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

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