A Synthesis of Empirical Research on Teaching Mathematics to Low-Achieving Students

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NICHCY’s Structured Abstract 16 describes the following:

Title | A Synthesis of Empirical Research on Teaching Mathematics to Low-Achieving Students

Authors | Baker, S., Gersten, R., & Lee, D.

Source Elementary School Journal, 103, 45-74.

Year Published | 2002

The purpose of this study was to synthesize research on the effects of interventions to improve the mathematics achievement of students considered low achieving or at risk for failure. Meta-analytic techniques were used to calculate mean effect sizes* for 15 studies that met inclusion criteria. Studies were coded according to 5 categories of mathematics interventions, and effect sizes were examined on a study-by-study basis within each of these categories. Results indicated that different types of interventions led to improvements in the mathematics achievement of students experiencing mathematics difficulty, including the following:

  • providing teachers and students with data on student performance;
  • using peers as tutors or instructional guides;
  • providing clear, specific feedback to parents on their children’s mathematics success; and
  • using principles of explicit instruction in teaching math concepts and procedures.

Mathematics ability plays an important role in daily living skills, college success, and a large number of careers. However, Americans of all ages struggle with math. The National Center for Education Statistics has reported that more than 90% of 17-year-olds struggle with multistep math problems and algebra; students who do not take algebra or geometry are far less likely to go to college than their peers who do (36% vs. 83%). The many students who are low achieving or at risk for failure in mathematics are of great concern to parents, teachers, and school administrators. This meta-analysis specifically focuses on the effectiveness of mathematics interventions designed to help low-achieving and at-risk students.

Research Questions
How effective are interventions designed to improve the achievement of students considered low achieving or at risk for failure in mathematics?

Research Design

  • Number of Studies Included | 15
  • Number of Subjects | N/A
  • Years Spanned | 1986-1999

Research Subjects
Students who were low achieving or at risk for failure in mathematics.

Age/Grade of Subjects
The majority of participants in these studies were in elementary school, though a few were in 7th to 9th grade.

Specified Disability
Low achieving or at risk for failure in mathematics.

A variety of mathematics interventions were examined, including:

  • Direct Instruction/Explicit Instruction: Teaching rules, principles, problem-solving methods, and math concepts in a systematic, structured fashion.
  • Contextualized Instruction: Focusing on real-world applications of mathematics and teaching the concepts behind mathematical problem-solving.
  • Parent Support Intervention: Communicating a student’s successes in mathematics to his or her parents through notes or phone calls.
  • Data/Recommendations to Teachers and Students: Providing data on student performance and, in some cases, recommendations about what kind of problems students need to work on as well.
  • Peer-Assisted Learning: Peer tutoring and other interventions where students are taught to help their classmates, answer questions for each other, and work together on mathematics assignments.

Duration of Intervention
All interventions lasted 90 minutes or more.


  • Providing students and teachers with feedback about how students were performing and what areas they needed to work on was an effective way of improving low-achieving or at-risk students’ math performance.
  • Peer-assisted learning was an effective way of improving student scores on computation problems, but on general math achievement the effect was mixed.
  • Direct or explicit instruction had a moderately strong effect on mathematics achievement.
  • Contextualized instruction showed mixed results that proved difficult to interpret.
  • Providing parents with feedback on their child’s math successes yielded small yet significant results in student achievement.

Combined Effects Size

  • Direct instruction/explicit instruction had a weighted effect size* of 0.58.
  • Contextualized instruction’s effect size was not significantly different from zero (d = 0.01).
  • Parent support interventions had an effect size of 0.42.
  • Providing data on student performance and, in some cases, making recommendations about what kind of problems they needed to work on yielded an effect size of 0.57.
  • Peer-assisted learning had an effect size of 0.62.

This meta-analysis found that there are several ways of improving the performance of low-achieving or at-risk students in mathematics.

  • One of the most consistently effective ways of improving math achievement for students considered at risk or low achieving is by providing both students and teachers with specific information about each student’s performance.
  • Peer tutoring or guidance was also shown to consistently enhance achievement.
  • Although it does not have as strong an effect as the first 2 methods listed, providing parents of low-achieving math students with specific feedback about their children’s successes in mathematics does positively impact the achievement of children at risk for mathematics failure.
  • A small body of research suggests that direct or explicit instruction techniques can be helpful in teaching math concepts and procedures.
  • Contextualized approaches, which were more recently developed than the other approaches, showed results too mixed to be interpreted at this point. The authors suggest that future research should begin with a more well-defined concept of “conceptualized approaches.” Then, once the best aspects of contextualized approaches have been determined, research should be conducted that combines them with other methods such as direct instruction with the same group of students.


* Terms Defined

Effect Size (ES or d) | A statistical calculation, often represented as ES or d, that measures the impact of an intervention. An effect size below d = 0.20 suggests that a treatment did not have a significant effect. An effect size of d = 0.20 is considered small or low; an effect size of d = 0.50 is considered moderate; an effect size of d = 0.80 or above is large.

Meta-Analysis | A widely-used research method in which (1) a systematic and reproducible search strategy is used to find as many studies as possible that address a given topic; (2) clear criterion are presented for inclusion/exclusion of individual studies into a larger analysis; and (3) results of included studies are statistically combined to determine an overall effect (effect size) of one variable on another.

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