Abstract
This study examines a sequence of four middle school algebra tasks through their enactment in three teachers’ classrooms. The analysis centers on the cognitive demand—the kinds of thinking processes entailed in solving the task—and the participatory demand—the kinds of verbal contributions expected of students—of the task as written in the instructional materials, as set up by the three teachers, and as discussed by the teachers and their students. Relationships between the nature of the task enactments and students’ performance on a pre- and post-test are explored. Findings include the fact that the enacted tasks differed from the written tasks with regard to both the cognitive demand and the participatory demand, which related to students’ lack of success on the post-test. Specifically, cognitive demand declined in the enacted curriculum at different points for different classes, and the participatory demand during enactment tended to involve isolated mathematical terms rather than students verbally expressing mathematical relations.
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Acknowledgments
This study was partially supported by the Michigan State University College of Natural Science. We thank Beth Herbel-Eisenmann, Ralph Putnam, Kristen Bieda, and Michael Steele for their guidance and support of this study. We also thank Kimberly Cervello Rogers, Project 2061, and all participating teachers and students.
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Appendix: Selected items from the pre- and post-tests
Appendix: Selected items from the pre- and post-tests
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Otten, S., Soria, V.M. Relationships between students’ learning and their participation during enactment of middle school algebra tasks. ZDM Mathematics Education 46, 815–827 (2014). https://doi.org/10.1007/s11858-014-0572-4
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DOI: https://doi.org/10.1007/s11858-014-0572-4