Co-Principal Investigator: Doabler, Christian

Purpose: The purpose of this initial efficacy study is to assess whether algebraic reasoning instruction, conducted within the context of word-problem intervention, leads to increases word-problem performance on one- and multi-step word problems. Research indicates students with mathematics difficulty (MD) demonstrate lower performance on setting up and solving word problems compared to peers without MD. The use of schemas has been shown to be an effective method of word-problem instruction for students with MD. Schemas represents the underlying structure of a word problem. With schema instruction, students can use mathematical equations (e.g., 45 – ? = 12) to represent the word problem and then use algebraic reasoning to solve the word problem. This study will show whether a word-problem intervention with embedded algebraic reasoning (RAAMPS) or a word-problem intervention without embedded algebraic reasoning (AMPS-without-AR) is more effective than business-as-usual instruction.

Project Activities: The researchers will recruit 150 students with MD each year for the first three years of the project. They will randomly assign students with MD to one of three conditions: word-problem intervention with algebraic reasoning instruction (RAAMPS); word-problem intervention without algebraic reasoning instruction (AMPS-without-AR); or business-as-usual comparison (i.e., no tutoring from research staff). Researchers will collect data to test the hypothesis that students who receive embedded algebraic reasoning instruction solve math equations derived from word problems more efficiently, and this, in turn enhances word-problem performance. They will also determine the cost effectiveness of this intervention.

Products: Products include information about the efficacy of RAAMPS over AMPS and business-as-usual for improving word-problem outcomes for students with MD. Dissemination products include a project website where the materials will be available in PDF format for interested teachers or other stakeholders to download and use. These print materials will be supplemented by videos that describe the tutoring program and provide examples of use of the tutoring materials. The project will also result in a released final data set, peer-reviewed publications and presentations as well as additional dissemination products that reach education stakeholders such as practitioners and policymakers.

Structured Abstract

Setting: The research will take place in elementary schools in Texas.

Sample: The sample includes approximately 450 fourth-grade students with or at-risk for mathematics difficulty (MD; defined as students who score below the 15th percentile on two word-problem measures). Researchers will recruit 150 participants each year for 3 years.

Intervention: The RAAMPS program is a 4th grade word-problem schema intervention focused on promoting students' solving of additive and multiplicative one- and multi-step word problems. The use of schemas has been shown to be an effective method of word-problem instruction for students with MD. In this intervention 5 critical schemas are used: total, difference, change, equal groups, and comparison. The fully-developed intervention is comprised of 48 sessions delivered in a one-to-one instructional format. Each session is delivered in 30-min sessions, 3 sessions per week for 16 weeks. Promoted within each session is students' use of precise math language and vocabulary. Beginning in week 1, students are introduced to an effective attack strategy for solving word problems. The algebraic reasoning component within RAAMPS is focused on promoting students' understanding of the equal sign as well as generating and solving equations. The algebraic reasoning component is embedded within each RAAMPS session.

Research Design and Methods: This study is a randomized-controlled efficacy trial in which students with MD are randomly assigned to 1 of 3 conditions: 2 competing word-problem interventions (designed to isolate the effects of algebraic reasoning with equation writing and equation solving) or a business-as-usual comparison. The researchers conduct the intervention under ideal conditions. Data is collected on student mathematics outcomes and reading scores to be used as moderators in data analyses. The data from the three years of student participants are combined for the analysis of the efficacy of the intervention.

Control Condition: Students in the business-as-usual comparison condition receive mathematics instruction as established by their teacher.

Key Measures: Researchers use a research developed word-problem screener and the standardized KeyMath3, Applied Problem Solving subtest, to determine if recruited students are students with MD. To assess the effects of the algebraic reasoning component within word-problem intervention, researchers use several researcher developed proximal measures (Word Problem Assessment, Identifying Schemas, Test of Equal Sign Understanding, Assessment of Equation Solving, and Order of Operations Assessment) and distal measures (KeyMath 3,Applied Problem Solving subtest; Iowa Test of Basic Skills, Math Problem Solving and Data Interpretation subtest; Test of Mathematical Abilities – Third Edition, Mathematical Symbols and Concepts subtest; Wide Range Achievement Test-5 (WRAT), Math Computation subtest). Researchers use two measures of reading to investigate reading scores as a moderator to response to intervention, WRAT-5 Word Reading and Woodcock-Johnson (WJ)-IV Passage Comprehension. Data are also collected on all costs associated with the 2 intervention programs and the business-as-usual comparison.

Data Analytic Strategy: The researchers use multi-level modeling techniques to test for the effects of study condition while appropriately controlling for variance associated with classroom effects. For the cost analysis, we account for all costs associated with the 2 intervention programs and the business-as-usual comparison. Multilevel, partially nested cross-classified models will be used to test the moderating effects of word reading and reading comprehension on word-problem performance. The research team will estimate the costs of the 2 intervention programs and the business-as-usual comparison using the Ingredients approach and the Center for Benefit-Cost Studies in Education's Cost Out Tool Kit to determine national pricing. For the cost-effectiveness analysis, researchers will calculate incremental cost-effectiveness ratios.

Related IES Projects: Developing Connections Between Word Problems and Mathematical Equations to Promote Word-Problem Performance Among Students with Mathematics Difficulty (R324A150078)