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How do students' behaviors relate to the growth of their mathematical ideas?
The purpose of this study is to analyze the relationship between student behaviors and the growth of mathematical ideas (using the Pirie-Kieren model). This analysis was accomplished through a series of case studies, involving middle school students of varying ability levels, who were investigating a combinatorics problem in after-school problem-solving sessions. The results suggest that certain types of student behaviors appear to be associated with the growth of ideas and emerge in specific patterns. More specifically, as understanding grows, there is a general shift from behaviors such as students questioning each other, explaining and using their own and others’ ideas toward behaviors involving the setting up of hypothetical situations, linking of representations and connecting of contexts. Recognizing that certain types of student behaviors tend to emerge in specific layers of the Pirie-Kieren model can be important in helping us to understand the development of mathematical ideas in children.Accepted Manuscript (AM
Beacon
The Beacon Newspaper, established in 1936, is William Paterson University's original student-run publication. Editorial opinion does not reflect that of the University, its administration, or faculty
Pioneer 2007
The annual student yearbook was first published in 1925 as "The Kokoon" when William Paterson University was Paterson State Normal School. The title changed over time but has been "The Pioneer" since 1941
Student behaviors and ways they are associated with the problem solving process
This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education in Lake Tahoe, Nevada.We analyze data from classrooms to build upon pilot research in which we found an association between certain types of student behaviors and the development of understanding. The pilot focused on an after school program in a suburban setting. In this case, we focus on several inner city classrooms. Our findings indicate that there are many similarities. These results may have important implications for understanding how student behaviors evolve over the course of a particular problem solving experience