Co-Principal Investigator: Barnes, Marcia

Purpose: The purpose of this efficacy study was to assess whether equation-solving instruction, conducted within the context of word-problem tutoring, led to improved word-problem solving outcomes. Word-problem proficiency is necessary to demonstrate successful mathematics performance. Many students, however, are inadequately prepared to solve word problems, and this is especially true for students with or at risk for mathematics difficulty (MD). Students with or at risk for MD demonstrate significantly lower word-problem performance and make significantly more errors when solving word problems than peers without MD. Given the importance of word-problem competency and the need to enhance this skill in students with MD, there is a critical need to determine the efficacy of word-problem interventions for students with MD.

Project Activities: The research team conducted a randomized controlled trial with third grade students with or at risk for MD using three conditions—two competing word-problem tutoring programs (with and without equation-solving instruction) and business-as-usual comparison—to examine the impact of the tutoring program on student word-problem solving abilities and the maintenance of these outcomes the following year.

Key Outcomes: The main findings of this project, as reported by the principal investigator, are as follows:

• Grade 3 students with or at risk for MD who participated in either word-problem tutoring program demonstrated a significant advantage at posttest on word-problem outcomes over students who did not participate in tutoring.
• Grade 3 students who participated in the word-problem tutoring with equation-solving instruction demonstrated a slight advantage in word-problem solving compared to students who participated in word-problem tutoring without equation-solving instruction. Additional analyses indicated that equal-sign understanding led to improved equation solving which, in turn, led to improve word-problem solving.
• On follow-up measures administered in grade 4, students who participated in word-problem tutoring demonstrated a continued advantage on word-problem outcomes compared to students in the control group, although the persistence of effects was limited to the equation-solving group.
• Passage comprehension and numbers reversed emerged as moderators, with higher pre-test scores leading to greater gains for certain groups. However, because the results of moderation analyses differed across intervention groups, the specific pattern of results may not be replicated with another sample.

Structured Abstract

Setting: The research took place in elementary schools in an urban area of Texas.

Sample: The study sample included third grade students with or at risk for MD, as determined by scoring below the 25th percentile on a word-problem measure. There were approximately 150 students recruited each year for 3 years, for a total of 456 students in the study.

Intervention: The interventions included two versions of a tutoring program focused on mathematics word problems. Because research indicates that using mathematical equations (e.g., 7 – __ = 5) to represent word problems is effective in enhancing word-problem performance for students with MD, one version of the intervention consisted of a combination of equation-solving and word-problem instruction, whereas the other version focused on word-problem instruction alone.

Research Design and Methods: This study was a randomized controlled trial in which students with MD were assigned to one of two competing word-problem tutoring programs (word-problem tutoring with and without equation-solving instruction) or a business-as-usual condition. The research team examined whether improvements in equation solving promoted superior word-problem performance as well as the role of equation solving as a mediator of word-problem performance. In addition, the research team investigated whether reading accuracy, reading fluency, passage comprehension, listening recall, counting recall, nonverbal reasoning, verbal reasoning, numbers reversed, and perceptual speed moderated the impact of the intervention on student outcomes.

Control Condition: Students in the business-as-usual comparison condition received mathematics instruction as established by their teacher and school. These students received small-group or individual tutoring as part of their special education or general mathematics curriculum.

Key Measures: To test the effects of equation instruction within word-problem tutoring, students were assessed on a variety of proximal and distal outcomes, including measures of word-problem solving, equation solving, calculations, computation, and quantitative concepts. These measures included Single-Digit Word Problems, Texas Word Problems, Equal Sign Tasks, and Open Equations. The following were included as potential moderators of word-problem solving: reading accuracy (Wide Range Achievement Test-Fourth Edition, Word Reading subtest); reading fluency (Test of Word Reading Efficiency-Second Edition); passage comprehension (Woodcock Johnson-Fourth Edition-WJIV, Passage Comprehension subtest); listening recall and counting recall (Working Memory Test Battery for Children, Listening Recall and Counting Recall subtests); nonverbal reasoning and verbal reasoning (Wechsler Abbreviated Scale of Intelligence-Second Edition, Matrix Reasoning, Vocabulary, and Similarities subtests); numbers reversed (WJIV, Numbers Reversed subtest); and perceptual speed (WJIV, Pair Cancellation and Letter-Pattern Matching). Fidelity of implementation was assessed using an observational checklist in the two active tutoring conditions and in the control condition.

Data Analytic Strategy: The study employed multilevel, partially nested, cross-classified models to test for the effects of study condition.

Related IES Projects: The Role of Algebraic Reasoning Within Additive and Multiplicative Multi-Step Problem Solving for Students With Mathematics Difficulty (Project RAAMPS) (R324A200176)

Products and Publications

ERIC Citations: Find available citations in ERIC for this award here.

Publicly Available Data: https://www.piratemathequationquest.com

WWC Review: Powell, S. R., Berry, K. A., & Barnes, M. A. (2020). The role of pre-algebraic reasoning with a word-problem intervention for third-grade students with mathematics difficulty. ZDM Mathematics Education, 52(1), 151–163. [WWC Report]

Project Website: https://www.piratemathequationquest.com