Description:

Purpose: The purpose of this project is to develop and pilot test an intervention for using students' errors to enhance their learning in mathematics, both by focusing instruction on the problem areas that are most in need of attention, and by examining and correcting the missteps that underlie students' errors. Recent research has shown that committing errors, as long as those errors are corrected, enhances learning as compared to error-free learning. The research team will address how to use errors effectively during practice and preparation for a test and will develop a set of materials to support the successful implementation of the learning from errors approach. This approach will be tested in courses designed to prepare middle and high school students for upcoming algebra and geometry tests.

Project Activities: In Year 1, the research team will conduct an initial pilot test to compare the learning from errors approach to business as usual instruction in algebra test preparation classrooms, and then will revise and improve the intervention based on the study's data as well as feedback from teachers. In Year 2, the research team will conduct another study in algebra test preparation classrooms using the revised intervention, and will again revise and improve the intervention based on the study's data and feedback from teachers. In Year 3, the research team will conduct a study with the revised intervention in geometry test preparation classrooms to see if the approach successfully extends to a new content area.

Products: This project will result in a fully developed set of materials designed to support the learning from errors approach and peer-reviewed publications.

Structured Abstract

Setting: Participating schools include urban middle and high schools in New York.

Sample: The Year 1 study will include 96 eighth grade students who will be taking the Algebra I (Common Core) Regents test. The Year 2 study will involve 96 eighth grade students and 96 ninth grade students who will be taking the Algebra I (Common Core) Regents test. The Year 3 study will include 96 ninth grade students who will be taking the Geometry (Common Core) Regents test.

Intervention: The research team will develop an intervention for using errors to help learning that will result in improved scores. The materials will include written and video descriptions of how to construct a profile of errors to identify areas where students are struggling as well as instruction and video demonstrations of intensive error-focused practice test feedback sessions to improve students' understanding of where they need the most help. In addition, there will be resources for how to address students' problem areas, including scripts for teachers to encourage students to view errors as opportunities for learning. The implementation will initially focus on the Algebra I (Common Core) Regents test, but in Year 3, it will be extended to the Geometry (Common Core) Regents test.

Research Design and Methods: In Year 1, the research team will conduct an initial pilot experiment that will compare the learning from errors approach to business as usual instruction in algebra test preparation classrooms. Participating students will be randomly assigned to one of four after-school test preparation classes. Two classes will receive the learning from errors intervention and two classes will receive business as usual instruction. All students will take pre-tests of their algebra knowledge as well as their attitudes towards errors at the start of the school year. Students will take a previously released Regents test on the first day of their test preparation class. Teachers will administer test preparation instruction based on condition, and test preparation sessions will be videotaped. The research team will collect students' end-of-year Algebra Regents test scores and state expected scores. In Year 2, the research team will conduct an implementation study that will include the same procedures as the Year 1 study; however, all students will receive the learning from errors intervention in their test preparation classes. In Year 3, the research team will conduct an implementation study similar to the Year 2 study, with the only difference being that the class will focus on preparation for the Geometry Regents test.

Control Condition: The Year 1 study will include a 'business as usual' comparison condition in which classroom teachers will complete standard after-school test preparation. The Year 2 and Year 3 studies do not include a control condition.

Key Measures: The primary measure for the studies in Years 1 and 2 will be students' performance on the Algebra Regents test (studies in Years 1 and 2). The primary measure for the Year 3 study will be students' performance on the Geometry Regents test. Across all studies, videos will be coded to examine and improve fidelity of implementation of the learning from errors approach.

Data Analytic Strategy: The research team will use a general linear model approach to analyze the data in this project. In the Year 1 study, students will be randomly assigned to condition, but teachers will not be randomly assigned. Consequently, teachers will be treated as fixed effects in the analysis. For the studies in Years 2 and 3, each child's expected performance score will be included as a covariate to examine whether the learning from errors approach improves scores over and above what is expected based on their background characteristics.

Products and Publications

Journal article, monograph, or newsletter

Metcalfe, J. (2017). Learning from Errors. Annual Review of Psychology, 68: 465–489.

Metcalfe, J. and Xu, J. (2017). Learning from One's Own Errors and Those of Others. Psychonomic Bulletin and Review.

Metcalfe, J., Schwartz, B.L., Bloom, P.A. (2017). Using Assessment to Individualize Early Mathematics Instruction. Cognitive Research: Principles and Implications, 2: 31.