Using meta-analysis, the results of 60 studies were combined to determine the effectiveness of mathematics instruction with manipulative materials. Students ranged in age from kindergarteners to college-age adults and studied a variety of mathematics topics. Results showed that mathematics achievement is increased through the long-term use of concrete instructional materials and that students' attitudes toward mathematics are improved when they have instruction with concrete materials provided by teachers knowledgeable about their use. Instruction with pictures and diagrams did not appear to differ in effectiveness from instruction with symbols.
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