and compare solution methods is a key component of reform efforts in mathematics, and comparison is emerging as a fundamental learning mechanism. To experimentally evaluate the effects of comparison for mathematics learning, the authors randomly assigned 70 seventh-grade students to learn about algebra equation…

We compared alternative instructional strategies for integrating knowledge of decimal place value and regrouping concepts with procedures for adding and subtracting decimals. The first condition was based on recent research suggesting that conceptual and procedural knowledge develop in an iterative, hand over hand fashion. In this iterative…

This project entailed a three-year efficacy evaluation of the Computer and Team Assisted Mathematical Acceleration (CATAMA) Lab developed by the Center for Social Organization of Schools at Johns Hopkins University. The CATAMA Lab was proposed as an immediate and practical approach to addressing the different types of math deficits held by…

This research was designed to investigate several primary questions in comparing the Logo floor turtle to the Logo screen turtle: (1) Do young children gain different geometric concepts from experiences with the floor turtle than they do with the screen turtle? (2) Do young children learn to use the four basic Logo commands more efficiently with…