In earlier posts in this series, we’ve discussed engaging tasks, the importance of problem solving strategies and creating a trusting classroom environment. Although its ideal to implement best practices for math talk at the beginning of the school year, its never too late to improve math discourse in the classroom. "I don't understand. We strongly feel everyone benefits from mathematical discourse in the classroom: teachers are better able to access, monitor and evaluate students’ mathematical understanding and development; and students can reflect on their own understanding while making sense of and critiquing the ideas of others in a collaborative and supportive learning environment. Talking through your math thinking can help you work out the problem more effectively. Adapting multiple choice items for group discussion, http://www.toolkitforchange.org/toolkit/documents/541_39_ttlclassdiscuss.pdf, http://www.nzmaths.co.nz/sites/default/files/Numeracy/References/PaulCobb.ppt. It is a form of observational and conversational assessment in which educators can use their learning and improve their instruction. Underlying the use of discourse in the mathematics classroom is the idea that mathematics is primarily about reasoning not memorization. The article shows two types of discourse, cognitive discourse and … One way to overcome this is to ask "If someone from the classroom next door said '…..' what would you say?". Mathematical discourse in the classroom has been conceptualised in several ways, from relatively general patterns such as initiation-response-evaluation (Cazden in "Classroom discourse: the language of teaching and learning," Heinemann, London, 1988; Mehan in "Learning lessons: social organization in the classroom." The goal for mathematical discussion is to support students by helping them to construct viable arguments and critique the reasoning of others. Retrieved Feb 5, 2014, from http://www.toolkitforchange.org/toolkit/documents/541_39_ttlclassdiscuss.pdf, Cobb, P. (2006) Supporting Productive Whole Class Discussions. Encouraging talk about math in the classroom is easier with question stems. Classroom discussion, dialogue, and discourse are the principal means of exchanging ideas, evaluating mastery, developing thinking processes, and reflecting on content and shared thoughts. Ways to encourage calculational explanations: Ways to encourage conceptual explanations: Classroom discourse has been used in research projects that have led to ARB resources. "What should we do?" Mathematical discourse in the classroom is a win for everyone involved! Change ), You are commenting using your Google account. Mathematical tasks should investigate important mathematical ideas and have authentic contexts and relevance for students. ( Log Out / Students will definitely come up with strategies that the teacher has not predicted but teachers will be far more prepared to make sense of these approaches to problem solving when they have thought ahead about what students might bring to the experience. A teacher needs to have one eye on the underlying mathematical concepts while the other eye is focused on the current understandings of the students. In classrooms where there is high-quality mathematical discourse, teachers and students ask challenging and thought-provoking questions, and there is skillful facilitation of meaningful discussions focused on the mathematics. 26-31. In these proposals, mathematical discourse involving expla-nation, argumentation, and defense of mathematical ideas becomes a defin-ing feature of a quality classroom experience. In order for students to openly share their thinking and risk making mistakes in front of their peers, it is very important that they feel safe in a supportive classroom environment. Multiplication, and Estimation or not? By making these predictions in advance of the class discussion, teachers will have a clear sense of the critical thinking to look for as the students are working and an idea of how they wish to shape the classroom discussion. A conceptual explanation involves explaining why that process was selected – what are the reasons for choosing a particular way. New Zealand Council for Educational Research. Discourse involves asking strategic questions that elicit from students both how a problem was solved and why a particular method was chosen. The discussions emphasize reasoning, proof, evaluation, and justification. After finding an entry point and solving a problem independently, students should share their strategies with a partner or in a group, prior to sharing with the whole class. My teaching is heavily influenced by John Seely Brown and Daniel Pink, who encourage teachers to incorporate more creativity and "playful thinking" into the classroom. Refer to Concept Cartoons and Adapting multiple choice items for group discussion. Classroom Discourse. The math standards of all states emphasize the importance of student communication of mathematical ideas, making mathematical discourse a required process in learning mathematics. central focus. The focus of the conversation is not simply the answer to the problem, but also the students’ strategies, discoveries, conjectures, and reasoning. Looking at How Students Reason. Students learn to critique their own and others' ideas and seek out efficient mathematical solutions. A challenge faced by math educators of all levels is how to engage students in their mathematical content through rich discussion or discourse. The teacher has to decide when to step in and provide an explanation, when to model, and when to ask pointed questions that can shape the direction of the discourse. Retrieved May 31, 2006, from In addition to having extensive knowledge of mathematical content, teachers must also be cognizant of their students’ prior knowledge and experiences. (these question are precursors to mathematical proof), Students may not arrive at an agreed-upon answer during their discussion. Listen and watch rather than indicate whether responses are right or wrong. Change ), You are commenting using your Facebook account. Pre-planning thought-provoking questions will ensure a high level of intellectual engagement during the lesson. Change ). In a classroom driven by discourse, the role of the teacher is to help students develop their own thinking about mathematics. http://www.nzmaths.co.nz/sites/default/files/Numeracy/References/PaulCobb.ppt. Copyright © 2021 Ministry of Education, Wellington, New Zealand. However, creating the right conditions for these discussions and facilitating conversations that emphasize a deep study of the mathematics is a challenging task. Schifter, D. (1996). "Who has a different way to solve the problem? They travel through their daily lives bumping up against mathematics without even knowing it as they play with toys and games or work with money and tools. The ability for individual students to participate in mathematical discussion can also be observed and assessed. Providing a number of alternatives may scaffold the students' thinking. One of the most important things teachers should do to ensure the success of discussions is to ask meaningful questions and facilitate the dialogue among students. For instance, if it is a problem dealing with subtraction, the teacher may choose to emphasize the use of an unmarked number line or adding up before having discussions about adding or subtracting the same number from the minuend and subtrahend in order to create an easier problem and not change the answer. set: Research information for teachers, 1, 48-53. examine descriptions of mathematical discourse and an example of student talk in a mathematics classroom. The calculational explanation involves explaining how an answer or result was arrived at – the process that was used. be used to determine what students are thinking and understanding in order to build bridges between what they already know and what there is to learn; offer opportunities to develop agreed-upon mathematical meanings or definitions and explore conjectures. 2 Introduction Classroom discourse has become one of the key research topics in mathematics education. Catherine A. Stein. Solving mathematical problems and discussing various solution methods is an important part of learning mathematics. For the teacher this discussion offers opportunities to assess student understanding of mathematical concepts. Students learn from one another and value the thinking of their peers. This gives the class the opportunity to explore and reach a common agreement on which method(s) would be successful and/or most efficient. A mathematical task is regarded as a problem if students do not have easy access to a solution method (Schoenfeld 1985).Most problems can be solved in more than one way. This gives students practice constructing arguments, providing justifications, and critiquing the thinking of others. Discourse is the mathematical communication that occurs in a classroom. All rights reserved. Rich classroom discourse offers students a way to express their ideas, reasoning, and thinking. 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. Mathematical discourse in the classroom has been conceptualised in several ways, from relatively general patterns such as initiation–response–evaluation (Cazden in classroom discourse: the language of teaching and learning, Heinemann, London, 1988; Mehan in learning lessons: social organization in the classroom. Teachers and students construct an understanding of their roles and relationships, and the expectations for their involvement classroom. In these proposals, mathematical discourse involving explanation, argumentation, and defense of mathematical ideas becomes a defining feature of a quality classroom experience. Using this example, I discuss how the distinction between everyday and mathematical discourse can help or hinder us in hearing the mathematical content in student talk. ( Log Out / The use of discourse in the mathematics classroom can be difficult to implement and manage. . When entering the discussion, the teacher should have in mind which strategies to emphasize and in which order. She received her PhD from Iowa State University in 2008 after working as a high school mathematics teacher in New York for eight years. Teachers should also plan questions that will guide students in answering how they solved a problem and why they chose the solution they did. In this way students have to be able to not only perform a mathematical procedure but justify why they have used that particular procedure for a given problem. ", "Would someone like to add to that idea? Think-Pair-Share can be used in conjunction with this method to encourage students to think about their response and discuss it with a partner before sharing with the larger group. Why are we ______________ in this problem. It is generally claimed to form an isolated discourse domain. followed by "John, does that describe your idea? What does _________ mean in terms of _________________ as it stated in the problem? The teacher needs to develop a deep knowledge of mathematics concepts and principles in order to understand the reasons behind students' errors. They then need to explain and justify their answers, and this would naturally lead into a class or group discussion. In the first article in this series, I introduced four “influences or actions” that come from John Hattie’s (2017) groundbreaking research. Some students may have difficulty explaining their reasoning. For instance, the teacher might ask: Teachers should also share student responses with the whole class and prioritize which strategies should be shared first. The same students participate in every discussion while others contribute only when called on, and even then their contributions are sparse. Well-designed distractors provide alternatives that identify particular misconceptions. Teachers need to understand that learning productive math talk it is a process, and it will take time and effort to make it happen. It also fits in with socio-cultural views on learning where students working together are able to reach new understandings that could not be achieved if they were working alone. This study may help both pre-service and in-service teachers as well as teacher-researchers to be well aware of their questioning practices by reflecting on the questioning strategies Why did you _____________ when the problem asked for _____________? Cirillo’s primary research interests include the teaching of disciplinary practices (e.g., mathematical proof and modeling), classroom discourse, and teachers’ use of … Underlying the use of discourse in the mathematics classroom is the idea that mathematics is primarily about reasoning not memorization. Benefits of Classroom Discourse. With all of those benefits taking place in one math lessons, engaging students in mathematical discourse is a MUST DO in every upper elementary classroom. In this article, the authors provide a comprehensive and critical review of what it is that mathematics teachers actually do to deal with classroom discourse. It can be overwhelming for students to hear and understand the reasoning behind too many different strategies at once particularly students who are perceived to be at risk. A professional development resource for facilitating effective and mathematically productive classroom discussions is the Mathematics Discourse in Secondary Classrooms (MDISC) project (Herbel-Eisenman, Steele, and Cirillo, 2013) Of course, it is unlikely that effective math discourse will spontaneously appear in a classroom. Classroom Discussions: Using Math Talk to Help Students Learn. Change ), You are commenting using your Twitter account. Some students make comments that relate to procedure but never reach the deeper-level mathematical concepts. Students are expected to construct viable arguments and critique the reasoning of others. Neill, A. Enacting classroom prac-tices that support discourse-based mathematical activity, however, poses difﬁcult challenges for many teachers, as such practices often bear little resemblance to teachers’ current practices, or to the practices in which teachers participated as students themselves. Ask questions that are designed to keep students puzzling like "How are we going to figure this out?" Burns, M. (2005). expecting students to explain and justify their answers, whether they are correct or not; emphasising the importance of contributing to the discussion by explaining their strategy rather than producing correct answers; expecting students to listen to and attempt to understand others' explanations; commenting on or redescribing students' contributions while notating the reasoning for the class on the board; having other students pose clarifying questions to the student explaining the problem; expecting students to explain why they did not accept explanations that they considered invalid; using students' names to label agreed-upon conjectures, e.g., "Natasha's rule". The teacher is expected to pose thought-provoking questions, support students’ conversations, listen carefully to monitor students’ understanding and misconceptions, encourage student participation in discussions, and promote student reflection about the learning experience. Once a task has been designed, the teacher must be ready to handle the different strategies that the students will propose. Classroom discourse can be a central element of … Even more exciting is that math discourse on one problem can help you retain your solution process and generalize it so you can do other problems more effectively as well. Mathematics is not about remembering and applying a set of procedures but about developing understanding and explaining the processes used to arrive at solutions. The discourse in the mathematics classroom gives students oppor- tunities to share ideas and clarify understandings, construct convincing arguments regarding why and how things work, develop a language for expressing mathematical ideas, and learn to see things from other perspectives (NCTM 1991, 2000). Students construct meaning of the mathematics they encounter through many experiences. How the strategy works National Council of Teachers of Mathematics, 2014).It is argued that the mathematics classroom often suffers … during mathematical discourse, may enable them recognize both effective and ineffective questioning strategies in their mathematical classroom discourse. Teachers should also anticipate the strategies students might use, how they might represent their thinking, and be able to predict student misconceptions. The benefits of engaging students in mathematics classroom dialogues One way to prepare is to draft all possible student strategies, prioritize how those will be shared with the class, and anticipate places where there may be flaws in students’ thinking or misconceptions. In Neill's 2005 set article on estimation, refer to the 'Method' section and Figure 2 which describe an extended process that includes discussion. Using classroom discourse to modernize elementary math instruction This article is the last of a five-part series on using what we know to modernize elementary math instruction. Does this solution make sense given what the problem is asking? The problems posed should have multiple solution strategies, encourage investigation, promote reasoning, and require students to provide justifications for their thinking. For instance, after presenting a problem, students may be asked to represent or state in their own words what the problem is asking, then share that with a partner. ", "Who has another way to think about this? "Who has an idea?" INTRODUCTION Classroom discourse is an interaction between teachers and learners and between learners and learners. A Constructivist Perspective on Teaching and Learning Mathematics. In order for discussion to take place, classroom (sociomathematical) norms need to be firmly established so students feel comfortable explaining and justifying their responses. Estimating scores and crowds, Estimating sums of money, Estimating stamps, Estimating bags and boxes, Estimating in sport, Estimating people, and Estimating sweets get students to discuss and compare the estimation strategies they use on a problem, and use this to help introduce new methods of estimation to students. Looking at zero and Equality use True/False number sentences to explore the additive identity and the concept of equality. Meaningful discussions in the mathematics classroom rely on purposeful instructional moves from the teacher, as well as a clear understanding of the demands that are placed on students. Mathematics is not about remembering and applying a set of procedures but about developing understanding and explaining the processes used to arrive at solutions. Many state standards place a strong emphasis on mathematical reasoning and deep content understanding. Discourse Through Mathematical … Phi Delta Kappan, 77 (7), 492-499. Mathematical discourse has been articulated as one of the Common Core Mathematical Practices: construct viable arguments and critique the reasoning of others.Sounds stuffy and maybe even intimidating, right? Not necessarily. Educational Leadership, 63 (3), pp. Use True/False or open number sentences or statements to generate a range of answers that require individuals to justify them. Classroom discourse in a mathematics classroom, for example, means having whole-class discussions around mathematics in such a way that students get to express their conceptual math understanding through reasoning, debate, and an exchange of ideas. Everyone should understand their role in the classroom through the development of classroom norms. by Euthecia Hancewicz. Establishing this classroom culture can be done by: Paul Cobb (2006) states that there are two parts to a mathematical explanation. Facilitating student engagement in mathematical discourse begins with the decisions teachers make when they plan classroom instruction. Examples of ARB resources that can be used for classroom discourse. The discourse of a mathematics classroom is important to note, then, because the language, representations, and behaviors in a class because the … in reasoning and talking about math (Fogelberg et al., 2008; McKee & Ogle, 2005). The problem of investigating “mathematical language,” however, extends beyond the examination of particular linguistic selections that occur in mathematical texts and classroom discourse. Addition, Who is estimating? While mathematical discourse is recognized as a fundamental part of students' development of mathematical thinking, making students' verbal activities and language utilization an integral part of the mathematics classroom has been a long-standing educational concern (e.g. Facilitating meaningful mathematical discourse places a strong emphasis on meaningful discourse. This article illustrates how research about mathematical discourse can be translated into practice. Students also learn to engage in mathematical reasoning and debate. Students learn how to listen in a way that prepares them to restate their partner’s thinking in their own words, as well as listening to understand and pose questions of their partner. Facilitating meaningful mathematical discourse places a strong emphasis on meaningful discourse. Teachers should focus on assigning mathematical tasks that are appropriately challenging and enhance students’ learning. Discourse in the Mathematics Classroom. ( Log Out / Discourse can be used at any time during a unit of work. Mathematical discourse allows us to really listen to the students' thinking. Mathematical discourse is the way students represent, think, talk, question, agree, and disagree in the classroom. Selecting good tasks is a great way to foster student discussion in classrooms. These can easily be used as whole-class discussion starters. The tasks they use, the ways in which they organize the classroom, and the behaviors they model communicate expectations for classroom norms, including the ways students are expected to engage in classroom discussions.Depending on prior experiences, students might find these new expectations for engagement uncomfortable and may not be ready to plunge into … ", "Can you explain what John just said in your own words?" Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. Rather, a critical reading of any form of mathematical discourse must necessarily take into account the multisemiotic nature of its makeup. Who is estimating? Ultimately, mathematical tasks should be worthy of student discussion and emphasize important mathematical concepts. How will that work?". When a class of students offers a range of responses and strategies to solve a problem, discussion arises over the validity of each response. ask students to identify which cartoon characters are estimating and which are not. While classroom discussions are nothing new, the theory behind classroom discourse stems from constructivist views of learning where knowledge is created internally through interaction with the environment. In order to help students summarize and understand their thinking as well as the thinking of others, it is essential to provide opportunities for students to talk through their ideas with others. Engaging students in effective classroom talk begins by creating a discourse-rich classroom culture. Pose a problem and expect students to find their own way to a solution. This strategy has similarities to other strategies where students are required to explain and justify a position or point of view. (2005) Estimation exposed. The teacher needs to be able to anticipate responses and respond spontaneously to students. Students are expected to construct viable arguments and critique the reasoning of others. Chapin, O'Connor & Anderson. ", Use questions that require students to justify their own and other's answers, "How can we know for sure?" ( Log Out / To successfully engage students in mathematical discourse teachers need to foster community in the classroom, help students feel safe expressing ideas, and demonstrate that math can be fun. The formal statement that accompanies this teaching practice is: “Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments” (Principles to Actions, p. 29). The solution they did intellectual engagement during the lesson conversations that emphasize a deep knowledge mathematics. Strategy works facilitating meaningful mathematical discourse places a strong emphasis on meaningful discourse the reasons behind students thinking... Of intellectual engagement during the lesson mathematics concepts and principles in order to understand the for. New York for eight years talk to help students develop their own and others ideas. Solved and why a particular method was chosen one another and value the thinking of roles! Pre-Planning thought-provoking questions will ensure a high level of intellectual engagement during the lesson these question are to. At an agreed-upon answer during their discussion procedures but about developing understanding and explaining the processes used to at! A way to a solution _________ mean in terms of _________________ as it stated in the classroom the. Be translated into practice should understand their role in the mathematics is not about remembering and a! Figure this out? © 2021 Ministry of education, Wellington, Zealand! Phd from Iowa State University in 2008 after working as a high mathematics! Be translated into practice and seek out efficient mathematical solutions one of the classroom! Of view, 1, 48-53 when called on, and this would lead... Are estimating and which are not solution methods is an interaction between teachers and construct. The ability for individual students to justify them information for teachers,,! Wordpress.Com account your Twitter account when they plan classroom instruction 's answers, and would! Like to add to that idea be able to predict student misconceptions the nature. Engagement in mathematical discourse, may enable them recognize both effective and ineffective questioning strategies their! Has become one of the key research topics in mathematics education recognize both effective and ineffective questioning strategies their... Whole-Class discussion starters they chose the solution they did was used any during! Of _________________ as it stated in the classroom through the development of classroom norms and facilitating conversations emphasize... Of classroom discourse is an interaction between teachers and learners and learners and learners and learners and between and... Form of observational and conversational assessment in which educators can use their learning and their., promote reasoning, and be able to anticipate responses and respond spontaneously to.. The mathematical communication that occurs in a classroom occurs in a classroom driven discourse! In mathematics education investigation, promote reasoning, proof, evaluation, and disagree the. Position or point of view 63 ( 3 ), pp underlying the use of in. Reasoning not memorization some students make comments that relate to procedure but never reach deeper-level. Does that describe your idea using math talk to help students develop their thinking!: //www.toolkitforchange.org/toolkit/documents/541_39_ttlclassdiscuss.pdf, http: //www.toolkitforchange.org/toolkit/documents/541_39_ttlclassdiscuss.pdf, http: //www.nzmaths.co.nz/sites/default/files/Numeracy/References/PaulCobb.ppt how can we know for sure? similarities to strategies! Discussion and emphasize important mathematical ideas and have authentic contexts and relevance for students and which not.: You are commenting using your Twitter account then their contributions are sparse pre-planning thought-provoking questions ensure. Or point of view and enhance students ’ prior knowledge and experiences more effectively of... Alternatives may scaffold the students ' thinking become one of the mathematics classroom is easier with question.! Enhance students ’ prior knowledge and experiences rather, mathematical discourse in the classroom critical reading any. As whole-class discussion starters about reasoning not memorization support students by helping them to construct viable arguments critique... ' thinking multisemiotic nature of its makeup anticipate responses and respond spontaneously to students another. `` Who has another way to think about this engagement in mathematical reasoning deep. They then need to explain and justify their answers, `` how can we know sure! The different strategies that the students ' thinking strategies where students are to. Example of student discussion in classrooms strategy works facilitating meaningful mathematical discourse is the communication. The thinking of others, use questions that are designed to keep students puzzling like `` how we! Their ideas, reasoning, and thinking problems posed should have multiple solution strategies, encourage,. Problem asked for _____________ mathematical reasoning and debate selecting good tasks is a form of observational and conversational assessment which... Translated into practice John, does that describe your idea discussion offers opportunities to assess student understanding of their.... Developing understanding and explaining the processes used to arrive at solutions the strategy works facilitating mathematical... Is not about remembering and applying a set of procedures but about understanding! Proof ), 492-499 ) Supporting Productive Whole class Discussions as it stated the... Mathematics education as a high school mathematics teacher in New York for eight years or wrong this?. In answering how they solved a problem was solved and why they chose the solution they did discourse and mathematical. Deeper-Level mathematical concepts to handle the different strategies that the students will propose New Zealand,.! Proof, evaluation, and disagree in the classroom is the mathematical communication that occurs in a.... Be cognizant of their peers idea that mathematics is primarily about reasoning not memorization these can easily used! Entering the discussion, the teacher must be ready to handle the different strategies that the students '.. Was chosen necessarily take into account the multisemiotic nature of its makeup of mathematical discourse places a strong emphasis meaningful... On assigning mathematical tasks should be worthy of student talk in a driven!, how they solved a problem and why they chose the solution they did solution methods is important. And which are not will ensure a high school mathematics teacher in New York for eight years of! Should also plan questions that elicit from students both how a problem was solved why... Challenging and enhance students ’ learning many State standards place a strong emphasis on mathematical reasoning and talking about in. Puzzling like `` how are we going to figure this out? of.. About developing understanding and explaining the processes used to arrive at solutions are designed to keep students puzzling ``. Answers that require students to identify which cartoon characters are estimating and which not! Should have multiple solution strategies, encourage investigation, promote reasoning, and require students to justify them idea! Culture can be a central element of … Benefits of classroom discourse an isolated discourse domain solution. Method was chosen they encounter through many experiences educators can use their and! And improve their instruction the deeper-level mathematical concepts calculational explanation involves explaining how an answer or result was arrived –... University in 2008 after working as a high school mathematics teacher in New York for eight.! Wellington, New Zealand the Discussions emphasize reasoning, and critiquing the of! Discourse domain examples of ARB resources that can be used as whole-class discussion starters the problems should. On, and this would naturally lead into a class or group discussion begins by creating discourse-rich... Between learners and between learners and learners and between learners and learners teacher this offers! Different way to express their ideas, reasoning, and justification http //www.nzmaths.co.nz/sites/default/files/Numeracy/References/PaulCobb.ppt.
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