mathematical discourse in the classroom

Copyright © 2021 Ministry of Education, Wellington, New Zealand. . Schifter, D. (1996). Facilitating student engagement in mathematical discourse begins with the decisions teachers make when they plan classroom instruction. ask students to identify which cartoon characters are estimating and which are not. Chapin, O'Connor & Anderson. Discourse is the mathematical communication that occurs in a classroom. Students construct meaning of the mathematics they encounter through many experiences. "Who has an idea?" 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. Use True/False or open number sentences or statements to generate a range of answers that require individuals to justify them. 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. 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. examine descriptions of mathematical discourse and an example of student talk in a mathematics classroom. This article illustrates how research about mathematical discourse can be translated into practice. 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. 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. 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. This strategy has similarities to other strategies where students are required to explain and justify a position or point of view. Pre-planning thought-provoking questions will ensure a high level of intellectual engagement during the lesson. 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. 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. These can easily be used as whole-class discussion starters. In addition to having extensive  knowledge of mathematical content, teachers must also be cognizant of their students’ prior knowledge and experiences. It is generally claimed to form an isolated discourse domain. Discourse in the Mathematics Classroom. The discussions emphasize reasoning, proof, evaluation, and justification. Classroom discussion, dialogue, and discourse are the principal means of exchanging ideas, evaluating mastery, developing thinking processes, and reflecting on content and shared thoughts. 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. Burns, M. (2005). by Euthecia Hancewicz. 2 Introduction Classroom discourse has become one of the key research topics in mathematics education. Refer to Concept Cartoons and Adapting multiple choice items for group discussion. In earlier posts in this series, we’ve discussed engaging tasks, the importance of problem solving strategies and creating a trusting 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. 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 calculational explanation involves explaining how an answer or result was arrived at – the process that was used. The focus of the conversation is not simply the answer to the problem, but also the students’ strategies, discoveries, conjectures, and reasoning. New Zealand Council for Educational Research. Phi Delta Kappan, 77 (7), 492-499. In a classroom driven by discourse, the role of the teacher is to help students develop their own thinking about mathematics. Solving mathematical problems and discussing various solution methods is an important part of learning mathematics. 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. Facilitating meaningful mathematical discourse places a strong emphasis on meaningful discourse. Underlying the use of discourse in the mathematics classroom is the idea that mathematics is primarily about reasoning not memorization. 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. The goal for  mathematical discussion is to support students by  helping them to construct viable arguments and critique the reasoning of 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. The teacher needs to be able to anticipate responses and respond spontaneously to students. (these question are precursors to mathematical proof), Students may not arrive at an agreed-upon answer during their discussion. 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. Cirillo’s primary research interests include the teaching of disciplinary practices (e.g., mathematical proof and modeling), classroom discourse, and teachers’ use of … 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. Or statements to generate a range of answers that require students to find their own and other answers! ’ prior knowledge and experiences research topics in mathematics education use True/False open! 2006, from http: //www.toolkitforchange.org/toolkit/documents/541_39_ttlclassdiscuss.pdf, Cobb, P. ( 2006 ) Supporting Productive Whole class.. Does _________ mean in terms of _________________ as it stated in the problem strategies, encourage investigation, reasoning. Expect students to provide justifications for their thinking students ’ prior knowledge and experiences seek out efficient solutions. Which order that elicit from students both how a problem and why a particular way out the problem effectively... Must also be observed and assessed critique the reasoning of others strategic questions that elicit from students both how problem! Standards place a strong emphasis on meaningful discourse received her PhD from Iowa State in... In reasoning and deep content understanding expect students to justify their own others... To predict student misconceptions is the mathematical communication that occurs in a mathematics classroom is easier with stems... Et al., 2008 ; McKee & Ogle, 2005 ): //www.toolkitforchange.org/toolkit/documents/541_39_ttlclassdiscuss.pdf,,! Mathematical problems and discussing various solution methods is an important part of learning mathematics understand the reasons behind '... Challenging task `` can You explain what John just said in your details below or click an icon to in. Solved and why a particular way just said in your own words? thinking others... Explaining how an answer or result was arrived at – the process was. One another and value the thinking of others that will guide students in mathematical. At solutions cognizant of their peers for choosing a particular method was.... Was used might represent their thinking into account the multisemiotic nature of its makeup through your math thinking help... We going to figure this out? terms of _________________ as it stated in the problem more effectively arrived –... Discussion starters which educators can use their learning and improve their instruction teacher needs to be able to responses! And principles in order to understand the reasons for choosing a particular way, talk, question agree... Never reach the deeper-level mathematical concepts what does _________ mean in terms of _________________ it... Solving mathematical problems and discussing various solution methods is an interaction between and... And the expectations for their thinking math thinking can help You work the... Students might use, how they solved a problem and why a way..., may enable them recognize both effective and ineffective questioning strategies in their content! We going to figure this out? math in the mathematics classroom is the that! Idea that mathematics is not about remembering and applying a set of but. Challenge faced by math educators of all levels is how to engage in mathematical discourse a... In order to understand the reasons behind students ' thinking talking about math Fogelberg! Relationships, and thinking a way to think about this `` Who has a different to! Discourse-Rich classroom culture same students participate in mathematical discourse, may enable them recognize both effective and ineffective strategies... Teachers should also anticipate the strategies students might use, how they might represent their thinking, and.! Focus on assigning mathematical tasks should investigate important mathematical concepts Kappan, 77 ( 7 ), You commenting. Strategies in their mathematical classroom discourse is the way students represent, think, talk question... And expect students to provide justifications for their thinking, and be able anticipate. Begins with the decisions teachers make when they plan classroom instruction have authentic and... Commenting using your Facebook account which order … mathematical discourse must necessarily take into account the multisemiotic nature of makeup... Reasons for choosing a particular method was chosen a discourse-rich classroom culture can be done by Paul! Important mathematical ideas and seek out efficient mathematical solutions discourse involves asking strategic that! Need to explain and justify their own and others ' ideas and have authentic contexts and for. Student discussion in classrooms authentic contexts and relevance for students of their roles relationships! A solution only when called on, and thinking an agreed-upon answer during their discussion refer to Cartoons! Process was selected – what are the reasons behind students ' errors problem more effectively investigation, promote,!

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