Getting students to react to each other by asking other students to react is something that happened only three times in the first lesson, but 29 times in the fourth lesson (for example: “Shall we ask Carolien to help you?”). Güçler, B. Deliberative discourse idealized and realized: accountable talk in the classroom and in civic life. https://doi.org/10.2307/3609122. Radboud Teachers Academy, Radboud University Nijmegen, Erasmusplein 1, 6525 HT, Nijmegen, The Netherlands, Chris Kooloos & Helma Oolbekkink-Marchand, Mathematical Institute, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany, Department of Mathematics, Radboud University Nijmegen, 9010, 6500 GL, Nijmegen, The Netherlands, You can also search for this author in https://doi.org/10.1080/07370008.2017.1362408. Sherin (2002) describes how a teacher gradually shifted his attention to process: fostering students contributions and discussion; and content: choosing particular mathematical ideas to pursue, and provides a filtering model for achieving a balance between the process and the content of classroom discourse. 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. Stone (Eds. Walshaw, M., & Anthony, G. (2008). During the 2016–2017 school year, both Anna and the researcher participated in a Teacher Design Team (TDT) at Radboud University Nijmegen. (1993, p. 99) call “talking about talking about mathematics”. Dortrecht: Kluwer Academic Publishers. mathematical ideas to be learned will be emphasized. 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. 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. For example, in Excerpt 1.1, line 7: “Yes. Graduate Semester | 1 credits | 4 Weeks Explore Our Offerings / Education ; Orchestrating Mathematical Discourse ; Start Date. Karsenty, R., & Sherin, M. G. (2017). The time span between consecutive lessons was one month for lessons 1 and 2, two months for lessons 2 and 3, and two weeks for lessons 3 and 4. The coding process resulted in a code manual with instructions for coding and descriptions of all the codes, including illustrative quotes. Studies in Philosophy and Education, 27(4), 283–297. Drageset, O. G. (2015). From line 8 until line 17, two students even talked to each other instead of talking to the teacher. The following section provides excerpts in which these changes are recognizable from the first and fourth lessons. Working through these practices involves considerable domain-specific work. Mathematical Discourse is also historically situated. Science Education, 90(4), 605–631. Sfard, A., Nesher, P., Streefland, L., Cobb, P., & Mason, J. The researcher, who is also the first author of this paper, combined his work as a PhD researcher with his work as a teacher of secondary school mathematics. I received this email, "Orchestrating mathematical discourse to enhance student learning", and wondered how many of my colleagues utilize mathematical discourse in the class? In total, five different solution methods were discussed: first, three incomplete or incorrect solution methods and subsequently, two correct solution methods. Additionally, a teacher may gain insight into “the students’ conceptual possibilities and current understandings” (Yackel and Cobb 1996, pp. Mathematical arguments can be presented for different purposes such as convincing, summarizing, or explaining. In the fourth lesson, 18 out of 23 students made a contribution to the discourse, which is more than 75%. 2 shows that the number of students who contributed to classroom discourse increased during the course of the four lessons. Orchestrating Mathematical Discourse: Affordances and Hindrances for Novice Elementary Teachers Lee, Carrie Wilkerson ProQuest LLC , Ph.D. Dissertation, North Carolina State University Important criteria of classroom discourse include that students share their ideas and make their thinking public, are involved in the discussion, and try to follow each other’s reasoning. Developing and orchestrating classroom discourse about students’ different solution methods is an essential yet complex task for mathematics teachers. https://doi.org/10.1207/S1532690XCI2004_1. Apr 05, 2021. Orlando: Academic Press. 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. Having their answers evaluated by peers encourages students to think about things from … 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. New York: Camebridge Universtity Press. Journal of Mathematics Teacher Education, 5(3), 205–233. Learning mathematics through conversation: is it as good as they say? In Fig. The lessons consisted of students working on a mathematical problem plus classroom discourse concerning students’ different solution methods. https://doi.org/10.1016/j.jmathb.2011.11.001. The relevant parts (each with a duration between 21 and 24 min) containing classroom discourse were transcribed. First, Anna and the researcher had a shared goal, i.e., developing classroom discourse in Anna’s classroom, such that students would share and discuss various solution methods. cr.) 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. In addition, steps that were unclear to students were made the subject of a discussion. Moreover, by comparing various solution methods, students can be supported in making important mathematical connections between different representations (Heinze et al. In most cases, such an utterance was followed by an encouraging action, after which the student continued and finished the solution method. The researcher’s role varied from interested fellow mathematics teacher, to didactical coach, to scholar with theoretical knowledge on classroom discourse. The cases described in previous studies usually involved a teacher highly skilled in orchestrating classroom discourse, or involved a teacher who had already been involved in an intensive professional development program. 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. Mathematical Discourse also involves different genres such as algebraic proofs, geometric proofs, and school algebra word problems. The teacher’s name and all students’ names are pseudonyms. One teacher together with one researcher collaboratively developed four discourse-based analytic geometry lessons. 2016) lead to most students attending years of outcome-oriented mathematics lessons. (2003). For example, students should be encouraged to both explicate their thinking and react to each other’s ideas. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Let l be the line given by the following vector equation: We consider the lines \(ax+2y=c\), where \(a\) and \(c\) are constants. 2006), or (whole-class) discussions (Richards 1991; Stein et al. Carolien seemed to be convinced (line 17). Understanding what students mean when they talk about mathematics is a complex task (Wallach and Even 2005), and identifying students’ mathematical thinking to build on during classroom discourse is even more complicated (Van Zoest et al. 13–51). Alice said she had something different from the point where the slope was calculated, but could not find the words to describe her method. All design and evaluation phases took place in meetings between Anna and the researcher, except the first design phase which took place in the context of the TDT. The teacher decided to set Joris’ method aside from the point where the slope was calculated, but did not correct the error. Discrepancies were discussed until a consensus was reached, resulting in adjustments to the code descriptions and framework. 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. For the Learning of Mathematics, 18(1), 41–51. How mathematics teachers can develop and orchestrate classroom discourse remains an important question for research, especially regarding various solution methods for mathematical problems in higher secondary school. During the first lesson, Anna attempted to orchestrate classroom discourse concerning students’ various solution methods for the first time. The five practices—anticipating, monitoring, selecting, sequencing, and connecting—should be carefully prepared to reduce complexity and in-the-moment decision making during classroom discourse. Gradually, the teacher tried to build the discussion on student ideas, using more divergent actions. 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 … This involves more than merely being able to solve routine tasks. The teacher’s role in classroom discourse and specific teacher actions formed another important topic of discussion. https://doi.org/10.1007/s10857-005-3849-2. Journal of Teacher Education, 59(5), 389–407. Number of students talking in classroom discourse. The analysis of teacher moves showed that teachers with higher levels of mathematical knowledge for teaching used more open-ended questioning and prompted more student contributions. 2008). Saldaña, J. 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. Stein et al. Whereas Drageset’s framework focusses specifically on the types of turns, we also took into account the content of utterances. Levav-Waynberg, A., & Leikin, R. (2012). The students were presented with a problem which involved calculating the distance between a point and a line in the Cartesian coordinate system. A study of whole classroom mathematical discourse and teacher change. In addition, teachers can explicitly state and discuss rules for communication.
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