ERIC Number: ED471760
Record Type: RIE
Publication Date: 2002
Problem Posing: What Can It Tell Us about Students' Mathematical Understanding?
Pirie, Susan E. B.
In 2001, at Snowbird, Utah, members of the [mu]-group from the University of British Columbia, under the guidance of Dr. Susan Pirie, engaged in an innovative, continuous session of linked papers which consider the notion and nature of mathematical understanding and reviewed a number of different theories and approaches to this phenomenon. We presented, discussed and contrasted a variety of key ideas in this area and considered their usefulness and applicability in analyzing the mathematical actions of pupils working in school classrooms. We also presented in detail how we undertake our video analysis and for this, the reader is referred to the paper by Pirie in last year's proceedings entitled "Analysis, Lies and Video-tape." This year we intend to use a slightly differently structured session to enable even greater audience participation, especially by those who are unable to attend the entire session. We will still be show-casing the collaborative work of the teachers and mathematics educators who are members of the [mu]-group, but we will offer an interactive symposium space in which to discuss three papers and three posters, all presented together in one long session. Participants will be invited to examine the presented research, and to enter into dialogue with the authors both as a group and individually. As part of a SSHRC funded project into the effects of Problem Posing on ways of understanding mathematics, [mu]-group members have taken a common mathematical prompt: "If the answer is 72, what is the question?" to a wide variety of students and explored the mathematical understanding revealed as the students grappled with posing problems from their own, individual, mathematical perspectives that fit the provided situation. Each researcher presented the problem as they saw fit to their students, given the students' level of mathematical knowledge and sophistication Our session as a whole will encompass papers and posters presented in interactive ways by: Susan Pirie, with a review of the group's theoretical position and methodological stance; Katharine Borgen, whose work is with Grade 9 students tackling mathematics in English which is their second language; Lionel LaCroix, who has taken the common prompt out of the classroom to an industrial-trades worker of 25 years experience of using mathematics in the workplace; Donna Jenner, who has taught and studied Grade 2/3 students working individually and in small groups. Shelley Saltzman, who has worked with a small group of Grade 4 students with learning difficulties in mathematics; Shevy Levy, who approached pairs of students of a wide variety of ages; Amy Bamford, who challenged her Grade 12, enriched curriculum class. Lyndon Martin will act as a discussant for the session. (Author)
Descriptors: Concept Formation, Educational Strategies, Elementary Secondary Education, Innovation, Mathematics Education, Problem Solving
ERIC/CSMEE Publications, 1929 Kenny Road, Columbus, OH 43210-1080. Tel: 800-276-0462 (Toll Free).
Publication Type: Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Note: In: Proceedings of the Annual Meeting [of the] North American Chapter of the International Group for the Psychology of Mathematics Education (24th, Athens, GA, October 26-29, 2002). Volumes 1-4; see SE 066 887.