| Recent changes in K–12 mathematics and collegiate calculus have inspired community college mathematics professors to increase the emphasis on student reasoning and understanding. Investigating the classroom teaching in two of these courses provided the researcher an opportunity to observe and identify teaching strategies that elicit student reasoning and student reasoning attributes. This dissertation investigates ways two experienced community college professors were able to elicit student reasoning within the classroom, ways students were able to reason with the mathematics, ways professors assessed student reasoning, and the students' perceptions about reasoning in mathematics and in the course.; Qualitative case studies were created from data sources consisting of observations of two mathematics units each professor taught, written artifacts, and interviews. Data analysis used constant comparison and analytic induction to identify similarities and differences in instructional modes, perceptions of student reasoning, ways each professor elicited student reasoning, instances of student reasoning, methods of assessing student reasoning, student perceptions about reasoning, and a narrative overview of the professors' courses. Findings may need to be interpreted with some caution because other factors, such as student motivation levels may have influenced the results. The most striking finding was the difference in instructional modes of two community college professors who were both committed to reform. Time spent in whole class discussion seemed to enhance the amount of reasoning observed in the classroom. Students that were able to review their reasoning and share their answers with other students and their teacher held a more positive belief about reasoning in mathematics on a survey and on their comments in class. Close monitoring of group activities and explicit assessment of reasoning seemed to enhance student reasoning.; The recommendations from this dissertation highlight the importance of student reasoning and possible ways to improve attempts to elicit student reasoning. Professors might benefit from collaboration on eliciting student reasoning. If professors wish to observe reasoning in class, then assessments might need to emphasize reasoning as well. This dissertation provides the opportunity for other professors to reflect on their understanding of eliciting student reasoning and continue the process of reforming mathematics teaching and learning. |
