Abstract
This paper compares task features and cognitive demand of proof tasks in two US high school geometry textbooks and considers how such differences influence geometry teachers’ facilitation of proof and students’ engagement with proof tasks during enacted lessons. Data were collected via interviews, task cover sheet-before implementation, task reflection sheet-after implementation, samples of students’ work, and classroom observations. Descriptive statistics were used to summarize task features and cognitive demands of proof within textbooks, and a grounded theory approach was used to analyze the enacted lessons. The results revealed variation in the nature of proof tasks within textbooks. Additionally, even though geometry textbooks may have higher-level demand proof tasks, there is no guarantee that such tasks would be assigned, or that the levels of cognitive demand of tasks will be maintained from the written to the enacted curriculum. Factors that can influence how teachers’ use textbooks include: beliefs, students’ disposition, and assessment. Thus, teachers’ actions can limit the extent students engage with proof. This study has implications for unpacking the complexities of students’ engagement with proof.
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Notes
Horizon Research, Inc. developed the artifact packet for the Cases of Reasoning and Proving (CORP) in Secondary Mathematics Project, with funding from the National Science Foundation (Award No. DRL-0732798). CORP seeks to develop curriculum that can be used for professional education that promotes reasoning and proving, and the development of mathematical knowledge needed for teaching.
The observation protocol was adapted from an instrument developed by Horizon Research, Inc. for CORP that documented how teachers use the proof tasks during the lesson.
The dates are read as month, day, and year, so 11-2-11 means November 2, 2011.
This is a standardized exam administered by the state, which assesses the state geometry curriculum.
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Sears, R., Chávez, Ó. Opportunities to engage with proof: the nature of proof tasks in two geometry textbooks and its influence on enacted lessons. ZDM Mathematics Education 46, 767–780 (2014). https://doi.org/10.1007/s11858-014-0596-9
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DOI: https://doi.org/10.1007/s11858-014-0596-9