Session Information
24 SES 09, Int. Contexts in Mathematics Education
Paper Session
Time:
2009-09-30
10:30-12:00
Room:
NIG, HS III
Chair:
Nadia Stoyanova Kennedy
Contribution
This report concerns an inquiry into the nature and character of the questions that US seventh graders have been observed to pose in philosophico-mathematical discussions, and into the patterns of conceptual development associated with those discussions. Drawing from the Philosophy for Children program (Lipman, Sharp, & Oscanyan, 1978)—a distinctive curricular and pedagogical approach designed to lead students toward collaborative inquiry into philosophical questions through narrative texts and communal dialogue—the study analyzes a series of critical discussions focused on certain philosophic-mathematical questions, prompted by a text in which fictional characters explore themes related to philosophy and history of mathematics. The working hypothesis of the study was that through teachers modeling for and coaching students in the formation of philosophical questions related to mathematics, and through the careful orchestration of math-related philosophical discussions, students would generate more questions that were philosophical rather than empirical, and would probe more deeply into the relation between mathematics and experience in their math classroom conversations. All discussions were initiated by questions posed by the students. The objective of the study were to trace the development of students' philosophical questions about mathematics, to determine whether those questions changed over the course of the contact period, and if so how.
Method
Data was collected from transcripts of video-sessions of discussions with a group of 20 seventh graders in a small private school in northern New Jersey. The discussions were conducted by a team of two facilitators on a weekly basis over the course of one school year. Each session started with reading aloud from the text in round robin fashion, followed by collecting student questions. The discussions that ensued took up one or more of the questions selected by the group for collaborative inquiry. The questions generated in the first five discussions were compared to the questions generated in the last five. The data was analyzed using a grounded theory approach—that is, categories and patterns emerged during analysis rather than as a result of the application of predetermined categories.
Expected Outcomes
The findings support previous results of research conducted on Philosophy for Children methodology—i.e., that careful modeling, coaching and facilitation of deliberate communal inquiry into philosophical-mathematical questions and concepts tends to help students generate questions that are philosophical rather than empirical, to target areas concerned with the structure, logic, and limitations of mathematics as a system, and to explore the relation between mathematics and human experience. Thus, we suggest that the introduction of a philosophical dimension into classroom mathematics offers the possibility of a deeper and broader epistemological approach to teaching and learning in the field.
References
Lipman,M., Sharp, A., & Oscanyan, F. (1978). Philosophy in the classroom (2nd edition). Philadelphia, PA: Temple University Press.
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