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IES Grant

Title: Enhancing the Mathematical Problem Solving Performance of Sixth Grade Students Using Schema-based Instruction
Center: NCER Year: 2006
Principal Investigator: Jitendra, Asha Awardee: University of Minnesota
Program: Science, Technology, Engineering, and Mathematics (STEM) Education      [Program Details]
Award Period: 3 years Award Amount: $1,432,796
Goal: Development and Innovation Award Number: R305K060002
Description:

Previous Grant Number: R305K060075
Previous Institution: Lehigh University

Purpose: Data indicate that by the eighth grade, U.S. students' mathematics performance is below the international average, especially in geometry, measurement, and proportionality. The problem of underachievement is particularly severe for high-risk groups, such as low-income and limited-English proficient students. Although there is emerging evidence to support reform based mathematics methods and curricula, data regarding the impact of these reforms for students at-risk for math failure are limited. The purpose of this study is to develop and evaluate the potential impact of schema-based instruction to enhance the mathematical problem solving performance of sixth grade students.

Project Activities: The researchers will develop an instructional intervention that focuses on critical concepts (e.g., ratios, proportions) and relations (e.g., multiplication and division) needed to understand mathematics content and to solve a range of problems encountered in everyday life. Specifically, the researchers will develop a set of lessons to promote students' understanding of problems involving multiplicative relations using Schema-Based Instruction. This intervention will use teacher-led discussions to show students how to symbolically represent problems using schematic diagrams, because many students fail to see or recognize the categorizations of multiplicative problems, and to understand that situations appearing as new can be understood using the categorizations offered by the schematic approach.

Products: The expected outcomes from this project include an empirically validated mathematics instructional approach for sixth grade students, and published papers.

Setting: The research will be conducted in Pennsylvania.

Population: Participants will be sixth graders from a middle school in a diverse, urban district. The school includes 27 sixth grade classrooms. Within the school, 25% of the students qualify for free or reduced lunch, and 31% are from minority backgrounds.

Intervention: The researchers will develop an instructional intervention that focuses on critical concepts (e.g., ratios, proportions) and relations (e.g., multiplication and division) needed to understand mathematics content and to solve a range of problems encountered in everyday life. Specifically, the researchers will develop a set of lessons to promote students' understanding of problems involving multiplicative relations using Schema-Based Instruction. This intervention will use teacher-led discussions to show students how to symbolically represent problems using schematic diagrams, because many students fail to see or recognize the categorizations of multiplicative, and to understand that situations appearing as new can be understood using the categorizations offered by the schematic approach. In addition, the project will include a manipulation of instructional intensity (e.g., ad hoc small group tutoring) that is known to moderate learning outcomes for students who are at-risk for math difficulties.

Research Design and Methods: The researchers will conduct experimental studies with 27 sixth grade teachers randomly assigned to experimental and control conditions to examine not only learning outcomes for all students, but also differential student effects. Specifically, the researchers will use pretest and posttest data to examine the impact of the problem-solving curriculum for levels of initial student ability status in the classrooms. In addition to randomly assigning teachers to conditions, the researchers will also match experimental and comparison classrooms on pretest data, and key demographic and variables.

Control Condition: Teachers in the comparison condition will implement problem-solving instruction on the same topics (e.g., multiplication) using the district adopted sixth grade textbook.

Key Measures: Key outcome measures include performance on word problem-solving tests, and on the Mathematics Problem Solving and Procedures Subtests of the Stanford Achievement Test-Tenth Edition.

Data Analytic Strategy: This development project is intended only to obtain evidence of the potential impact of the intervention; initial analyses will be at the level of the student.

Project Website: http://www.cehd.umn.edu/EdPsych/MARS/About.html

Related IES Projects:Learning of Ratio and Proportion Problem-Solving Using Schema-Based Instruction: Efficacy and Sustainability (R305A110358)

Publications

Book chapter

Jitendra, A.K., Woodward, J., and Star, J.R. (2011). Middle School Students' Thinking About Ratios and Proportions. In R. Gersten, and R. Newman-Gonchar (Eds.), Understanding RTI in Mathematics (pp. 127–150). Baltimore, MD: Paul H. Brookes.

Journal article, monograph, or newsletter

Jitendra, A.K., and Star, J.R. (2011). Meeting the Needs of Students with Learning Disabilities in Inclusive Mathematics Classrooms: The Role of Schema-Based Instruction on Mathematical Problem-Solving. Theory into Practice, 50(1): 12–19.

Jitendra, A.K., and Star, J.R. (2012). An Exploratory Study Contrasting High- and Low-Achieving Students' Percent Word Problem Solving. Learning and Individual Differences, 22(1): 151–158.

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., Lein, A.E., Star, J.R., and Dupuis, D.N. (2013). The Contribution of Domain-Specific Knowledge in Predicting Students' Proportional Word Problem-Solving Performance. Educational Research and Evaluation, 19(8): 700–716.

Jitendra, A.K., Star, J.R., Dupuis, D.N., and Rodriguez, M. (2013). Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students' Proportional Reasoning: A Randomized Experiment. Journal of Research on Educational Effectiveness, 6(2): 114–136.

Jitendra, A.K., Star, J.R., Rodriguez, M., Lindell, M., and Someki, F. (2011). Improving Students' Proportional Thinking Using Schema-Based Instruction. Learning and Instruction, 21(6): 731–745.

Jitendra, A.K., Star, J.R., Starosta, K., Leh, J.M., Sood, S., Caskie, G., Hughes, C.L., and Mack, T.R. (2009). Improving Seventh Grade Students' Learning of Ratio and Proportion: The Role of Schema-Based Instruction. Contemporary Educational Psychology, 34(3): 250–264.

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.


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