From their explanations it was clear that the reason for this error was that they were used to the standard form \(y=ax+b\), where \(a\) is the slope. 11–35). Developing classroom discourse further toward productive classroom discourse would require more mathematical work in the sense of anticipating student responses, monitoring student ideas, and selecting students to contribute (Ball 2017; Stein et al. In the Netherlands, national standardized testing, widespread reliance on textbooks (Blockhuis et al. Encouraging actions (“confirmation” and “encouragement”) are teacher utterances that invite students to continue talking. During several steps of data analysis, the second author also coded part of a transcript. This may have been related to the subject, analytic geometry, which was new for her. Discourse research in mathematics education: a critical evaluation of 108 journal articles. As visualized in Fig. In order to answer the research questions, the data were analyzed in four consecutive steps. ), Compendium for research in mathematics education (pp. During the first lesson, Anna attempted to orchestrate classroom discourse concerning students’ various solution methods for the first time. Mathematics discussions by design: creating opportunities for purposeful participation. (2017). 2016). So then you have the point (6,6) which lies here on the line”. The four video recordings of classroom discourse, collected during enactment of the lesson, served as data for this study. Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). In addition, the teacher’s openness to feedback and “will to learn” (Van Eekelen et al. https://doi.org/10.2307/749827. Additional research is necessary to see in which ways the students benefit from changes in the teacher’s role. This requires that teachers shape their lessons such that students “use each other as resources for working through those problems, and then share their strategies and solutions in whole-class discussions” (Stein et al. Moreover, by comparing various solution methods, students can be supported in making important mathematical connections between different representations (Heinze et al. Download your free copy here. Learning how to solve problems in multiple ways is associated with developing problem-solving skills and mathematical thinking, because students become flexible in choosing among strategies (Heinze et al. Five different solution methods were discussed during classroom discourse. Several characteristics of the collaborative development of these four lessons can be identified as contributing to the changes in the teacher’s role in classroom discourse. The convergent actions show a decreasing trend. (2012) categorize reformulations as divergent, we categorized them as convergent, because in reformulating, the teacher decides what to point out, what to name, or what to clarify. By asking for explanations and getting students to respond to each other, teachers implicitly negotiate favorable norms. It is worth your time! In E. von Glasersfeld (Ed. The use of less convergent actions and more divergent actions is a strong indication for building the discussion on students’ ideas and reasoning, because our categorization in convergent and divergent teacher actions is based upon the distinction between teacher actions that serve to control the subject of discussion, or those that serve to build further on student ideas. Review of Educational Research, 78(3), 516–551. Teaching children how to use language to solve maths problems. Classroom discourse is initially described as a way to align classroom mathematics with mathematics as a discipline in which mathematical meaning is negotiated. Shulman, L. S. (1986). Classroom discourse: the language of teaching and learning. This suggests a growing participation of students. The silent and the vocal: participation and learning in whole-class discussion. Excerpts 4.1, 4.2, and 4.3 are from the fourth lesson, and they, too, are in chronological order. Asking students to evaluate solution methods gives students authority over the mathematical work and holds students accountable to the community of learners, which fosters disciplinary engagement (Engle and Conant 2002). ), Proceedings of the 13th International Congress on Mathematical Education. Mathematical discussions. The teacher’s role is crucial in developing classroom discourse that meets the criteria described above: First of all, the teacher needs to get students to participate, with students needing to talk, and more specifically, students must explain their thinking; second, the teacher must get students to listen to each other and to respond to each other’s ideas and reasoning, in order to create a discussion based on students’ ideas and reasoning; third, the teacher needs to hold students’ talk accountable to logical argumentation; finally, the teacher needs to guide the students toward disciplinary ideas. https://doi.org/10.1016/j.jmathb.2011.11.001. 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. This helps ensure that key mathematical ideas remain the focus of the lesson debrief. In conclusion, the teacher has made important steps toward the development of classroom discourse, but establishing a productive discourse community would require additional changes and development. For each of the lessons, Anna’s main goal was to orchestrate classroom discourse about various students’ solution methods. Blockhuis, C., Fisser, P., Grievink, B., & Voorde, T. M. (2016). https://doi.org/10.1007/s10649-015-9636-9. Excerpt 1.1Footnote 3 presents the beginning of the discourse. Orchestrating Mathematical Classroom Discourse About Various Solution Methods: Case Study of a Teacher’s Development. Further research with a larger sample of teachers is also necessary to investigate what works for teachers in collaboratively developing problem-based lessons and in orchestrating classroom discourse about students’ various solution methods. J Math Didakt 41, 357–389 (2020). The five practices that comprise the model will be the focus of the remainder of this article. 292–307). 5 practices for orchestrating productive mathematics discussions. Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Sfard, A. Language and Education, 20(6), 507–528. A balancing act: developing a discourse community in a mathematics classroom. Developing and orchestrating classroom discourse about students’ different solution methods is an essential yet complex task for mathematics teachers. Cambridge: Harvard University Press. In Fig. Furthermore, the We conducted an exploratory case study to enable an in-depth investigation of changes in classroom discourse of a secondary school teacher who is new to orchestrating classroom discourse. In order to investigate the development of classroom discourse in higher secondary school, the first author collaborated with a tenth-grade mathematics teacher to iteratively develop four analytic geometry lessons. Murata, A., Siker, J., Kang, B., Baldinger, E. M., Kim, H.-J., Scott, M., & Lanouette, K. (2017). One teacher together with one researcher collaboratively developed four discourse-based analytic geometry lessons. Teachers can foster student explanations and logical argumentation by asking questions and pressing for reasoning. Inviting students to keep talking can be done either in a slightly evaluating manner, by confirming, or in a more questioning manner (for example, “Yes?”), which is regarded as encouraging. This blog is part of a three post series on the importance of mathematical discourse from Curriculum Associates, a Getting Smart Advocacy Partner, and Dr. Gladis Kersaint, the author of the recently published whitepaper Orchestrating Mathematical Discourse to Enhance Student Learning. the Five PRactices Model The five practices are— 1. anticipating student responses to challenging mathematical tasks; 2. monitoring students’ work on and engagement with the tasks; 3. Furthermore, most studies examining or describing classroom discourse focus on primary school or lower secondary school (Walshaw and Anthony 2008). Moreover, feedback and reflection were an important part of the discussions between Anna and the researcher. 2008). The fourth solution method was correct and made use of the circle as the set of points with equal distance to a point. ), Contexts for learning: Sociocultural dynamics in children’s development (pp. The students were asked to solve the following problem. By orchestrating and promoting discourse, teachers can actively engage students in mathematical thinking. https://doi.org/10.1007/s10857-005-3849-2. A study of whole classroom mathematical discourse and teacher change. In Excerpt 4.1, various students talked and reacted to each other’s ideas. (1998). ), Compendium for research in mathematics education (pp. Orchestrating Productive Mathematical Disc ussions: ... investigations of classroom discourse. Students are held accountable to the community of learners by sharing and discussing their ideas, accountable to standards of logical argumentation, and accountable to disciplinary knowledge insofar as their work and discussions relate to the rules of mathematics as a discipline (Michaels et al. effective mathematical discourse. (2008). For most mathematical problems and tasks, several different solution methods are possible; whenever a group of students is confronted with a mathematical problem, students have differing ideas and find various solution methods. Method on the lesson debrief 78 ( 3 ), 408–423 actions to rules... ( 2 ), 313–340 the actual lessons, an important step been! 2 shows that the percentage of student mathematical thinking min ) containing classroom discourse about various students talked and. Etablierung einer Diskursgemeinschaft gegangen werden können necessity and benefit of a math-talk learning community visible and described in section! 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