Skip Navigation
Funding Opportunities | Search Funded Research Grants and Contracts

IES Grant

Title: Learning of Ratio and Proportion Problem-Solving Using Schema-Based Instruction: Efficacy and Sustainability
Center: NCER Year: 2011
Principal Investigator: Jitendra, Asha Awardee: University of Minnesota
Program: Science, Technology, Engineering, and Mathematics (STEM) Education      [Program Details]
Award Period: 4 years Award Amount: $4,593,808
Type: Efficacy and Replication Award Number: R305A110358

Co-Principal Investigator: Jon Star (Harvard University)

Purpose: The mathematics performance of U.S. students by Grade 8 is below the international average on more advanced mathematics topics including geometry, measurement, and proportionality. One explanation for the lower levels of performance may be students' difficulties with proportional reasoning, which is considered to be a capstone of elementary mathematics and a necessity for the more advanced mathematics that students encounter in high school and college. Building upon work from a prior IES Goal 2 Development grant, the goal of this project is to evaluate the efficacy of an intervention (schema-based instruction or "SBI") aimed at improving 7th grade students' learning of ratio and proportion. The primary objective of this project is to assess the immediate and long-term impact of SBI on students' mathematics problem solving and proportional reasoning. Secondary objectives include: (1) evaluating the immediate and long-term impact of SBI on student outcomes; (2) studying the implementation factors that are associated with effectiveness; (3) assessing SBI and teacher classroom characteristics that moderate the impact of student-level characteristics on mathematical problem solving and proportional reasoning; and (4) evaluating the effects of the intervention on students' metacognitive strategy knowledge and their acceptance of SBI.

Project Activities: Two efficacy studies will be conducted across two sites. In Study 1, the researchers will work with 7th grade students and teachers from small and moderately sized schools and districts in Minnesota (MN). As part of their comparison group, the researchers will also look at rural schools. and 7th grade students and teachers from urban high-needs districts on the east coast (EC) to examine the impact of the intervention. The researchers will randomly assign 100 teachers and their students at each site to either the SBI or control condition. In Study 2, the researchers will evaluate the sustainability of the intervention by examining student learning in SBI-experienced classrooms compared to SBI-novice classrooms for both the MN and EC school sites. Teachers who were in the control condition in Study 1 will be given the SBI intervention during Study 2. These novice SBI teachers will be compared to the experienced SBI teachers from Study 1.

Products: Products will include evidence of the efficacy of SBI to improve students mathematical problem solving and proportional reasoning. Peer reviewed publications will also be produced.

Structured Abstract

Setting: This study will take place in small and moderately sized schools and districts in Minnesota and large urban high need districts on the East Coast of the United States (e.g., Baltimore, Philadelphia, New York City, and Boston).

Population: Approximately 200 seventh-grade teachers and their students, 100 teachers at each site, will participate in the efficacy and sustainability studies.

Intervention: Drawing upon schema theory, SBI is designed to improve students' problem- solving performance by helping students more effectively categorize problems according to their structure and identify the underlying mathematical problem to be solved. Visual representations in the form of schematic representations are used to aid in problem categorization. Further, SBI addresses integrating conceptual knowledge of principles in the domain with procedural knowledge of specific actions for solving problems, flexibility in strategy use, and metacognitive strategy knowledge. The content is organized around two major units Ratios/Proportions and Percent. The SBI intervention is intended to provide students with an understanding of proportions (including ratio, rate, and percent) and specific methods associated with enhanced problem solving performance. The curriculum includes 21 lessons that are completed in 29–30 sessions, with each session lasting approximately 50 minutes in duration. The intervention constitutes about 6 weeks of instruction.

Control Condition: Control group classrooms will receive business-as-usual instruction for mathematical problem solving and proportional reasoning. The amount of instruction provided will be the same as the SBI group (i.e., 6 weeks).

Research Design and Methods: Researchers will use a multi-wave, cluster randomized design with random assignment of classrooms to the treatment group to evaluate the efficacy of the SBI curriculum on student outcomes and teachers' ability to sustain the intervention without ongoing support from the research team.

Key Measures: Researchers will use a project-developed mathematical problem-solving test as the primary outcome measure for pre-, post- and retention-tests. The statewide mathematics tests and the Stanford Open-Ended Assessment in mathematics will serve as additional measures of student achievement. A metacognitive strategy knowledge assessment and a student acceptability survey will provide secondary outcomes measures addressing students' metacognition of the problem-solving process and treatment students' acceptance of the SBI curriculum and its perceived effectiveness. Researchers will also collect teacher-level data using: (a) entrance/exit interviews of teachers' personal and professional backgrounds as well as their perceptions of the professional development and subsequent teaching experiences; and (b) an assessment to measure teachers' mathematical knowledge for teaching the instructional content of the intervention (ratios and proportion).

Data Analytic Strategy: The efficacy of the intervention will be evaluated using a series of hierarchical linear models (HLMs). Specifically, to test the impact of SBI on change in student outcomes over time, a three-level HLM will be used with the pre-test, post-test, and retention outcomes treated as repeated measures that are nested within students who are nested within classrooms/teachers.

Project Website:

Related IES Projects: Enhancing the Mathematical Problem Solving Performance of Sixth Grade Students Using Schema-based Instruction (R305K060002)


Book chapter

Vig, R., Star, J.R., Dupuis, D.N., Lein, A.E., and Jitendra, A.K. (2015). Exploring the Impact of Knowledge of Multiple Strategies on Students' Learning About Proportions. In J.A. Middleton, and J. Cai (Eds.), Large-Scale Studies in Mathematics Education (pp. 61–73). New York: Springer.

Journal article, monograph, or newsletter

Jitendra, A.K., Dupuis, D.N., Star, J.R., and Rogriguez, M.C. (2016). The Effects of Schema-Based Instruction on the Proportional Thinking of Students With Mathematics Difficulties With and Without Reading Difficulties. Journal of Learning Disabilities, 49 (4): 354–367.

Jitendra, A.K., Harwell, M.R., Dupuis, D.N., and Karl, S.R. (2017). A Randomized Trial of the Effects of Schema-Based Instruction on Proportional Problem-Solving for Students With Mathematics Problem-Solving Difficulties. Journal of Learning Disabilities, 50 (3): 322–336.

Jitendra, A.K., Harwell, M.R., Dupuis, D.N., Karl, S. R., Lein, A.E., Simonson, G. & Slater, S.C. (2015). Effects of a Research-Based Intervention to Improve Seventh-Grade Students' Proportional Problem Solving: A Cluster Randomized Trial. Journal of Educational Psychology, 107 (4): 1019–1034.

Jitendra, A.K., Harwell, M.R., Karl, S.R., Dupuis, D.N., Simonson, G., Slater, S.C., and Lein, A.E. (2016). Schema-Based Instruction: Effects of Experienced and Novice Teacher Implementers on Seventh Grade Students' Proportional Problem Solving. Learning and Instruction, 44 : 53–64.

Jitendra, A.K., Harwell, M.R., Karl, S.R., Simonson, G.R., and Slater, S.C (2017). Investigating A Tier 1 Intervention Focused on Proportional Reasoning: A Follow-Up Study. Exceptional Children, 83 (4).

Lein, A.E., Jitendra, A.K., Starosta, K., Dupuis, D.N., Hughes, C., and Star, J. (2016). Assessing the Relation between Seventh-Grade Students' Engagement and Mathematical Problem Solving Performance. Preventing School Failure, 60 (2): 117–123.