Libro Blanco del Deporte

In informal discussion duri ng the first week of the study Moana indicated her need to further consider how she could change the interaction patterns. Our collaborative review of events in this first week and examination of classroom video recordings led to a closer examination of the communication and participation framework. Smaller, more incremental steps (see Appendix K) in the communication and participation patterns were planned to guide the change.

In the first instance to remediate how the students interacted, Moana noted the need for an immediate focus on increasing student cooperation in listening and talki ng. So that she could carefully guide and shape how the students participated in mathematical activity Moana returned to teaching mathematics in a large group. At this stage she had seen how the students quickly lost focus of the discussion and became disruptive in the smal l groups. Not using small groups was thus an intermediary step; she eventually wanted to develop student ability to work in them.

Her immediate action as she led whole class mathematical activity and discussion was to ask the students to talk together in pairs. For example, in one of these early lessons Moana made an array of two sets of eight counters then directed the students to consider: If I 've got one set of eight there and another set of eight, how many sets of eight have I got ? I don 't want you to answer that. I want you to talk. I want you to turn and talk to each other. Following their discussion she asked one member to report what the other had explained. In another instance, she provided a problem and required that together they make a conjecture and discuss their reasoni ng but she emphasised their need to both be able to report back. At other times, to keep the focus on listening and sense-making she asked one member of the pair to explain their reasoning and then asked the other to outline and model with materials what their partner said.

Through daily discussion and our i nformal analysis of how different students participated in the mathematical talk Moana began to more confidently outline her requirements for col laborative activity. Initially she had depended on i nstructions and strategies she saw

modeled by other study group members when she viewed video records of their classrooms but now she tentatively explored and developed her own repertoire of talk. She used thi s to establish with the students what she meant by active participation and collective engagement i n mathematical discourse. Each lesson began with an outline of her requirements for active participation and she closely monitored how the students worked together. In the following vignette examples are provided of how she adapted her instructions specifical l y to what she saw happening during shared mathematical activity.

Shaping ways to talk and actively listen to mathematical reasoning

Moana observed that the students had begun to record without discussion. She intervened and told them :

Moana Before you pick up a pen or touch the paper you need to discuss it first and I want you to show me how you can work together listening and bui lding on each other' s thinking with those questions.

( Term 2 Week 6)

After Moana had explained a problem and provided concrete material she stopped them and directed:

Moana I want you to talk to each other before you even touch the sticks. Lots of talking and listening and I might ask you what someone said, not you, so you need to discuss thi ngs please and make sense of what someone else says. Listen carefully to each other. I want you to discuss what is happening in your patterns of two . . . and how many you have.

( Term 2 Week 6)

Conflicts in changing beliefs, reshaping the rules of talk.

The classroom culture and the interactions i n it had previously been shaped by the beliefs Moana had about the nature of mathematics and what it meant to learn mathematics. These beliefs remained robust throughout the first part of this study. Researchers (e.g., Boaler, 2002a; Lampert, 200 1 ) argue that students in schools learn particular mathematical dispositions through the 'school mathematics' they experi ence. Beliefs that mathematics ideas are predetermined and unarguable are fostered when prior learning experiences emphasise scripted construction of roles, rules and procedures (Hamm & Perry, 2002). This had been Moana ' s prior experiences and she in turn had constructed a culture in which her students were developing similar dispositions and beliefs. Moana illustrated this view in a

reflection, recorded after a lesson, as to why the students had difficulties engaging i n the talk: I have always told them, not asked them to talk together. I am used to doing the talking and they are used to me talking too.

Although Moana discussed the changes she wanted to make to classroom communication and participation patterns with me and the other study group members she was ambivalent about them. She was aware of the contradi ctions she was causing in her students' beliefs about what constituted a mathematics lesson. She noted as she reviewed a video record of a lesson observation at the end of the second week: I really wanted these children to do this but they really couldn 't see any sense in it at all . . . it was more of the mechanical or cosmetic workings on how I wanted them to go about talking and listening. Researchers (e.g., Ball & Lampert, 1 999; Mercer, 2000; Wells, 1 999) report that students may be c hal lenged by the different rol es and scripts they are required to take when shifting fro m conventional to inquiry classrooms . Conflicts and contradictions i n the students' bel iefs were expected given the former sociocultural norms which had prevai led including the e xternal attribution of authority to the teacher and more able or domi nant students

Contradictions existed also because although Moana had taken small incremental steps towards change, she retained the central position as the authority in the classroom. When she viewed a video excerpt of a classroom observation she critically described her pedagogical actions as: book style participation norms . . . going through the cosmetics . . . but not really going into it .. . not really actually unearthing it .. . yes you must validate everybody 's answers but at the end of the day just give me the answer. Hamm and Perry (2002) maintain that teachers relinquishing authority to the c lassroom community, stepping away "from a central role as classroom leader to allow true public discourse about mathematical ideas" (p. 1 36), comprises a major challenge . Moana illustrated the on-going difficulties she had in adopting a more facilitative approach although she remai ned critically aware of her i ntentions to do so.

7.3.3 CONSTRUCTIN G M ORE I NCLUSIVE SHARING OF THE TAL K IN T H E