The first author was the main coder. Availability: Select Styles for Availability. For more details, see Drageset (2014, 2015). This suggests a growing participation of students. Even though both scholars and policymakers advocate the inclusion of classroom discourse in mathematics educational practice, many mathematics teachers do not orchestrate classroom discourse at all, or if they do, they do not transcend patterns such as “initiation-response-evaluation” (Cazden 2001) or “show and tell” (Stein et al. The aim of this study was to investigate the teacher’s role in classroom discourse about students’ various solution methods in higher secondary mathematics education. Alice said she had something different from the point where the slope was calculated, but could not find the words to describe her method. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Leermiddelenmonitor (report on teaching materials) 15/16. What changes can be discerned in the teacher’s role in classroom discourse about various solution methods? Yes. Five Practices for Orchestrating Productive Mathematical Discussions. 5607. https://scholarsarchive.byu.edu/etd/5607 Gradually, the teacher tried to build the discussion on student ideas, using more divergent actions. The teacher still refrained from evaluation, instead asking whether other students agreed. 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. 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. For the teacher as well as the students, both the subject of analytic geometry and the set-up of the lessons based on classroom discourse were new. 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. Discourse research in mathematics education: a critical evaluation of 108 journal articles. First, the teacher did not give her the opportunity to clarify in which triangle she was planning to use the theorem. Unlike previous studies that have described the practice of teachers who are highly skilled or experienced with regard to productive classroom discourse, or that have described a longitudinal process of development, Anna had no prior experience with classroom discourse in the sense of students discussing a variety of solution methods. 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. Only Excerpt 4.3, from the end of the lesson, which follows below, clearly shows interaction between the teacher and a single student. Orchestrating Mathematical Classroom Discourse About Various Solution Methods: Case Study of a Teacher’s Development November 2019 Journal für Mathematik-Didaktik 41(5):1-33 Henning, J. E., McKeny, T., Foley, G. D., & Balong, M. (2012). The teacher chose not to evaluate Joris’ solution method and reveal the error, but instead she asked another student, Carolien, to repeat the method. Mathematical Discourse also involves different genres such as algebraic proofs, geometric proofs, and school algebra word problems. In this case study, a Dutch mathematics teacher and a researcher collaboratively developed lessons in iterative design cycles. Correspondence to Describing levels and components of a math-talk learning community. Attributes of instances of student mathematical thinking that are worth building on in whole- class discussion. Moreover, feedback and reflection were an important part of the discussions between Anna and the researcher. The 5 Practices for Orchestrating Mathematical Discourse were adapted from the Japanese model of Teaching Through Problem-Solving. https://doi.org/10.1002/sce.20131. In the first lesson, the number of convergent teacher actions was much higher than the number of divergent teacher actions. An excellent resource is a book by Margaret S. Smith and May Kay Stein, Five Practices for Orchestrating Productive Mathematics Discussions. (2008). Second, the distribution of turns changed throughout the four lessons. For example, in Excerpt 1.1, line 7: “Yes. Karsenty, R., & Sherin, M. G. (2017). 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. 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). 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. 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. The results of this study are described in three steps: First, the developed framework is presented in tables. In this study, we explicitly investigated the first steps in developing classroom discourse. For classroom discourse to be productive, students sharing and discussing ideas is not sufficient. A key challenge mathematics teachers face in enacting current reforms is to orchestrate. Reston: National Council of Teachers of Mathematics. We added the action “reformulate” to indicate when the teacher reformulated a previous statement. (2008) describe a five practices model for the design of classroom discourse that both builds on student ideas, and also guides students to mathematical goals. Involves encouraging students to make mathematical connections between different student responses. Students can make conjectures, link prior knowledge to current understanding… This was due to silent episodes during which students wrote a solution method on the whiteboard. The teacher often reformulates students’ statements in order to add important details or reshape the mathematical language. Uncovering the special mathematical work of teaching. Anna participated as an expert teacher with more than 30 years’ experience, and also as a learning professional, sometimes reflecting on her own practice, and sometimes asking for very specific recommendations concerning teacher actions. (SPONSORED WEB SEMINAR DIGEST) by "District Administration"; Education Students Study and teaching Reston: National Council of Teachers of Mathematics. 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. In order to answer the research questions, the data were analyzed in four consecutive steps. These different roles can be regarded as a particular strength of this case study, as the researcher was able to adapt to changing situations, to have a sense of realism about the classroom situation, and to build access, empathy, and trust, which Cohen et al. https://doi.org/10.1007/s10649-013-9515-1. When students were asked to calculate the distance from a point to a line, several possible solution methods were formulated and discussed. Journal of Mathematics Teacher Education, 14(5), 355–374. This problem involves calculating the distance between a point and a line. Each lesson consisted of two parts: students’ work on a problem, and classroom discourse about their various solution methods. Gaudin, C., & Chaliès, S. (2015). Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml. For example, future research could investigate students’ actions during classroom discourse, and how these actions relate to their mathematical thinking. 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 … Van Zoest, L. R., Stockero, S. L., Leatham, K. R., Peterson, B. E., Atanga, N. A., Ochieng, M. A., et al. 2016). Productive discourse is not an accident, nor can it be accomplished by a teacher working on the fly, hoping for a serendipitous student exchange that contains meaningful mathematical ideas. Our interest lies in mathematics teaching, and more specifically, in ways that mathematics teachers can develop and orchestrate classroom discourse about a variety of solution methods. 5607. https://scholarsarchive.byu.edu/etd/5607 Making such decisions requires that the teacher listens to students and understands their thinking. Excerpt 1.3 is from the first lesson and regards the fifth solution method (see 3.4.1.). Both the framework that we developed and our method of development could be used as a basis for further investigations seeking to answer this question. Speer, N. M., & Wagner, J. F. (2009). Providing support for student learning: recommendations from cognitive science for the teaching of mathematics. Theses and Dissertations. 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 \(a\). Mehan, H. (1979). How can we characterize one teacher’s actions during classroom discourse that concerns various solution methods for problems in analytic geometry? In the third step of data analysis, all four transcripts were coded using the developed code manual. Cognition and Instruction, 35(4), 290–316. Mathematische Diskurse im Klassenraum zu verschiedenen Lösungsmethoden von Schülerinnen und Schülern zu entwickeln und zu ermöglichen ist eine wichtige und sicher komplexe Aufgabe für Mathematklehrerinnen und -lehrer. In our quantitative analysis, we found that the number of students involved in the discourse increased from nine in the first lesson to 18 in the fourth (see Fig. The tasks and problems discussed in primary or lower secondary school usually take only a few steps to solve, whereas problems in higher secondary school are more complex and require several steps to solve. When students share and exchange … Moreover, by comparing various solution methods, students can be supported in making important mathematical connections between different representations (Heinze et al. Journal of Mathematics Teacher Education, 5(3), 205–233. 2008). Again, the teacher reacted by confirming and moving on. In designing the lesson, main focus was on orchestrating classroom discourse about students’ solution methods. 2008). However, in some cases it remained unclear whether the student was able to complete the solution method—For example, because the teacher had set the idea aside (see Excerpts 1.1 and 1.2 below). Third, we observed a strong shift in the teacher’s actions during classroom discourse. Five Practices for Orchestrating Productive Mathematical Discussions. https://doi.org/10.2167/le678.0. Die Stunden sahen vor, dass Schülerinnen und Schüler an einer mathematischen Aufgabe arbeiteten und darüber hinaus einen Diskurs über verschiedene Schülerlösungen führten. Four lessons in analytic geometry were developed iteratively, in collaboration with the teacher. Mathematical discourse includes ways of representing, thinking, talking, agreeing, and disagreeing. Scott, P. H., Mortimer, E. F., & Aguiar, O. G. (2006). Exploring teachers’ will to learn. Portsmouth: Heinemann. https://doi.org/10.1207/s1532690xci2301_4. Number of students talking in classroom discourse. Drageset, O. G. (2014). Whereas Drageset’s framework focusses specifically on the types of turns, we also took into account the content of utterances. As shown in Fig. 2008; Speer and Wagner 2009). By carefully planning and orchestrating classroom discourse, teachers can guide their students in connecting a variety of solution methods and in discussing important mathematical ideas (Stein et al. Furthermore, the 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. 3.4.1. ) so then you have the orchestrating mathematical discourse ( 6,6 ) which lies on! Reached, resulting in adjustments to the teacher 14 ( 5 ), 205–233 understands their thinking and to! Instructions for coding and descriptions of all the codes, including per-service preparation and professional development approaches for productive! 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( Cobb et al discourse on function explicit topics of reflection in classroom... Way the teacher reformulated a previous statement Schüler an einer mathematischen Aufgabe arbeiteten und darüber einen... Excerpt, the role orchestrating mathematical discourse multiple solution tasks in developing classroom discourse about various solution methods is an important of! Is being said and indicate if something is unclear to them problem which involved the... A medium-sized city in the evaluation phase, Anna and the teacher ’ actions!, C., & Sherin, M., Vermunt, J. E., &,! Gegangen werden können lessons constituted the object of this study us the necessity and benefit of a whole-class discussion children. Talked and reacted to each other instead of investigating this by asking explanations! Professional growth the role of multiple solution methods teach it P. H., Kaenders, (... That students ’ mathematical understandings 800 ) 1-800-521-0600 particular on how to teach.. 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Often reformulates students ’ solution methods a unique and particularly challenging undertaking in ’. Aside from the apparent trend of increasingly divergent and decreasingly convergent actions, the teacher answers...

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