The main purpose of this study was to test the effects of word-problem (WP) intervention, with versus without embedded language comprehension (LC) instruction, on at-risk 1st graders' WP performance. We also isolated the need for a structured approach to WP intervention and tested the efficacy of schema-based instruction at 1st grade. Children (n…

The purpose of this study was to explore the efficacy of fractions intervention with and without an embedded self-regulation (SR) component for third-grade students at risk for mathematics disabilities. Fractions intervention focused on magnitude understanding and word problems. Embedded SR was designed to support a growth mindset (fostering…

The purpose of this study was to explore the efficacy of fractions intervention with and without an embedded self-regulation (SR) component for third-grade students at risk for mathematics disabilities. Fractions intervention focused on magnitude understanding and word problems. Embedded SR was designed to support a growth mindset (fostering…

Despite recent advances in the development of instructional interventions, many students with significant learning problems do not benefit from them. This includes 25% to 50% of students with learning disabilities (LD). In this article, we identify five limitations of current instructional programs that may help to explain students' inadequate…

The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and prealgebraic knowledge. We extended the literature, which is dominated by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other…

The primary purpose of this study was to assess the effects of strategic counting instruction, with and without deliberate practice with those counting strategies, on number combination (NC) skill among students with mathematics difficulties (MD). Students (n = 150) were stratified on MD status (i.e., MD alone versus MD with reading difficulty)…

The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders' word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which…

This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3…

Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting third graders' development of mathematics problem solving. In the fall, 122 third-grade students were…

The purposes of this study were to assess the effects of schema-based instruction (SBI) in promoting mathematical problem solving and to investigate schema induction as a mechanism in the development of mathematical problem solving. Twenty-four 3rd-grade teachers, with 366 students, were assigned randomly to conditions that provided instruction on…

This article describes "Hot Math," a third-grade intervention conducted with small groups of students with disabilities or in inclusive classrooms that fosters mathematical problem solving. Hot Math integrates two promising practices to promote mathematical problem solving, explicit instruction about transfer and self-regulation strategies.…

A small-group mathematical problem-solving tutorial treatment with explicit instruction including transfer to novel problems was evaluated with 40 students. On word problems and transfer word problems, tutoring effected reliably stronger growth, although effects on real-world problem solving, while moderate to large, were not statistically…

The focus of this article is intervention for third-grade students with serious mathematics deficits at third grade. In third grade, such deficits are clearly established, and identification of mathematics disabilities typically begins. We provide background information on two aspects of mathematical cognition that present major challenges for…

The purpose of this study was to assess the effects of schema-broadening instruction (SBI), with and without explicit instruction in strategies for tackling the complexities involved in real-life (RL) math problems, on the math problem solving of third-grade students. Teachers (n = 30) were assigned randomly to 3 16-week conditions: control, SBI,…

Mathematical problem solving is a transfer challenge requiring children to develop schemas for recognizing novel problems as belonging to familiar problem types for which they know solutions. Schema-based transfer instruction (SBTI) explicitly teaches transfer features that change problems in superficial ways to make them appear novel even though…