TY - JOUR
T1 - Opportunities to Engage with Proof: the Nature of Proof Tasks in Two Geometry Textbooks and Its Influence on Enacted Lessons
AU - Sears, Ruthmae
AU - Chávez, Óscar
PY - 2014/10/1
Y1 - 2014/10/1
N2 - 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.
AB - 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.
KW - Proof
KW - Geometry
KW - Textbooks
KW - Task features
KW - And levels of cognitive demands
UR - https://digitalcommons.usf.edu/tal_facpub/228
UR - https://doi.org/10.1007/s11858-014-0596-9
U2 - 10.1007/s11858-014-0596-9
DO - 10.1007/s11858-014-0596-9
M3 - Article
VL - 46
JO - ZDM
JF - ZDM
ER -