Redirecting involves changing the course of interaction, progressing involves moving the process forward, and focusing involves pausing the process to enlighten details or deepen the discussion.Footnote 2 In our analysis, we were particularly interested in whether classroom discourse was in line with critical characteristics, as elaborated in the theoretical framework. Reston: National Council of Teachers of Mathematics. More recently, Güçler (2016) used Sfard’s concept of metadiscursive rules (Sfard 2008) to show that making these rules explicit in discussion fosters students’ mathematical learning. 2012) and our collected data, we developed a framework for analyzing teacher actions during classroom discourse, and this framework was in turn used to describe changes in the teacher’s role in classroom discourse throughout the four lessons. 2016), and the procedural presentation of mathematics in the current textbooks (Gravemeijer et al. It may take place between partners, small groups, or as a whole class. 2009). A balancing act: developing a discourse community in a mathematics classroom. Cambridge: Harvard University Press. In the second and third lessons, the teacher frequently used regulating actions to articulate rules for participating in classroom discourse. The importance of engaging students in meaningful mathematical discussion has long been identified as an essential component of students’ mathematics learning. Four lessons in analytic geometry were developed iteratively, in collaboration with the teacher. In collaboration with the teacher, four lessons in analytic geometry were developed. Deliberative discourse idealized and realized: accountable talk in the classroom and in civic life. Students can make conjectures, link prior knowledge to current understanding… The problems were based on tasks from the textbook, yet modified in the sense that students were not provided with a step-by-step procedure: the students were instead challenged to solve the problems according to their own approach. (2017) found that whereas participating in discourse-based instruction does support mathematical learning of the whole group, on an individual level the amount of words spoken by students does not necessarily predict their learning. Young, Jeffrey Stephen, "Orchestrating Mathematical Discussions: A Novice Teacher's Implementation of Five Practices to Develop Discourse Orchestration in a Sixth-Grade Classroom" (2015).All Theses and Dissertations. We added the action “reformulate” to indicate when the teacher reformulated a previous statement. Blockhuis, C., Fisser, P., Grievink, B., & Voorde, T. M. (2016). Journal for Research in Mathematics Education, 27(4), 458–477. Van Eekelen, I. M., Vermunt, J. D., & Boshuizen, H. P. A. Journal of Mathematics Teacher Education, 14(5), 355–374. The purpose of this study was to examine the mathematical discourse within novice elementary teachers' classrooms. Cognition and Instruction, 23(1), 87–163. The fourth solution method, which was presented by Inez, did not involve the error and was almost correct. Stanford: Stanford University. Asking good questions and promoting discourse is an integral part of the teaching and learning in a classroom. This trend indicates the shifting away from teacher-centered patterns of classroom discourse and toward building the discussion on students’ thinking. https://doi.org/10.1002/sce.20131. As shown in Fig. In summary, the distribution of turns shifted from sequences of interaction between the teacher and one student in the first lesson, toward the teacher getting students to react to each other and various students alternating turns in the fourth lesson. Generally, students are accustomed to memorizing and practicing such step-by-step procedures. Design experiments in educational research. Emmanuelle had an idea for a solution method which uses Pythagoras’ theorem. (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. This suggests a growing participation of students. The development was content-focused on analytic geometry and in particular on how to teach it. Third, we elaborate on the changes in the teacher’s role in classroom discourse, classified into three categories: solution methods, distribution of turns, and teacher actions. Walshaw, M., & Anthony, G. (2008). https://doi.org/10.1007/s11858-009-0214-4. These patterns do not meet the criteria for classroom discourse elaborated above, because they challenge students to try to guess what their teacher is thinking instead of building on and deepening students’ thinking. 3 shows that the percentage of student utterances greatly increased from the first to the second lesson. Encourage students to engage in productive mathematical discourse both with each other and with you. Excerpt 4.2 presents the discourse that followed. 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 The teacher chose not to evaluate Joris’ solution method and reveal the error, but instead she asked another student, Carolien, to repeat the method. https://doi.org/10.1007/978-3-319-62597-3. Karsenty, R., & Sherin, M. G. (2017). Leermiddelenmonitor (report on teaching materials) 15/16. Here is the second of five questions and responses from Gladis Kersaint’s blog post, Orchestrating Mathematical Discourse to Enhance Student Learning.Though written for K-12, adult learners would benefit from these suggestions, as well – especially as learners prepare to enter the workforce. (2016). The following section provides excerpts in which these changes are recognizable from the first and fourth lessons. (pp. Polya, G. (1957). Portsmouth: Heinemann. Involves encouraging students to make mathematical connections between different student responses. Vol. Orlando: Academic Press. Theses and Dissertations. In other words, we made the tasks into genuine problems. Ryve, A. ProQuest LLC, Ph.D. Dissertation, North Carolina State University. A fourth-grade class needs 5 leaves each day for a caterpillar. Discourse begins with a mathematical challenge that is worthy of exploration and deepens students’ mathematical understandings. This conclusion is consistent with previous research that shows that developing productive classroom discourse is a complex and long-term process (e.g., Hufferd-Ackles et al. Anna’s reaction to Aad’s incomplete solution method was to set the idea aside and demonstrate what she meant by distance (lines 9 and 10). By the time students reach the tenth grade they have hardly experienced or been involved in whole-class discussions that incorporate various solution methods. Second, the distribution of turns changed throughout the four lessons: in the first lesson, the teacher did most of the talking, and the discourse consisted mainly of sequences of a single student and the teacher alternating turns until the teacher turned to a new student. Working through these practices involves considerable domain-specific work. Notably, during the first lesson we counted six instances of “demonstrate”, during the second and third lessons we counted no instances, and during the fourth lesson only one such instance was observed (see Excerpt 4.3). Conceptualizing talk moves as tools: professional development approaches for academically productive discussions. The teacher’s reaction to incomplete or incorrect solution methods changed from setting them aside, to attempting to get other students to determine and solve the mathematical error. When the problem is not the question and the solution is not the answer: mathematical knowing and teaching. In mathematics education, students should learn to think mathematically. https://doi.org/10.1207/s1532690xci2301_4. 2008). “Evade answer” refers to students abstaining from answering. Attributes of instances of student mathematical thinking that are worth building on in whole- class discussion. During the first lesson, Anna attempted to orchestrate classroom discourse concerning students’ various solution methods for the first time. Cazden, C. B. Please select Start Date. In the quantitative phase a series of multi-level, means-as-outcomes regression analyses were conducted with a sample of 119 novice elementary teachers to examine how teacher attributes and school contextual variables accounted for variance in the level of mathematical discourse community and the level of student explanation and justification. Educational Researcher, 32(1), 9–13. ), Contexts for learning: Sociocultural dynamics in children’s development (pp. Saldaña, J. Furthermore, most studies examining or describing classroom discourse focus on primary school or lower secondary school (Walshaw and Anthony 2008). 2004; Nathan and Knuth 2003). Our categorization in convergent, divergent, encouraging, and regulating actions was partially based upon the framework of Henning et al. The enactment phases are the actual lessons, and the classroom discourse during the enactment phases constituted the object of this study. Five Practices for Orchestrating Productive Mathematical Discussions. 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; … The framework by Drageset (2015) categorizes teacher and student actions during classroom discourse in order to investigate patterns in interactions between students and teacher. 2008, p. 315). Convergent actions are teacher-led. https://doi.org/10.1017/CBO9780511499944. In addition to negotiating social norms, Yackel and Cobb (1996) describe how negotiating sociomathematical norms (e.g., what counts as a mathematical justification or what counts as a mathematically different solution method) is inherent in classroom discourse and strongly influences the mathematical disposition of students. Effective orchestration of classroom discourse shifts students’ cognitive attention from problem solutions and procedural rules to sense-making and the reasoning that leads to a solution (Yackel and Cobb 1996). We also found that the teacher spoke more than all students combined during the first lesson and spoke less than the students during the other lessons, as portrayed in Fig. Henning et al. Los Angeles: SAGE. Apparently, after repeatedly using divergent actions and trying to let the students solve the error, the teacher returned to using convergent actions, and eventually chose to demonstrate the different uses of the letter \(a\).