Opportunities to engage with proof: the nature of proof tasks in two geometry textbooks and its influence on enacted lessons

• Published in: ZDM Vol. 46; no. 5; pp. 767 - 780
• Main Authors: Sears, Ruthmae, Chávez, Óscar
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-10-2014; Springer Nature B.V
• Subjects: Algebra; Cognition & reasoning; Cognitive tasks; Demand; Education; Educational Environment; Geometry; High Schools; Learning; Mathematics; Mathematics Education; Original Article; Secondary School Mathematics; Secondary schools; Students; Teachers; Textbooks; United States > US; Geometry; Proof; And levels of cognitive demands; Textbooks; Task features
• ISSN: 1863-9690; 1863-9704
• DOI: 10.1007/s11858-014-0596-9

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.