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…

This study compared the effectiveness of a diagrammatic and a keyword method of teaching mathematics problem solving to 70 learning-disabled junior high school students. Results indicated no significant difference between problem-solving performance by students taught with different methods. Potential factors explaining inconsistencies between…

An explicit strategy method developed from a composite of basal arithmetic texts was used for mathematics problem-solving instruction for a group of fourth graders. Posttest results were positive. Implications for teaching mathematics problem solving to low performing students are discussed. (Author/DF)

The purpose of this research was to design and evaluate a computer based adaptive strategy for teaching mathematics. Results indicated preference for materials with personalized examples for motivation and meaningful learning of problem solving procedures. Practical advantages of the computer-based model for adapting instruction are also…

This report presents results from the "Ready To Learn" Prekindergarten Transmedia Mathematics Study, a principal part of the summative evaluation of "Ready To Learn," which is a partnership between the US Department of Education, the Corporation for Public Broadcasting, and PBS. Researchers found that preschool children who…

This study employed a cluster randomized trial design to evaluate the effectiveness of a research-based intervention for improving the mathematics education of very young children. This intervention includes the "Building Blocks" mathematics curriculum, which is structured in research-based learning trajectories, and congruous…

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…

John Saxon's incremental development model has been proclaimed as a superior teaching strategy for mathematics. This study evaluated the Saxon approach and textbook using 276 Algebra I students in experimental and control groups. The groups were compared in cognitive and affective areas. Results are presented. (Author/MT)

We report the results of a preregistered, cluster randomized controlled trial of a mathematics learning intervention known as interleaved practice. Whereas most mathematics assignments consist of a block of problems devoted to the same skill or concept, an interleaved assignment is arranged so that no 2 consecutive problems require the same…

In a randomized field trial with 2,850 seventh-grade mathematics students, we evaluated whether an educational technology intervention increased mathematics learning. Assigning homework is common yet sometimes controversial. Building on prior research on formative assessment and adaptive teaching, we predicted that combining an online homework…

Background: A key learning outcome in problem-solving domains is the development of procedural flexibility, where learners know multiple procedures and use them appropriately to solve a range of problems (e.g., Verschaffel, Luwel, Torbeyns, & Van Dooren, 2009). However, students often fail to become flexible problem solvers in mathematics. To…

Analyses of literacy and numeracy levels worldwide by the Organisation for Economic Cooperation and Development suggest that the U.S. population has one of the lowest numeracy levels among developed nations. Sixty-four percent of American adults are unable to use math and interpret math problems that most higher-level jobs require, and a full 30…

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…

Researchers and practitioners indicate students require explicit instruction on mathematics vocabulary terms, yet no study has examined the effects of an embedded vocabulary component within mathematics tutoring for early elementary students. First-grade students with mathematics difficulty (MD; n = 98) were randomly assigned to addition tutoring…