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ERIC Number: ED562326
Record Type: Non-Journal
Publication Date: 2015
Reference Count: 24
Improving Procedural Knowledge and Transfer by Teaching a Shortcut Strategy First
DeCaro, Marci S.
Society for Research on Educational Effectiveness
Students often memorize and apply procedures to solve mathematics problems without understanding why these procedures work. In turn, students demonstrate limited ability to transfer strategies to new problem types. Math curriculum reform standards underscore the importance of procedural flexibility and transfer, emphasizing that students need to understand and flexibly adapt strategies when encountering various problem situations. Drawing on research in both education and cognitive psychology, this study tests the theory that initially instructing students on complex algorithms leads them to rigidly apply these procedures, overlooking more efficient shortcut strategies even when they are later introduced. The study was conducted in two private schools in a large urban area. Participants were 54 second- and third-grade children who scored below 50% on a pretest measuring knowledge of math equivalence (age M = 8.05 years, SD = 0.51; 74% female, 15% ethnic minorities). A pretest--intervention--immediate posttest--delayed retention test design was used. Students were randomly assigned to one of two between-subjects conditions. Although students in both conditions completed the exact same learning activities, providing instruction on shortcut strategies first improved students' ability to solve math equivalence problems and transfer concepts and procedures to solve novel, difficult problems. Students also demonstrated greater procedural flexibility, when measured as greater use of multiple, correct strategies. However, differences between conditions were not found on a separate procedural flexibility subscale, or on a measure of conceptual knowledge. Taken together, these findings provide strong initial support for the proposed theory and use of a shortcut-first intervention, and stand in stark contrast to the traditional method of instructing students on complex strategies first. Future research is needed to determine if the benefits of this method of supporting procedural knowledge, flexibility, and transfer in early algebra learning extends to more complex algebra learning in later school years. Tables and figures are appended.
Descriptors: Teaching Methods, Transfer of Training, Mathematics Instruction, Problem Solving, Learning Strategies, Private Schools, Urban Schools, Elementary School Mathematics, Elementary School Students, Grade 2, Grade 3, Pretests Posttests, Arithmetic, Intervention
Society for Research on Educational Effectiveness. 2040 Sheridan Road, Evanston, IL 60208. Tel: 202-495-0920; Fax: 202-640-4401; e-mail: firstname.lastname@example.org; Web site: http://www.sree.org
Publication Type: Reports - Research
Education Level: Elementary Education; Grade 2; Primary Education; Early Childhood Education; Grade 3
Authoring Institution: Society for Research on Educational Effectiveness (SREE)