Teachers’ and Students’ Negotiation Moves When Teachers Scaffold Group Work

Abstract

Group work has been a main activity recommended by mathematics education reform. We aim at describing the patterns of interaction between teachers and students during group work. We ask: How do teachers scaffold group work during a problem-based lesson? We use data from a problem-based lesson taught in six geometry class periods by two teachers who did not routinely implement problem-based small group work. We applied systemic functional linguistics to examine teacher and student moves when the teachers assisted the groups. We found that the teachers’ scaffolding moves exemplified analytic and social scaffolding because the teachers made the content needed for solving the problem explicit, and, also, encouraged students. The students’ performance of moves showed how they controlled the timeliness and the content of the scaffolds. The findings support prior research on classroom norms that increase student opportunities for conceptual agency and illustrate how those opportunities emerge.

Notes

We use the term problem-based instruction to describe the activity of teaching and the term problem-based lesson to talk about the specific lesson where the teachers implemented problem-based instruction.

As we will explain later, in using the system of negotiation in systemic functional linguistics, the IRF pattern is equivalent to the sequence of moves dK1^K2^K1.

Martin (1992, p. 48) noted that the work of Berry (1981) and Ventola (1987) has shown that in an action exchange, when goods or services are provided, the exchange is realized non-verbally. In contrast, when the delivery of goods and services is delayed, the exchange is realized verbally. For example, if the teacher asks, “Can you come to the board?” and the student replies, “I’ll go tomorrow,” the student is giving a verbal response delaying the provision of goods and services.

Thanks to James Martin who directed us to his earlier work.

O’Donnell (1999) discusses an alternative perspective regarding the use of the terms “synoptic” and “dynamic” in relation to models of interaction as opposed to moves. He also provides examples of Berry's (1981) work to make the case of its dynamic nature. Thanks to Margaret Berry for directing us to this work.

It is standard notation that the symbol “^” is used to denote a connection between successive moves in an exchange. For example, “dK1^K2^K1” means that the exchange consists of three moves starting with a dK1 move, followed by a K2 move, and concluding with a K1 move.

In compliance with our Institutional Review Board protocols, we use pseudonyms for persons and institutions.

Mr. Vincent decided to make slight changes to the problem when he assigned it to his regular-level classes. Specifically, Mr. Vincent decided to eliminate the third leg of the trip. As a result, Wallace's path only included two lines. The problem still involved making the diagram, adding auxiliary lines, and applying the Pythagorean Theorem. For the sake of simplicity, we only include here the version of the problem that was used in most classes and its solution.

The mathematics teachers at the school decided to alter the order of the topics stipulated in the textbook and taught the unit on right triangles immediately after the unit on congruent triangles.

There was a teacher assistant in Mr. Vincent's 3rd period, but the segments where he assisted the groups were not part of the study.

Table 8 shows the conclusion of the sequence of exchanges in this segment where Mr. Vincent assisted the group. At the end of this sequence of exchanges, the students determine that they can use the Pythagorean Theorem.

We appreciate the feedback of an anonymous reviewer regarding these potential applications.