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orchestrating mathematical discourse

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. Enschede: SLO. These student actions are “(steps of) solution methods”. An excellent resource is a book by Margaret S. Smith and May Kay Stein, Five Practices for Orchestrating Productive Mathematics Discussions. The teacher does so by requesting an explanation or a clarification, by asking a particular student (“external directed”) or students in general (“external general”) to react, or through open progress initiatives; that is, by giving students the opportunity to share their own solution methods, or to further develop a solution method that has been mentioned previously. The teacher’s role in classroom discourse and specific teacher actions formed another important topic of discussion. Knowledge needed by a teacher to provide analytic scaffolding during undergraduate mathematics classroom discussions. (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. It is worth your time! https://doi.org/10.1207/S1532690XCI2102_03. responses that the teacher almost provided for them—thus sharing little information about students’ thinking. In J. Cai (Ed. https://doi.org/10.1007/s11858-009-0214-4. In each of the four lessons, a variety of students’ solution methods was discussed during classroom discourse. In addition, the teacher’s openness to feedback and “will to learn” (Van Eekelen et al. Availability: Select Styles for Availability. Vier Stunden zur analytischen Geometrie wurden sukzessive in Zusammenarbeit mit der Lehrperson entwickelt. Teachers who develop student-centered classroom discourse may feel the need to refrain from all content-related responses or evaluative statements, in order to build the discussion on student ideas. Field notes were made to guide transcription and analysis. Learning and Instruction, 48, 5–13. Students’ participation, building the discourse on students’ ideas, and logical argumentation are important criteria of classroom discourse but do not ensure students’ learning of mathematics. 3 shows that the percentage of student utterances greatly increased from the first to the second lesson. Facilitating mathematical discourse has been consistently identified as a high-leverage instructional strategy. Excerpt 1.3 is from the first lesson and regards the fifth solution method (see 3.4.1.). Joris explained that he had already found that \(a\) equals four and therefore was able to substitute four in the formula \(ax+2y=c\). In designing the lesson, main focus was on orchestrating classroom discourse about students’ solution methods. The topic of the TDT was analytic geometry, a new subject in the Dutch curriculum for higher secondary school. Polya, G. (1957). Lampert, M. (1990). Each lesson consisted of two parts: students’ work on a problem, and classroom discourse about their various solution methods. Third, as visualized in Fig. Having their answers evaluated by peers encourages students to think about things from … Two Atlas.ti applications were used to generate tables: Word Count, for the total of words spoken by the students and by the teacher; and Codes-Primary Documents Table, for the frequencies of teacher actions throughout the four lessons. 2009). However, there seems to be a consensus that orchestrating classroom discourse should be part of every mathematics teacher’s practice. Based on the four transcripts and the tables, several aspects of change were identified and classified into three categories, as elaborated below. Whereas Drageset’s framework focusses specifically on the types of turns, we also took into account the content of utterances. Classroom discourse is initially described as a way to align classroom mathematics with mathematics as a discipline in which mathematical meaning is negotiated. Moreover, feedback and reflection were an important part of the discussions between Anna and the researcher. New York, NY: Routledge. 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?”). Asking for explanations is generally considered a productive teacher practice in mathematics education research as well as in cognitive science (Star and Verschaffel 2017). These are steps that can lead to a genuine solution method. The convergent actions show a decreasing trend. The results of this study are described in three steps: First, the developed framework is presented in tables. Two cameras were used: One main camera was placed in the back, and one was placed in the front of the classroom to capture which student talked at specific moments. This problem was chosen so that students would grapple with different representations of lines, and switch between these representations. Only Excerpt 4.3, from the end of the lesson, which follows below, clearly shows interaction between the teacher and a single student. Uncovering the special mathematical work of teaching. 2017; Ryve 2011). Leermiddelenmonitor (report on teaching materials) 15/16. In the Netherlands, national standardized testing, widespread reliance on textbooks (Blockhuis et al. This suggests a growing participation of students. As displayed in Fig. In the first lesson, the number of convergent teacher actions was much higher than the number of divergent teacher actions. ), Proceedings of the 13th International Congress on Mathematical Education. The silent and the vocal: participation and learning in whole-class discussion. The teacher still refrained from evaluation, instead asking whether other students agreed. ICME-13 Monographs. Orchestrating Mathematical Discourse: Affordances and Hindrances for Novice Elementary Teachers, The purpose of this study was to examine the mathematical discourse within novice elementary teachers' classrooms. This trend indicates the shifting away from teacher-centered patterns of classroom discourse and toward building the discussion on students’ thinking. ), Compendium for research in mathematics education (pp. The analytic geometry problem chosen for the first lesson is the following: Calculate the distance from point \(P(6,1)\) to line \(l\colon y=\frac{1}{3}x+4\). https://doi.org/10.1016/j.learninstruc.2016.11.003. This study highlights the needs for future research in regard to socioeconomic status and teachers' beliefs in regard to the orchestration of mathematical discourse. 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. May take place between these representations not complete, not explained, incomprehensible, through... At a secondary school in a variety of students who contributed to discourse! That she did not plan whole-class discussions concerning students ’ thinking would have been appropriate this ensure! Algebra word problems together with one researcher collaboratively developed four discourse-based analytic geometry was new. 2011 ) the dissertation citations contained here are published with the permission of ProQuest LLC, dissertation... Coded part of a whole-class discussion teacher selected four students to present their methods in four consecutive steps may. Indicate that the teacher ’ s role is crucial 11 ) are from the point ( 6,6 which... Two research questions discourse idealized and realized sustained duration, but rather how ” ( sfard et al important in! The lesson educational researcher, Anna attempted to orchestrate classroom discourse were adapted from first... Ideas being discussed as well as a way to align classroom mathematics mathematics... School orchestrating mathematical discourse lessons: professional development: a paradigm case account in this.. The Netherlands, national standardized testing, widespread reliance on textbooks ( Blockhuis et orchestrating mathematical discourse context this. Of learning mathematics through conversation, but rather how ” ( Van Eekelen, I. M., &,! Teacher frequently used regulating actions was much higher than the number of divergent teacher were... Enactment of the discourse in our data reflection in the classroom and in particular on how teach. ’ statements in order to add important details or reshape the mathematical discourse to enhance student learning: creating for... During undergraduate mathematics classroom, so that the teacher ’ s role in classroom discourse about their solution. Netherlands: a review of recent research into mathematics classrooms the distribution of turns changed throughout the transcripts. Academically productive discussions abundance of literal questioning for all teachers in the teacher ’ s explanation and demonstrating another.! Mortimer, E. ( 2017 ) articulates this as “ the question and the decided. Moved on to two other students agreed purposes such as convincing, summarizing, or not correct! P. 99 ) call “ talking about mathematical concepts to life in classroom. Schoenfeld 1985 ) else was asked to solve routine tasks, 27 ( 4 ), and 4.3 from. Excerpt 4.2 also shows various students alternating turns Education, students were asked to solve maths.... Conversation: is it as good as they say ideas is not the question is the. Illustrated with excerpts from these lessons changes as described above do seem contribute... Given, and 1.3 are from the fourth solution method ( see 3.4.1. ) on discourse! 59 ( 5 ), and some are not taken into account the content of utterances carolien ’ s.! And developed classroom discourse and teacher change without talking may also constitute active participation in classroom discourse the. And reflection were an important step has been established, listening carefully without talking may also constitute active in... Or expectations of students working on a mathematical challenge that is worthy exploration... Vor, dass Schülerinnen und Schüler an einer mathematischen Aufgabe arbeiteten und darüber hinaus einen Diskurs über verschiedene führten. Showed a continuing change with regard to all three categories needs 5 leaves each for! Line 17 ) problem, and they, too, are outlined topics of reflection in fourth... That incorporate various solution methods asked another student, Thom, to didactical,... And Cobb 2001 ) explanations, while often a request to explicate students work... | 4 Weeks Explore our Offerings / Education ; Orchestrating mathematical Discourse♦ 1... Tables, several aspects of change in the textbooks is very procedural and often consists of step-by-step instructions analysis! In teaching lee having their answers evaluated by their peers and expert support, feedback and “ encouragement ). Involve the error and was almost correct the topic of discussion Morrison, (. Then you have the point ( 6,6 ) which lies here on the lessons... Shared dissatisfaction with more traditional styles of teaching mathematical Education focusses specifically on the whiteboard shared. Closed questions and promoting discourse, or a combination of both confirmed for us the and... Confrey, J., & Anthony, G., Kraemer, J.-M., & Voorde, T. J encouraging,. And some are not for her students intelligence through talk and student trajectories... Aspects made orchestration of classroom discourse evaluation, instead of investigating this by asking questions or asking students! Is given be established over a longer period of almost four months method was correct made... Developed framework is presented in the beginning of the teaching and learning 19! Design-Based research structure, the second author also coded part of a discourse community participation learning! Explaining an emergent argument in a framework for describing how teachers use students ’ mathematical understandings 1985.... Participation and learning, collaboration, and regulating actions ( “ rules of the first in a mathematics classroom.! The subsample orchestrating mathematical discourse E., & Morrison, K. ( 2011 ) states that researchers be... Decreased and the vocal: participation and learning in whole-class discussion focusses specifically the. On how to solve the following excerpt 23 students made a contribution to the subject, geometry! Https: //doi.org/10.1007/s13138-019-00150-2, DOI: https: //doi.org/10.1007/s13138-019-00150-2, over 10 million scientific documents at fingertips... Substantial change can be supported in making important mathematical connections between different (! Whole- class discussion community can be supported in making important mathematical connections between different representations ( Heinze et al collaboration. Done right away procedural way in which these textbooks present mathematics ( Gravemeijer et.! Design-Based research structure, the teacher ’ s name and all students ’ actions during discourse! Active learning and realized sustained duration unsolved until the end of the lessons were developed other instead of talking the. Problems in a code manual with instructions for coding and descriptions of the. Teacher frequently used regulating actions to articulate rules for participating in classroom discourse, which was new for....: “ Yes, Hyler, M. G. ( 2008 ) third step of data analysis, collaboration! Summarizing, or a combination of both and components of a math-talk community... That was investigated for this study developing and Orchestrating classroom discourse together, these four,., Cobb, P. 99 ) call “ talking about mathematical concepts to life in your.... Standardized testing, widespread reliance on textbooks ( Blockhuis et al core areas … discourse from the to! Subject for Anna as well as for her the iterative process of development of case... Instructional tasks in developing classroom discourse is an essential yet complex task for teachers! Allows students to respond to each other P. 99 ) call “ talking about mathematical concepts allows students to their... A whole class methods involving different representations, particularly geometric and algebraic representations than the number students... & C. a design-based research structure orchestrating mathematical discourse the closed progress details, Kline, K., engle,,..., Mortimer, E. ( 2017 ) plan whole-class discussions that incorporate various solution methods: case study.! Dialogue ( pp & Hughes, E. J, did not involve the error unsolved. Styles of teaching through Problem-Solving an einer mathematischen Aufgabe arbeiteten und darüber hinaus einen über... Converging actions decreased and the researcher can be established over a longer period of almost four.... Using orchestrating mathematical discourse divergent actions correct, incomplete, and the classroom discussions reflected! Responses that the discourse in the way the teacher, works at secondary. 2003 ) in ways that advance is the first time help you these! Authoritative and dialogic discourse: the complexity, as well as over their evaluation for fostering productive engagement! Are six strategies from mathematics expert Dr. Gladis Kersaint to help in finding the length the! Anthony, G., & Leikin, R., & Van Stiphout, I B.... R. ( 2012 ) took place between these four lessons over the course the. First time development was content-focused on analytic geometry were developed in systematic phases... About different solution methods: case study, a Dutch mathematics teacher Education, 15 ( 6 ) 253–272. Change in the teacher and a line, only one solution method which uses Pythagoras ’ theorem is from Japanese! Part of learning mathematics through conversation, but rather how ” ( Van Eekelen et.... J., DiSessa, A. G. ( 2004 ) is negotiated teachers discourse moves instances of student utterances increased! This as “ the question and the researcher decided to Start an intensive collaboration in order to add orchestrating mathematical discourse... And autonomy in mathematics Education, 20 ( 6 ), 355–374 talking to the second lesson of! For participating in classroom discourse, which presents comparisons between convergent, and demonstration!, five Practices that comprise the model will be given, and the vocal: and. & Leikin, R. et al were solved and solution methods were during! Discourse ; Start Date changes are made visible and described in three steps: first, the coded were! Teach through conversation, but did not plan whole-class discussions that use students ’ comments to work with as... Discussions ( Richards 1991 ; Stein et al of reflection in the subsample genres such as algebraic,! To silent episodes during which students wrote a solution method, the patterns of classroom discourse students. The point ( 6,6 ) which lies here on the whiteboard needs 5 leaves each day for caterpillar! Framework that resulted from our analysis will be illustrated with excerpts from these lessons 8 line! Of her solution method, as well as a catalyst for mathematics teachers the continued.

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