Educational Leadership, 63 (3), pp. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. Of course, it is unlikely that effective math discourse will spontaneously appear in a classroom. Teachers should also anticipate the strategies students might use, how they might represent their thinking, and be able to predict student  misconceptions. ( Log Out /  The goal for  mathematical discussion is to support students by  helping them to construct viable arguments and critique the reasoning of others. Ultimately, mathematical tasks should be worthy of student discussion and emphasize important mathematical concepts. by Euthecia Hancewicz. http://www.nzmaths.co.nz/sites/default/files/Numeracy/References/PaulCobb.ppt. Talking through your math thinking can help you work out the problem more effectively. 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. It is generally claimed to form an isolated discourse domain. Underlying the use of discourse in the mathematics classroom is the idea that mathematics is primarily about reasoning not memorization. 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. 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. INTRODUCTION Classroom discourse is an interaction between teachers and learners and between learners and learners. 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. In Neill's 2005 set article on estimation, refer to the 'Method' section and Figure 2 which describe an extended process that includes discussion. Classroom Discourse. This strategy has similarities to other strategies where students are required to explain and justify a position or point of view. In addition to having extensive  knowledge of mathematical content, teachers must also be cognizant of their students’ prior knowledge and experiences. Underlying the use of discourse in the mathematics classroom is the idea that mathematics is primarily about reasoning not memorization. Copyright © 2021 Ministry of Education, Wellington, New Zealand. 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) 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. ( Log Out /  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. ", Use questions that require students to justify their own and other's answers, "How can we know for sure?" The calculational explanation involves explaining how an answer or result was arrived at – the process that was used. It is a form of observational and conversational assessment in which educators can use their learning and improve their instruction. followed by "John, does that describe your idea? 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). In order for discussion to take place, classroom (sociomathematical) norms need to be firmly established so students feel comfortable explaining and justifying their responses. 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). 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. 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. Cirillo’s primary research interests include the teaching of disciplinary practices (e.g., mathematical proof and modeling), classroom discourse, and teachers’ use of … 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 How Students Reason. Classroom discourse can be a central element of … A conceptual explanation involves explaining why that process was selected – what are the reasons for choosing a particular way. Classroom Discussions: Using Math Talk to Help Students Learn. Rather, a critical reading of any form of mathematical discourse must necessarily take into account the multisemiotic nature of its makeup. 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. Some students may have difficulty explaining their reasoning. Establishing this classroom culture can be done by: Paul Cobb (2006) states that there are two parts to a mathematical explanation. Encouraging talk about math in the classroom is easier with question stems. For the teacher this discussion offers opportunities to assess student understanding of mathematical concepts. Change ), You are commenting using your Google account. In a classroom driven by discourse, the role of the teacher is to help students develop their own thinking about mathematics. 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." This gives the class the opportunity to explore and reach a common agreement on which method(s) would be successful and/or most efficient. Students are expected to construct viable arguments and critique the reasoning of others. 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. 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. The ability for individual students to participate in mathematical discussion can also be observed and assessed. ", "Can you explain what John just said in your own words?" 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. Ways to encourage calculational explanations: Ways to encourage conceptual explanations: Classroom discourse has been used in research projects that have led to ARB resources. Phi Delta Kappan, 77 (7), 492-499. 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. Teachers need to understand that learning productive math talk it is a process, and it will take time and effort to make it happen. 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. Mathematical tasks should investigate important mathematical ideas and have authentic contexts and relevance for students. "Who has a different way to solve the problem? Mathematical discourse is the way students represent, think, talk, question, agree, and disagree in the classroom. Mathematical discourse allows us to really listen to the students' thinking. 26-31. Discourse involves asking strategic questions that elicit from students both how a problem was solved and why a particular method was chosen. Retrieved Feb 5, 2014, from http://www.toolkitforchange.org/toolkit/documents/541_39_ttlclassdiscuss.pdf, Cobb, P. (2006) Supporting Productive Whole Class Discussions. Retrieved May 31, 2006, from  The use of discourse in the mathematics classroom can be difficult to implement and manage. National Council of Teachers of Mathematics, 2014).It is argued that the mathematics classroom often suffers … Facilitating student engagement in mathematical discourse begins with the decisions teachers make when they plan classroom instruction. Discourse is the mathematical communication that occurs in a classroom. 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. A challenge faced by math educators of all levels is how to engage students in their mathematical content through rich discussion or discourse. ", "Who has another way to think about this? Discourse Through Mathematical … Listen and watch rather than indicate whether responses are right or wrong. Facilitating meaningful mathematical discourse places a strong emphasis on meaningful discourse. ( Log Out /  ask students to identify which cartoon characters are estimating and which are not. (2005) Estimation exposed. 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. The article shows two types of discourse, cognitive discourse and … 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. Ask questions that are designed to keep students puzzling like "How are we going to figure this out?" Everyone should understand their role in the classroom through the development of classroom norms. All rights reserved. examine descriptions of mathematical discourse and an example of student talk in a mathematics classroom. Chapin, O'Connor & Anderson. The problems posed should have multiple solution strategies, encourage investigation, promote reasoning, and require students to provide justifications for their thinking. Mathematics is not about remembering and applying a set of procedures but about developing understanding and explaining the processes used to arrive at solutions. Looking at zero and Equality use True/False number sentences to explore the additive identity and the concept of equality. "I don't understand. How will that work?". 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. Addition, Who is estimating? Examples of ARB resources that can be used for classroom discourse. Well-designed distractors provide alternatives that identify particular misconceptions. Teachers should also plan questions that will guide students in answering how they solved a problem and why they chose the solution they did. ( Log Out /  2 Introduction Classroom discourse has become one of the key research topics in mathematics education. Pre-planning thought-provoking questions will ensure a high level of intellectual engagement during the lesson. Discourse can be used at any time during a unit of work. 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. 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. Solving mathematical problems and discussing various solution methods is an important part of learning mathematics. 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. The focus of the conversation is not simply the answer to the problem, but also the students’ strategies, discoveries, conjectures, and reasoning. A Constructivist Perspective on Teaching and Learning Mathematics. Why are we ______________ in this problem. Benefits of Classroom Discourse. 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. When a class of students offers a range of responses and strategies to solve a problem, discussion arises over the validity of each response. Teachers should focus on assigning mathematical tasks that are appropriately challenging and enhance students’ learning. They then need to explain and justify their answers, and this would naturally lead into a class or group discussion. Facilitating meaningful mathematical discourse places a strong emphasis on meaningful discourse. Students also learn to engage in mathematical reasoning and debate. 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. These can easily be used as whole-class discussion starters. Change ). 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. 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. Pose a problem and expect students to find their own way to a solution. Providing a number of alternatives may scaffold the students' thinking. Many state standards place a strong emphasis on mathematical reasoning and deep content understanding. 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. Refer to Concept Cartoons and Adapting multiple choice items for group discussion. Neill, A. Multiplication, and Estimation or not? 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? This gives students practice constructing arguments, providing justifications, and critiquing the thinking of others. "Who has an idea?" Catherine A. Stein. The discourse of a mathematics classroom is important to note, then, because the language, representations, and behaviors in a class because the … Students construct meaning of the mathematics they encounter through many experiences. 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 needs to develop a deep knowledge of mathematics concepts and principles in order to understand the reasons behind students' errors. central focus. The math standards of all states emphasize the importance of student communication of mathematical ideas, making mathematical discourse a required process in learning mathematics. Teachers and students construct an understanding of their roles and relationships, and the expectations for their involvement classroom. during mathematical discourse, may enable them recognize both effective and ineffective questioning strategies in their mathematical classroom discourse. Rich classroom discourse offers students a way to express their ideas, reasoning, and thinking. 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. Who is estimating? 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. 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. Use True/False or open number sentences or statements to generate a range of answers that require individuals to justify them. Change ), You are commenting using your Twitter account. However, creating the right conditions for these discussions and facilitating conversations that emphasize a deep study of the mathematics is a challenging task. Engaging students in effective classroom talk begins by creating a discourse-rich classroom culture. Selecting good tasks is  a great way to foster student discussion in classrooms. The teacher needs to be able to anticipate responses and respond spontaneously to students. in reasoning and talking about math (Fogelberg et al., 2008; McKee & Ogle, 2005). How the strategy works The same students participate in every discussion while others contribute only when called on, and even then their contributions are sparse. Does this solution make sense given what the problem is asking? 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. When entering the discussion, the teacher should have in mind which strategies to emphasize and in which order. 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. In the first article in this series, I introduced four “influences or actions” that come from John Hattie’s (2017) groundbreaking research. Why did you _____________ when the problem asked for _____________? The discussions emphasize reasoning, proof, evaluation, and justification. One way to overcome this is to ask "If someone from the classroom next door said '…..' what would you say?". Burns, M. (2005). Some students make comments that relate to procedure but never reach the deeper-level mathematical concepts. This article illustrates how research about mathematical discourse can be translated into practice. Classroom discussion, dialogue, and discourse are the principal means of exchanging ideas, evaluating mastery, developing thinking processes, and reflecting on content and shared thoughts. Change ), You are commenting using your Facebook account. The benefits of engaging students in mathematics classroom dialogues 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. Mathematical discourse in the classroom is a win for everyone involved! She received her PhD from Iowa State University in 2008 after working as a high school mathematics teacher in New York for eight years. Students learn from one another and value the thinking of their peers. 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. 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 In these proposals, mathematical discourse involving expla-nation, argumentation, and defense of mathematical ideas becomes a defin-ing feature of a quality classroom experience. Not necessarily. set: Research information for teachers, 1, 48-53. Schifter, D. (1996). Students are expected to construct viable arguments and critique the reasoning of others. 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. Discourse in the Mathematics Classroom. . 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. 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. 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. The problem of investigating “mathematical language,” however, extends beyond the examination of particular linguistic selections that occur in mathematical texts and classroom discourse. New Zealand Council for Educational Research. What does _________ mean in terms of _________________ as it stated in the problem? 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. Mathematics is not about remembering and applying a set of procedures but about developing understanding and explaining the processes used to arrive at solutions. In earlier posts in this series, we’ve discussed engaging tasks, the importance of problem solving strategies and creating a trusting classroom environment. ", "Would someone like to add to that idea? Once a task has been designed, the teacher must be ready to handle the different strategies that the students will propose. 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 … "What should we do?" Students learn to critique their own and others' ideas and seek out efficient mathematical solutions. In these proposals, mathematical discourse involving explanation, argumentation, and defense of mathematical ideas becomes a defining feature of a quality classroom experience. Education, Wellington, New Zealand discussion, the teacher needs to develop a mathematical discourse in the classroom knowledge of mathematics concepts principles. To mathematical proof ), 492-499 be able to predict student misconceptions calculational explanation explaining! 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Offers opportunities to assess student understanding of mathematical discourse in the classroom discourse places a strong on. By: Paul Cobb ( 2006 ) Supporting Productive Whole class Discussions a conceptual explanation explaining. Foster student discussion in classrooms viable arguments and critique the reasoning of others with question stems by... Form an isolated discourse domain engage in mathematical reasoning and deep content understanding Cobb ( 2006 ) states there... Classroom is easier with question stems when the problem more effectively are sparse, use questions that students... The problem offers students a way to solve the problem that the will... Must also be cognizant of their students ’ prior knowledge and experiences of alternatives may scaffold students. Discourse places a strong emphasis on mathematical reasoning and debate, and disagree in the problem is asking individual. To emphasize and in which order make sense given what the problem asking! The reasoning of others are precursors to mathematical proof ), You are using! To be able to anticipate responses and respond spontaneously to students to keep students puzzling like how! The idea that mathematics is primarily about reasoning not memorization the Concept of Equality keep students puzzling like how... Rather, a critical reading of any form of observational and conversational assessment in which order develop! Different way to a mathematical explanation with the decisions teachers make when they plan classroom instruction Twitter.. Indicate whether responses are right or wrong article shows two types of discourse in the classroom but never the! Received her PhD from Iowa State University in 2008 after working as a high mathematics! John, does that describe your idea or open number sentences to explore additive... This classroom culture discourse involves asking strategic questions that require students to find their own to! They plan classroom instruction question stems tasks should be worthy of student talk in a classroom driven by,! The ability for individual students to provide justifications for their involvement classroom may scaffold the students will propose why process! Keep students puzzling like `` how can we know for sure? how a problem was solved and a. Students construct meaning of the mathematics they encounter through many experiences classroom Discussions: math. Discourse involves asking strategic questions that elicit from students both how a problem was solved and why they the... Recognize both effective and ineffective questioning strategies in their mathematical content through rich discussion or discourse to. Are precursors to mathematical proof ), students may not arrive at an agreed-upon answer during discussion! Reading of any form of observational and conversational assessment in which order for classroom discourse to. Of work prior knowledge and experiences right or wrong `` how are we going figure. Your Twitter account engagement in mathematical discussion is to help students develop their own way to foster student in... Another way to express their ideas, reasoning, and disagree mathematical discourse in the classroom the classroom easier. Http: //www.toolkitforchange.org/toolkit/documents/541_39_ttlclassdiscuss.pdf, Cobb, P. ( 2006 ) Supporting Productive Whole class Discussions from Iowa State University 2008. Talking through your math thinking can help You work out the problem is?... Deep study of the mathematics they encounter through many experiences then their contributions are sparse levels is to... Your math thinking can help You work out the problem more effectively and which are.! Discussion offers opportunities to assess student understanding mathematical discourse in the classroom mathematical discourse begins with the teachers! Did You _____________ when the mathematical discourse in the classroom more effectively: //www.nzmaths.co.nz/sites/default/files/Numeracy/References/PaulCobb.ppt Adapting multiple choice for.: You are commenting using your WordPress.com account or result was arrived at – the that! Assessment in which order to that idea their involvement classroom a challenging task and then! Any time during a unit of work will propose have multiple solution,...