Taking into account that Anna is an experienced teacher who was involved in intensive curricular discussions with the researcher, this case study serves as an additional example that developing productive classroom discourse is a challenging process. Alice said she had something different from the point where the slope was calculated, but could not find the words to describe her method. cr.) Each lesson consisted of two parts: students’ work on a problem, and classroom discourse about their various solution methods. Field notes were made to guide transcription and analysis. When a student makes a remark concerning a solution method as a whole, we assign the action “remark about solution method”. In our study, instead of providing students with a single procedure, the teacher presented them with open problems, and orchestrated classroom discourse about students’ different solution methods. Enschede: SLO. Gravemeijer, K., Bruin-Muurling, G., Kraemer, J.-M., & Van Stiphout, I. Note: Orchestrating Discourse Teaching Tool available in Lesson Support. The tension between authoritative and dialogic discourse: a fundamental characteristic of meaning making interactions in high school science lessons. https://doi.org/10.1080/07370008.2017.1362408. Teachers can foster student explanations and logical argumentation by asking questions and pressing for reasoning. During several steps of data analysis, the second author also coded part of a transcript. Calculate for which values of \(a\) and \(c\), the line goes through point \(P\left(1,5\frac{1}{2}\right)\) and perpendicular to \(l\). https://doi.org/10.1016/j.jmathb.2011.11.001. However, a slight break in this trend appeared between the third and fourth lessons. Richards, J. 2016) lead to most students attending years of outcome-oriented mathematics lessons. A student action is “external” when it involves a student who was not part of the original interaction, but who makes a remark concerning the content of the discussion. This goal was based on an underlying shared vision as well as a shared dissatisfaction with more traditional styles of teaching. Furthermore, most studies examining or describing classroom discourse focus on primary school or lower secondary school (Walshaw and Anthony 2008). The 5 Practices for Orchestrating Mathematical Discourse were adapted from the Japanese model of Teaching Through Problem-Solving . Discrepancies were discussed until a consensus was reached, resulting in adjustments to the code descriptions and framework. The teacher actions are divided into four main categories: 1) convergent actions, 2) divergent actions, 3) encouraging actions, and 4) regulating actions. Ball, D. L. (2017). Journal for Research in Mathematics Education, 27(4), 458–477. In the design phase, Anna and the researcher chose an appropriate problem and discussed the lesson plan. In our study, classroom discourse about various solution methods was a new practice for Anna and her students, yet considerable changes took place throughout the four lessons. The role of multiple solution tasks in developing knowledge and creativity in geometry. After the first student had finished explaining his solution method (which included the error), the teacher asked another student to repeat the method. Orchestrating Mathematical Classroom Discourse About Various Solution Methods: Case Study of a Teacher's Development Author(s): Kooloos, C ; Oolbekkink, H. ; Kaenders, R ; Heckman, G 3, fewer words were spoken in the third lesson. Therefore, Anna and the researcher decided to start an intensive collaboration in order to develop classroom discourse that concerns variations in solution methods. https://doi.org/10.1207/s1532690xci2301_4. This study highlights the needs for future research in regard to socioeconomic status and teachers' beliefs in regard to the orchestration of mathematical discourse. Excerpts are numbered according to lesson and time. Since our framework was developed by analyzing a teacher’s first steps in orchestrating classroom discourse, and since the collaboration with Anna was focused especially on “getting students to talk”, the framework may be especially useful for studies that focus on teachers’ beginning process of developing a discourse community and establishing favorable norms within their lessons. Math talk and student strategy trajectories: the case of two first grade classrooms. They conclude that once a discourse community has been established, listening carefully without talking may also constitute active participation in classroom discourse. Making such decisions requires that the teacher listens to students and understands their thinking. ), Compendium for research in mathematics education (pp. Journal for Research in Mathematics Education, 32(3), 236–266. In this study, we explicitly investigated the first steps in developing classroom discourse. Michaels, S., O’Connor, C., & Resnick, L. B. (2011). The 5 Practices for Orchestrating Mathematical Discourse were adapted from the Japanese model of Teaching Through Problem-Solving. The collaboration between Anna and the researcher can be characterized by three central aspects: goal, roles, and topic. Developed code manual with instructions for coding and descriptions of all the codes, per-service... Not logged in - arguments can be perceived in the first student to be a consensus that Orchestrating discourse... Development, are in chronological order researchers should be guided toward certain disciplinary mathematical ideas instructions... H., Kaenders, R., & O ’ Connor, C. 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