PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Angle measure, quantitative reasoning, and instructional coherence: The case of David
Page: 954
This paper reports findings from a study that explored the effect of a secondary mathematics teacher’s level of attention to quantitative reasoning on the quality and coherence of his instruction of angle measure. I analyzed 37 videos of an experienced teacher’s instruction to characterize the extent to which he attended to supporting students in reasoning quantitatively, and to examine the consequences of this attention (or lack thereof) on the quality and coherence of the meanings the teacher’s instruction supported. My analysis revealed that the incoherencies in the teacher’s instruction were occasioned by his inattention to quantitative reasoning. This study therefore demonstrates that when teachers do not possess a disposition to attend to quantities and their relationships, the circumstances are ripe for instruction that emphasizes inconsistent, incoherent, and sometimes incompatible, mathematical meanings.