Abstract
This study examined the effects of types of representations, constructivist teaching approaches, and student engagement on middle school algebra students' procedural knowledge and conceptual understanding. Data gathered from 16 video lessons and algebra pretest/posttests were used to run three multilevel structural equation models. Symbolic representations (p < .02), shared meanings (p < .05), and meaningful feedback (p < .10) significantly increased procedural and conceptual understanding. Enactive representations significantly increased procedural knowledge (p < .05). There was also a significant relationship between the two types of learning at the within level (p < .01) and between level (p < .05).
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