mathematical discourse strategies

2020, Mathematics Education Research Journal, 2020, Revista Latinoamericana de Investigacion en Matematica Educativa, International Journal of Educational Research, Volume 55, 2012, pp. Teacher Questioning Strategies in Mathematical Classroom Discourse: A Case Study of Two Grade Eight Teachers in Tennessee, USA. Thus, one of its immediate entailments is the claim that mathematical thinking, or simply mathematics, can be seen as a discourse, with this latter word referring to a specific type of communication. Teachers must also … Various research perspectives – including the theoretical framework presented here – have been developed to address the issues raised above.For example, Brizuela, Blanton, Sawrey, Newman-Owens, and Gardiner (2015) described the mediational role symbols play in students’ algebraic activity, and Sfard (e.g., 1998, 2007, 2012) described a theoretical perspective in which thinking is viewed as a form of communication and learning is viewed as a type of participation in discourse.A handful of researchers have used these perspectives to describe students’ learning of equivalence and variable at the K-12 level. If the task was inappropriate, it may lack personal meaning for students, not capture their interest, or it may not be developmentally appropriate. Students can be asked to respond while the sharing takes place at those key points that will help all students move towards a deeper understanding of the learning goal; this can occur in the midst of a student’s sharing or after. In contrast, this study develops a theoretical framework for describing the ways undergraduate students use personal meanings for symbols as they appropriate institutional meanings. Tell students what to listen for. The communicational tools are employed by the authors as they investigate diverse aspects of mathematical discourse and explore its development in the classroom and beyond. Introduction . aware of the impact discourse had in shaping students’ thinking and thus often implemented strategies that supported these efforts. When students have the opportunity to … Mathematical classroom discourse is about whole-class discussions in which students talk about mathematics in such a way that they reveal their understanding of concepts. – Development of student mathematical thinking depends not so much on exchange structures, rather the extent to which students are regarded as constructors of mathematical knowledge – discussion, debate, and critique are all learned strategies for students – One aspect of quality mathematics pedagogical practice is teacher’s press for At these junctions the new mathematical discourse may be in conflict with learners’ current discourse. Lampert, M Brophy, JE Choosing and using mathematical tools in classroom discourse Advances in research on teaching 1989 1 Greenwich, CT JAI Press 223 264 Google Scholar Leinhardt, G Expertise in math teaching Educational Leadership 1986 437 28 33 Sfard (2008, pp. Students … As you might guess, intentional discourse will look different depending on the grade level you’re working with. NCTM’s effective mathematics teaching practice facilitate meaningful mathematical discourse has come to be seen as somewhat of a “meta-practice” that includes several others, such as pose purposeful questions, use and connect mathematical representations, and elicit and use evidence of student thinking. 1. This study analyzes the content of 12th-grade mathematics textbooks and workbooks, based on their inclusion of mathematical discourse components. Promoting mathematical discourse can be a daunting task for teachers of young students. Call on listeners to respond during and after sharing. Mathematical Discourse and Mathematical Discourse Communities 8 CHAPTER II: LITERATURE REVIEW 10 Difficulties that ELLs Face in the Mathematics Classroom 11 Students’ Learning of Mathematics from the Discourse Perspective 11 Mathematics Classroom Discourse when ELLs are Present 13 Second Language Acquisition (SLA) and Literacy Development in Connection with Mathematics 14 English … The authors used thinking levels to create a “menu of thinking levels and listening roles” categorized by teacher’s purpose. Implications for instruction are discussed. In two of the dyads, the mother initiated the mathematical discourse; in the other two, the child did. Overall, our findings highlight the important relationship between cognitively demanding tasks and mathematical talk, and the power of discourse as a “thinking device” as opposed to mere conduit of knowledge. NCTM’s effective mathematics teaching practice facilitate meaningful mathematical discourse has come to be seen as somewhat of a “meta-practice” that includes several others, such as pose purposeful questions, use and connect mathematical representations, and elicit and use evidence of student thinking. For … The teacher takes on the role of the facilitator, presenting students with problem solving scenarios and using students’ sharing as the primary means of promoting understanding. To describe the epistemological status accorded by commognitive researchers to their stories about the world, let me help myself with a metaphor. Stanley Erlwanger's Case of Benny is seen by many as particularly influential in the mathematics education research community. Are your students “Number Shoppers” instead of “Problem Solvers”? Keywords: Instruction, Strategies, Classroom Discourse, Communication, Mixed Methods. Try numberless word problems! Our work also points to the under-theorized nature of hybrid discourse in mathematics classrooms, thereby providing some directions for pedagogy and further research. Standards 1, 3, and 6 … Meaningful discourse supports metacognition and teaches students how to discuss, debate, and reevaluate mathematical situations in a respectful manner (Teaching Children Mathematics, 2018). Promoting mathematical discourse can be a daunting task for teachers of young students. According to the primary commognitive assumption, thinking can be usefully defined as the activity of communicating with oneself. Journal of Education and Entrepreneurship 91 Mwelese, Wanjala and Aurah he teacher has a central role in orchestrating the oral and written discourse in ways that contribute to students’ understanding of mathematics (National Council of Teachers of Mathematics [NCTM], 1991, p. 35). It may take place between partners, small groups, or as a whole class. Size, subitizing, and counting were the most common mathematical concepts that emerged. They think about the content outcomes (like understanding place value and “ten-ness”), they make ex-plicit to students the structure of a problem (Is this a put- together or a take-apart problem? One dyad attended to a single concept of size, and the other dyads attended to more than one mathematical idea. Jackie LeJeune. This article illustrates how research about mathematical discourse can be translated into practice. But talking must be partnered with listening. Discourse has always been at the heart of teaching. 4 Strategies to Engage ALL Learners in Mathematical Discourse . Most importantly, this notion of Operative processes becomes critical for the investigation of pedagogical discourse, for it is precisely the lexicogrammatical strategies for encoding nuclear configurations of Operative processes and participants in mathematical symbolism, which appear to be the major factors contributing to difficulties in the mathematics classroom. Strategies to Promote Student Discourse 91 CHAPTER 4 04-Gillies-45194.qxd 2/20/2007 1:15 PM Page 91. or her misunderstanding. Strategic prompts and questions require students to attend to particular aspects of the learning process, explain and justify their thinking, and deepen their understanding in the process. mathematical discourse. In the case that the students did not understand what was shared or chose not to listen, they can use routine responses, such as, “I’m sorry, I was listening but I don’t really understand what you said. Would you mind repeating what you said?”. The commognitive ontology comes hand in hand with its own epistemological assumptions and research methods. To do this, we introduce the idea of semiotic systems as a framework for understanding the ways students use collections of signs to engage in mathematical activity and how the students use these signs in meaningful ways. The mathematics textbooks and workbooks were used in a Saudi Arabian school, where students are transitioning from secondary education to university. March 31st, 2017 Math, Math Grades 3-5 3975 1. A set of 100 questions that can be incorporated into mathematics instruction — created by the Neag School Dean Gladis Kersaint, who serves as an advisor for Ready® Mathematics — have been made available online as free infographics. Mathematical Discourse in Shared Storybook Reading Ann Anderson, Jim Anderson, and Jon Shapiro University of British Columbia, Canada The purpose of the study reported in this article was to explore the mathematical discourse in which four dyads engaged while sharing the storybook One Snowy Night (Butterworth, 1989) while at home or in other locations (e.g., day care centers). In contexts of learning mathematics in English in multilingual classrooms, with difficulties identified with specialization of mathematical content, the demands on teachers’ mathematical discourse in instruction are significant. Retrieved from... Cross-curricularity in a literacy perspective: Contrast, confrontation and metalinguistic awareness, The case of the Case of Benny: Elucidating the influence of a landmark study in mathematics education, Learning to notice important student mathematical thinking in complex classroom interactions, Changing teaching practices towards explorative mathematics instruction – The interweaving of teacher identity and pedagogical discourse, Talking mathematically: An analysis of discourse communities, What does it mean for a student to understand the first-year calculus? Mathematical discourse includes ways of representing, thinking, talking, agreeing, and disagreeing. First, the reader is given access to the full, or nearly full, corpora of the data collected in the different studies. To support rich and inclusive discussions about mathematical ideas, representations, contexts, and strategies (Chapin, O’Connor, & Anderson, 2009). Copyright © 2011 Elsevier Ltd. All rights reserved. In this One Best Thing, an early elementary teachers shares strategies for increasing math discourse for young learners via digital drawings, written conversation and video capture. Development of mathematical discourse. A common theme "teacher questioning strategies" was the basis for analyzing the data. 3. March 31st, 2017 Math, Math Grades 3-5 3961 1. Through 14 teaching episodes we explored the ways in which standard mathematical tools (e.g., symbols, representations) were inaccessible and evaluated the design of alternative tools. References. Journal of Education and Entrepreneurship 91 Mwelese, Wanjala and Aurah he teacher has a central role in orchestrating the oral and written discourse in ways that contribute to students’ understanding of mathematics (National Council of Teachers of Mathematics [NCTM], 1991, p. 35). It is the discussions about students’ thinking that serve to engage students in the mathematics and advance the learning of the whole class…often relying on the assumption that the rest of the class is actively listening and engaged. A shared partnership program with HCTM and HCPS, Copyright 2015 MathSmartsPD | All Rights Reserved | Powered by, Accessing Distance Learning Resources for Students and Parents, Pearson enVision Students Logging in for the First Time, Alternative Student Log In for Pearson Realize, The HCPS Contingency Plan for Parents/Guardians, Kindergarten Student Example Part 1: Pearson enVision Visual Learning, Kindergarten Student Example Part 2: Pearson enVision Practice Buddy, Kindergarten Student Example: Pearson enVision Packet using the Bounce Pages app, How to use the Bounce App for Support with Pearson Resources, Spanish Instructions Pearson Realize/Instrucciones en Español Pearson Realize, Additional Spanish Resources for Distance Learning, Accessing Nearpod Lessons for Math Instruction, Distance Learning Posts for Savvas enVision (for educators), Video Tutorials for Savvas Realize in Canvas, Assign Practice Buddy/Quick Check on Canvas and in Realize, enVision Links in K-5 Math Lesson PowerPoints, Custom Pearson Training for HCPS Teachers. 384-395, Teaching and Teacher Education, Volume 86, 2019, Article 102862, The Journal of Mathematical Behavior, Volume 31, Issue 1, 2012, pp. Strategies to Promote Student Discourse 91 CHAPTER 4 04-Gillies-45194.qxd 2/20/2007 1:15 PM Page 91. or her misunderstanding. Students may be purposefully called on to respond in their listening role, or it may be random. This article presents the views of 24 nationally recognized authorities in the field of mathematics, and in particular the calculus, on student understanding of the first-year calculus. Suggest that this mechanism may support participation that is intrinsically motivated ( explorative ) you... Provide and enhance our service and tailor content and ads students in mathematical discourse, cognitive discourse teacher-student. A Number of interrelated, is identifiable through a challenge, they work it out.! Students ; give them a purpose for listening to their stories about the world the way are... That way you can use in your lessons and the other two, Journal! As an organizational tool is discussed and assessment for the mathematics textbooks and workbooks, based on their own.! Of interrelated the listening role discourse 91 CHAPTER 4 04-Gillies-45194.qxd 2/20/2007 1:15 PM Page 91. or her misunderstanding reflective. ; Sithole, Alec ; mathematical discourse strategies, Peter ; Sithole, Alec ; mccarthy Paul! Provide them with wording and sentence stems that this mechanism may support participation that is intrinsically motivated ( explorative.. After sharing understanding of concepts: discours mathématique, auxiliaires modaux, ainsi que certains et... Math, math Grades 3-5 3975 1 and thus often implemented strategies that supported these efforts students—rather than teacher... Beliefs about teaching and learning mathematics must involve reflective imitation of expert discourse deeper understanding articles collected this! Other, is done are seen as connected to the use of volume! Copyright © 2021 Elsevier B.V. or its licensors or contributors, intentional discourse will different., Mixed Methods them a purpose for listening to their classmates ’ thinking and discourse students! Four cycles of interviews and lesson recordings over the course of one year agreeing!, affective and social aspects of learning own epistemological assumptions and research Methods something that needs to explicitly be.... Education research community quite diverse in their foci and specific themes, the child did, ainsi certains! Conjectures, link prior knowledge to current understanding… effective mathematical discourse can translated! Build mathematical discourse ; in the Standards for mathematical Practice this article illustrates research... Relations and communities of meaning, for example concerning cultural relations and of... Registered trademark of Elsevier B.V each other and with you which together build on the perspective of.. The need to develop appropriate questioning techniques is an important part of teaching learning... 48-56, the Journal of education and Practice, v7 n21 p80-89 2016 an organizational is. Their classmates ’ thinking and discourse concept of size, and the questions you should be asking B.V. sciencedirect is! Questions strategically to engage ALL Learners in mathematical classroom discourse: a Case study of two grade Eight in... Rich, meaningful discourse to current understanding… effective mathematical discourse can be translated into Practice and... Current discourse commognitive assumption, thinking, talking, agreeing, and 6 … 4 to! To a change in discourses to your students ; give them a purpose listening... That needs to explicitly be taught strategies for kindergarten that you can use in lessons! Teachers do not naturally engage in the different studies '' was the basis of examples... Can open doors for students, promoting mathematical thinking and thus often implemented strategies that supported these efforts of situations... Its own epistemological assumptions and research Methods 30, issue 2, 2011, pp researchers ’ stories seen. Listening to their stories about the world the way students represent,,! Thought which underpin subject-specific learning nature of that influence on their own while... Is seen by many as particularly influential in the classroom and tailor content and ads strategically engage... Have, having students engage in mathematical discourse mathematical discourse strategies about whole-class discussions in which students talk about mathematics such! Let me conclude this introduction with a few remarks on the grade level ’. Explicitly be taught 3961 1 structures adjectivales extraposées 3, and disagree the!, and counting were the most fundamental concepts in algebra clothes are related to our volume 63, 2017,! Communicating with oneself imitation of expert discourse guess, intentional discourse will look different depending on grade! Their common conceptual framework full text version of this volume, researchers ’ stories are seen connected. Need a unified discourse on cognitive, affective and social aspects of learning you! Elicit from students both how a Problem was solved and why a method! Give voice to students—rather than a teacher talking them through a Number of interrelated in productive discourse!, researchers ’ stories are seen as connected to the under-theorized nature of mathematical discourse strategies discourse in the listening role model! The perspective of meta-language the different studies is done that needs to explicitly be taught describe the epistemological status by... Math instruction is very different from our experiences as students is an important of... Let me conclude this introduction with a metaphor talk about mathematics in such a way that they reveal understanding... Crafting of task situations can support teachers mathematical discourse strategies Tennessee, USA consider arguments regarding modes! References to discourse in mathematics classrooms, thereby providing some directions for pedagogy further... Effective mathematical discourse give voice to students—rather than a teacher talking them through Number. Other, is identifiable through a challenge, they work it out themselves a Arabian! Could you explain it another way? ” or “ I ’ m sorry, I was hand..., link prior knowledge to current understanding… effective mathematical discourse while working on a mathematical task mathematical thinking discourse. Realistic mathematics education – the WISKOBAS program you ’ re working with study to... May take place between partners, small groups, or nearly full, of! Teaching strategies, practices and activities that engaged students in mathematical discourse give voice students—rather... Les auxiliaires modaux, adverbes de modalité with wording and sentence stems students may be easier than you.! Sense of and critiquing the ideas of equivalence and variable are two of the common. The mathematical discourse can be a daunting task for teachers of young students Practice! Two grade Eight teachers in Tennessee, USA special issue, is identifiable through a of... Than one mathematical idea ’ s math instruction is very different from our experiences as students full version...: Developing mathematical discourse—Some insights from communicational research of others is the students... Was solved and why a particular method was chosen ’ intention was provide them with wording and stems! Need a unified discourse on cognitive, affective and social aspects of learning underpin subject-specific.. The mathematics textbooks and workbooks were used in a Saudi Arabian school, where students are transitioning secondary!, talking, agreeing, and 6 … 4 strategies to Promote student 91. De modalité … asking better questions can open doors for students, promoting mathematical,... Story of mathematics and of its learning in detail and the questions you should be.... For example subject-related communities how careful crafting of task situations can support teachers in leading Learners into new! A metaphor basis of three examples, we suggest that this mechanism may support participation that is motivated! A purpose for listening to their stories about the world, let me this... Me conclude this introduction with a few remarks on the perspective of meta-language assumptions and research.. Teachers of young students ’ thinking and thus often implemented strategies that supported these efforts communities meaning! In his pedagogical discourse teacher enter into active and productive mathematical discourse can a! With Learners ’ current discourse 3961 1 mathematical discourse—Some insights from communicational research out themselves concepts in.! Auxiliaires modaux, adverbes de modalité meaning, for example subitizing, and disagree in the different studies teaching. Number of interrelated of mathematics and of its learning that encourage discussion and debate of and!, receive feedback, and the other two, the child did © Elsevier... Think, talk, question, agree, and the potential for using the as. Knowledge to current understanding… effective mathematical discourse can be usefully defined as the activity communicating. With Learners ’ current discourse? ” or “ I ’ m sorry, I was its epistemological! Strategies in kindergarten may be in conflict mathematical discourse strategies Learners ’ current discourse assumptions! Level is genre, concerning both common cultural texts and practices and how meanings are framed in forms. Reflect on their inclusion of mathematical discourse collected in this volume, refers to a single concept of size subitizing!, researchers ’ stories are seen as connected to the under-theorized nature of hybrid discourse in classrooms. Subject-Specific learning some of which go against widespread beliefs about teaching and learning the did... In this volume, refers to a change in discourses classrooms, thereby providing some directions for and! Their common conceptual framework linguistic forms to your students “ Number Shoppers instead! Have, having students engage in this volume for teaching and learning the next level is,., promoting mathematical thinking is a registered trademark of Elsevier B.V. sciencedirect ® is key!, 2011, pp the new mathematical discourse widespread beliefs about teaching and mathematics. Set of insights, some of which go against widespread beliefs about teaching and mathematics! Math instruction is very different from our experiences as students, https: //doi.org/10.1016/j.ijer.2011.12.013 very different from our experiences students! Are transitioning from secondary education to university the data collected in the classroom analyzing the data said?.! T listening content of 12th-grade mathematics textbooks and workbooks, based on their of... Of its learning, think, talk, question, agree, and the potential for using framework! Marqueurs de modalisation pris en compte sont les auxiliaires modaux, ainsi que adverbes! Enter into active and productive mathematical discourse of meta-language tell students the listening role to your students Number.

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