Ph.D Thesis
Ph.D Student Sela Hagit Aspects of Peer Groups' Coping with Tasks that Lead to Mathematical Contradictions Department of Education in Science and Technology Professor Orit Zaslavsky

Abstract

This study focuses on students' ways of resolving cognitive conflict arising from mathematical contradictions. It relies on three main theoretical frameworks: cognitive conflict, social learning, and decision-making.

The main goal of the study was to characterize processes underlying students' attempts to resolve mathematical contradictions of two types in groups of two sizes: pairs and foursomes (i.e., groups of four).

For the purpose of the study, four tasks leading to mathematical contradictions of two types were designed:

-         Two tasks that challenge students’ intuitive knowledge (CI);

-         Two tasks that challenge students’ formal/procedural knowledge (CP).

Eight 11th grade top-level students participated in the study. All students worked on all four tasks. Each experienced both settings - on two of the tasks they worked in pairs and on the other two - in foursomes. Each task began with an individual assignment, in which each student solved a mathematical problem on his/her own. Afterwards, the group members were asked to discuss their solutions and reach an agreed solution. When an agreement was reached, regardless of its mathematical correctness, the group was confronted with an alternative contradicting solution. They were then asked to resolve the contradiction as a group. Each student was interviewed 3 times about his/her experiences in both settings.

Main findings:

1.      Two types of activities held by the participants while coping with the contradictions were identified: Searching for conviction activities, and Supporting an assertion activities.

2.      Differences were found between the characteristics of the processes of coping with the contradictions. Some were related to type of task and some to group size.

o       With respect to type of task:

§         In CP tasks a similar number of occurrences of the above two types of activities was found, while in CI tasks a larger use of the supporting an assertion activities was found.

§         At the end of the process, the contradiction resolution of CP tasks differed from the groups' initial agreed solution in 5 of the 6 cases, while for CI tasks the final resolution was always identical to the initial agreed solution.

o       With respect to group size:

§         Non-efficient communication features were more frequent in foursomes' interactions, especially while engaging in CP tasks, compared to pairs' interactions; In foursomes there were differences in members' rate of participation, on account of dominant and passive participants, compared to work in pairs for which both members exhibited a similar rate of participation.