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Manipulatives: The effective way

Evans, D.; Carnine, D.
This study compared the effect of two instructional strategies on the efficient and effective development of procedural and conceptual mathematics knowledge of elementary students. The first strategy, referred to as the manipulative strategy, advocated the use of concrete objects with which students first explore the concept of borrowing. The second strategy was developed from the Direct Instruction program, Connecting Mathematics Concepts and advocated for students to be taught with conceptual elements that underlie the rules of borrowing. Twenty-six students from two second and third grade classrooms participated in this study were randomly assigned to an instructional group. Students received instruction with each approach during separate phases. A battery of tests were administered prior to, during, at the conclusion of, and three weeks after the intervention. Results indicate that students can be taught to become somewhat procedurally proficient with either strategy. Additionally, conceptual understanding can be developed to a similar level with both treatments. The authors conclude that either a symbolic or concrete representation can be successful if a skill is explicitly taught in a meaningful way, and that conceptual understanding can be promoted using that representation. However, instruction takes significantly more time when initial instruction involves concrete representation. (Copyright © 2011, National Institute for Direct Instruction (NIFDI). All rights reserved).
Research areas:
Main publication type:
Program Effectiveness
Connecting Math Concepts; math; math concepts; math procedures; Explorations; Math Their Way
DI News
Design type:
Alternating treatment single study design
Fidelity monitored:
Students included:
Elementary students, low-SES students, special education students, students with learning disabilities, general education students
Pacific Northwest, elementary school
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