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IES Grant

Title: MathByExample: Dislodging Misconceptions Before They Take Root
Center: NCER Year: 2015
Principal Investigator: Donovan, Suzanne Awardee: Strategic Education Research Partnership (SERP) Institute
Program: Science, Technology, Engineering, and Mathematics (STEM) Education      [Program Details]
Award Period: 4 years (7/1/2015-6/30/2019) Award Amount: $1,499,889
Type: Development and Innovation Award Number: R305A150456

Co-Principal Investigator: Julie Booth (Temple University)

Purpose: The purpose of this project is to develop and test the promise of MathByExample, an intervention targeting key mathematics concepts and common misconceptions for students in Grades 4 and 5. The current project builds on a previous IES funded project (Transforming Algebra Assignments) , AlgebraByExample, which targeted key algebraic concepts for middle school and high school students. Findings from the AlgebraByExample pilot study revealed that many student misconceptions and errors in mathematics have their roots in earlier grades. To help address mathematics misconceptions before students begin to learn algebra, the researchers will develop a downward extension of the AlgebraByExample intervention for students in Grades 4 and 5.

Project Activities: The researchers will develop and test a set of mathematics assignments for Grades 4 and 5 that includes examples of solved math problems designed to directly target key concepts and common student misconceptions, and practice problems for students to solve with prompts for student explanation.

Products: The products of this project include a set of assignments for Grades 4 and 5 targeting key mathematics concepts and common student misconceptions and teacher resources for implementing the assignments. Researchers will also produce peer-reviewed publications.

Structured Abstract

Setting: Researchers will develop and test the intervention in suburban school districts in North Carolina, Illinois, and Massachusetts, and an urban school district in Maryland.

Sample: During the initial development phase of the project, two to three teachers per participating school district will help develop and refine the intervention. When testing the feasibility and promise of the intervention, 30 teachers and their students each in Grades 4 and 5 will participate in the study. Participating schools are diverse in their racial, ethnic, and socioeconomic characteristics.

Intervention: MathByExample materials will consist of seven blocks of assignments each for Grades 4 and 5. Each assignment block will consist of four to six individual assignments. The assignments will consist of approximately eight items, with items alternating between solved math problems and practice problems to solve. In a worked example, students are asked to study a problem solution rather than solve a problem themselves. Teachers will mark examples as incorrect or correct and this will be accompanied by prompts that target common misconceptions and errors. The assignments will be integrated into the regular routines of the classroom and existing teachers' practices. They can be administered individually or in groups as a do-now, pretest review, exit ticket, or post-lesson practice.

Research Design and Methods: An iterative development process will be used with feedback collected from teachers, mathematics experts, and students to inform revisions. In Year 1, each 5th grade assignment block will be tested with three pairs of participating teachers. Within each pair of teachers, one will be randomly assigned to participate in the MathbyExample condition, and the other teacher will be assigned to the control condition. Later in the school year, the teachers will implement a second study block, with the assignment to experimental and control conditions switched (e.g., the teachers in the MathByExample condition will now be in the control condition during the second study block and vice versa). During Year 2, the researchers will use the same methods to develop and test the Grade 4 assignments.

Pilot studies will be conducted in Year 2 for the developed Grade 5 MathByExample materials and in Year 3 for the developed Grade 4 MathbyExample materials. The pilot study will be a year-long randomized control trial in classrooms to test whether using the entire set of assignment blocks for Grades 4 and 5 will significantly improve student learning and algebra readiness. Thirty teachers and their students at each grade level will be randomly assigned to the MathbyExample condition or to the control condition. Data will be collected before, during, and after a set of assignments are administered.

Control Condition: The control condition for the pilot studies will be students receiving business-as-usual instruction and assignments in mathematics.

Key Measures: Key student outcome measures include researcher developed measures assessing students' procedural and conceptual knowledge of mathematics concepts, an algebra readiness assessment. Other measures include released math items from the standardized tests used by the participating school districts, student motivation questionnaires, and classroom observations will also be used.

Data Analytic Strategy: Surveys and process data collected as part of the iterative development process will be analyzed using descriptive statistics. Data from the pilot study to assess the promise of the intervention will be analyzed using a two level hierarchical linear model with students nested within classrooms.

Related IES Projects: Transforming Algebra Assignments (R305A100150)


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

Select Publications

Book chapters

Booth, J.L (2017). Translating knowledge of children's thinking to improve education. In P. Lemaire (Ed.), Cognitive Development from a Strategy Perspective: A Festschrift for Robert Siegler.

Journal articles

Booth, J.L., McGinn, K.M., Young, L.K., & Barbieri, C. (2015). Simple practice doesn't always make perfect evidence from the worked example effect. Policy Insights from the Behavioral and Brain Sciences, 2 (1): 24–32. Full text

McGinn, K., Young, L., & Booth, J. (2019). Self-explanation prompts explained. Australian Primary Mathematics Classroom, 24(4), 18–22. Full text


McGinn, K.M., Booth, J.L., & Young, L. K. (2017). The interaction of worked-examples/self-explanation prompts and time on algebra conceptual knowledge. In Proceedings of the 39th Annual Meeting of the Cognitive Science Society (pp. 2687–2692). Full text