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Güçler, B. 2009). Journal of Mathematics Teacher Education, 18(3), 253–272. Together, these four lessons constituted the case that was investigated for this study. responses that the teacher almost provided for them—thus sharing little information about students’ thinking. We report on classroom discourse about students’ solution methods in four analytic geometry lessons in higher secondary school. This study reports on the first stages of classroom discourse development of one Dutch higher secondary school mathematics teacher who had no prior experience in including classroom discourse in her teaching practice. 2017; Ryve 2011). The convergent actions show a decreasing trend. Star, J. R., & Verschaffel, L. (2017). Fig. Feb 08, 2021. ORCHESTRATING PRODUCTIVE MATHEMATICAL DISCUSSIONS 315 promoting productive disciplinary engagement to explain how the practices work ... ics in part by helping students learn mathematical discourse practices (e.g., Chapin, O’Connor, & Anderson, 2003; … Ryve, A. 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 How do students benefit from having their answers evaluated by their peers? Michaels, S., & O’Connor, C. (2015). The patterns of interaction shifted away from patterns in which the teacher alternates turns with a single student and does most of the thinking, such as the “initiation-response-evaluation” pattern (Cazden 2001), or alternations between closed progress details and teacher-led responses, as described by Drageset (2015). Orchestrating Productive Mathematical Disc ussions: ... investigations of classroom discourse. Mathematical discussions. Each lesson consisted of two parts: students’ work on a problem, and classroom discourse about their various solution methods. 2003). Based on the four transcripts and the tables, several aspects of change were identified and classified into three categories, as elaborated below. Since the end of the twentieth century, a growing emphasis has been placed on classroom discourse in mathematics education research, as shown in several review studies (e.g., Herbel-Eisenmann et al. There is a wide consensus within the field that it is very challenging for the teacher to conduct class discussions that both build on student ideas and highlight key mathematical … https://doi.org/10.2307/3609122. Blockhuis, C., Fisser, P., Grievink, B., & Voorde, T. M. (2016). This study highlights the needs for future research in regard to socioeconomic status and teachers' beliefs in regard to the orchestration of mathematical discourse. https://doi.org/10.3102/0013189x032001009. Mathematical Discourse also involves different genres such as algebraic proofs, geometric proofs, and school algebra word problems. A short description of the first and fourth lessons will be given, and the changes will be illustrated with excerpts from these lessons. Henning et al. https://doi.org/10.3102/978-0-935302-43-1_27. An excellent resource is a book by Margaret S. Smith and May Kay Stein, Five Practices for Orchestrating Productive Mathematics Discussions. Having their answers evaluated by peers encourages students to think about things from … Regarding student actions, we also added, “(steps of) solution methods”, to indicate when a student’s utterance comprised part of a possible solution method. Kooloos, C., Oolbekkink-Marchand, H., Kaenders, R. et al. Thinking as communicating: human development, the growth of discourses, and mathematizing. Today’s headlines emphasize the need to prepare students for science, technology, engineering, and mathematics (STEM) careers; yet preparing students to be mathematically literate in today’s world is a heavy charge. Let l be the line given by the following vector equation: We consider the lines \(ax+2y=c\), where \(a\) and \(c\) are constants. 2016), and the procedural presentation of mathematics in the current textbooks (Gravemeijer et al. ), Proceedings of the 13th International Congress on Mathematical Education. The researcher’s role varied from an interested colleague, investigating the practice of teaching mathematics in a new way; to a scholar, theoretically well-informed on mathematical classroom discourse; to a didactical coach, fostering and joining in reflection, and giving specific recommendations for teacher actions. Shifting from teacher-centered toward student-centered teaching requires a renegotiation of classroom norms and appropriate teacher practices. In G. Kaiser (Ed. 2006) may have strongly influenced the changes in her role during classroom discourse. The results of this study are described in three steps: First, the developed framework is presented in tables. The framework was developed during data analysis, and combines aspects of two existing frameworks, those of Drageset (2015) and Henning et al. 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. In order to answer the research questions, the data were analyzed in four consecutive steps. However, she became more aware of the importance of discourse in learning mathematics and her role therein, which influenced the way she interacted with students. The four video recordings of classroom discourse, collected during enactment of the lesson, served as data for this study. These aspects made orchestration of classroom discourse about different solution methods a unique and particularly challenging undertaking in Anna’s context. The coding manual for qualitative researchers. First, the teacher’s reactions to solution methods changed considerably throughout the lessons we studied. ORCHESTRATING CLASSROOM DISCOURSE •Design of Instruction: writing or selecting a problem or task •Anticipatinglikely student responses to cognitively demanding mathematical tasks •Monitoringstudents’ responses to the tasks during the explore phase •Selectingparticular … Educational Researcher, 32(1), 9–13. J Math Didakt 41, 357–389 (2020). In J. Cai (Ed. 2008). Enschede: SLO. This confirmed for us the necessity and benefit of a deeper, qualitative analysis. Third, the topic of discussion was either mathematics—in particular analytic geometry—or classroom discourse, or a combination of both. Math talk and student strategy trajectories: the case of two first grade classrooms. 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. To answer our second research question, we identified three main aspects of change in the teacher’s role in classroom discourse. (1991). Excerpts are numbered according to lesson and time. Cambridge: Harvard University Press. Apr 05, 2021. The first three solution methods involved one specific error, that is, these three students calculated the slope of lines perpendicular to \(l\), which is four, and substituted that slope for \(a\). In total, five different solution methods were discussed: first, three incomplete or incorrect solution methods and subsequently, two correct solution methods. Whereas Anna did increasingly succeed in building the discussion on students’ ideas, she struggled with making different solution methods the subject of discussion, and in helping students make connections between the different solution methods. In order to investigate the extent to which classroom discourse in the four lessons was in line with these characteristics, some codes were adjusted and a new categorization was established to distinguish convergent, teacher-led actions from divergent, student-led actions (Henning et al. ZDM Mathematics Education, 41(5), 535–540. School contextual factors, including socioeconomic status and teacher support, and teachers' mathematical knowledge for teaching and beliefs were predictive of different dimensions of mathematical discourse. Although Henning et al. (2016). Describing levels and components of a math-talk learning community. 2008). Graduate Semester | 1 credits | 4 Weeks Explore Our Offerings / Education ; Orchestrating Mathematical Discourse ; Start Date. Journal of Teacher Education, 59(5), 389–407. In addition, the patterns of interaction changed from involving one student and the teacher, to involving more students alternating turns. The 5 Practices for Orchestrating Mathematical Discourse were adapted from the Japanese model of Teaching Through Problem-Solving . https://doi.org/10.2307/749877. The participation of teacher and students in classroom discourse, and the categorization of teacher actions are both illustrated in this section. In the fourth lesson, students were encouraged to react to each other (for example: “Well, just ask him”). Educational Studies in Mathematics, 91(3), 375–393. In the third step of data analysis, all four transcripts were coded using the developed code manual. Developing classroom discourse demands a renegotiation of social norms, especially if students are unaccustomed to thinking of their own solution methods, to sharing them in whole-class discussions, and to listening to each other. Speer, N. M., & Wagner, J. F. (2009). First, the teacher’s reaction to students’ solution methods changed from either setting them aside or confirming them, to making the solution method the subject of discussion by probing for explanations or asking other students to react. A reformulation can also be used to rectify and model the use of mathematical language or to facilitate communication, for example by naming a geometric object involved in a solution method. Five different solution methods were discussed during classroom discourse. Yackel, E., & Cobb, P. (1996). Engle, R. A., & Conant, F. R. (2002). In this exploratory single-case study, we characterized and analyzed classroom discourse during four lessons to describe changes in the teacher’s role in classroom discourse. 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. Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). My learners often get frustrated with me because I am always striving to great this type of communication both verbally in the face-to-face classroom but also written in my online classes. 2016), and the procedural way in which these textbooks present mathematics (Gravemeijer et al. 2006), or (whole-class) discussions (Richards 1991; Stein et al. It is worth your time! Knowledge needed by a teacher to provide analytic scaffolding during undergraduate mathematics classroom discussions. The relevant parts (each with a duration between 21 and 24 min) containing classroom discourse were transcribed. Also, what distinguishes the context of higher secondary school from primary or lower secondary school is the students’ long-term prior experience with mathematics lessons. Teachers can foster student explanations and logical argumentation by asking questions and pressing for reasoning. Or been involved in whole-class discussions that use students ’ mathematical understandings was! Individual context, an important part of learning orchestrating mathematical discourse class in which third! Lesson plan steps that were unclear to them 4 ), 355–374 in the. Problems and discussing various solution methods involving orchestrating mathematical discourse representations ( Heinze et al seems to be (! Many differing ways of representing, thinking, talking, agreeing, and mathematizing with teacher-led ”! 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