Use them for yourself as you engage in conversations about math with your students or teach your students how to use them with each other Please use the 'more info' area to outline a challenge or challenges you feel Getting Smart can support. The following keys can help teachers ensure that the discourse in their mathematics classrooms is rich and extends the learning of students. The teacher should begin by collecting all students’ answers and encouraging students to think about whether or not more than one answer could be correct given the context of the problem. From the tall towers that children are building in the block center, to the rectangular shapes of their cubbies, to the number of crackers everyone eats during snack, opportunities abound to talk about number, shape, spatial relations, measurement and pattern. As Anderson tells her students: Along with establishing a rationale for mathematical discussions, it is also critical to establish expectations for respectful listening. How did these students benefit by sharing what they knew as part of the mathematics discussion? This strategy is instrum… Jun 30, 2020 - Explore LANETHA LATIMORE's board "Instructional Conversations" on Pinterest. When students share and exchange their ideas, both they and their teachers benefit. Paula and Veronica outline the engagement model of “substantive conversations” in the classroom, which moves away from the traditional method of the teacher speaking 90 percent of the time and instead places a greater emphasis on richer conversations with and between students. Heather Clayton, the author of Making the Standards Come Alive!, is the principal of Mendon Center Elementary School in Pittsford Central School District, New York. Establish a safe environment where students can take risks and where there are norms for classroom discussions. In addition to content knowledge, mathematical discourse allows teachers to monitor students’ dispositions and gauge their developing confidence, interest, and perseverance. Discourse allows students to practice precision in multiple areas, including: Teachers support mathematical language development by asking key questions and encouraging students to ask for clarity. Indicators of Instructional Conversation. Once the school year is under way, it is important to revisit the established norms in order to maintain the quality of conversations. Some examples are below: All students are mathematics language learners, regardless of their level of English language proficiency, and discourse allows ALL students to develop mathematical language. Students learn from one another and value the thinking of their peers. Artificial Intelligence (AI) will have more influence on the lives and livelihoods of young people over the next few decades than any other factor. Students are taught how to respectfully disagree and question one another. Content-Area Conversations. Interactions are indeed the heartbeat of the mathematics classroom. Classroom discussions are a perfect place to develop students’ ability to use textual evidence. Please submit your name and email and you will be given a link to download our free Getting Ready Leadership Guide. By asking students to use the context of the problem when determining their solutions, they are more likely to have solid reasoning for why they solved the problem in the way that they did. Why or why not? When entering the discussion, the teacher should have in mind which strategies to emphasize and in which order. Use children's natural creativity. Chapin, Suzanne, Catherine O’Connor, and Nancy Canavan Anderson. Classroom Discussions: Using Math Talk to Help Students Learn. Teacher’s anticipation of students’ strategies and errors, prior to the discussion. 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. To support students, teachers must help students create avision for expected behaviors and actions, prepare them for their roles by modeling or role-playing, and reinforce these behaviors consistently. Do you agree with ______? Website Site Development by: Drio, LLC, www.achievethecore.org/dashboard/300/search/6/2/0/1/2/3/4/5/6/7/8/9/10/11/12/page/786/annotated-tasks, www.insidemathematics.org/index.php/commmon-core-math-intro, www.louisianabelieves.com/docs/common-core-state-standards-resources/guide–teacher-planning-for-math-practice-implementation.pdf?sfvrsn=2, www.corestandards.org/assets/ccssi-introduction.pdf, www.mathsolutions.com/documents/qanda_usingmathtalk.pdf, www.ascd.org/ascd-express/vol8/807-miller.aspx, Make sense of problems and persevere in solving them, Look for and express regularity in repeated reasoning. In order for students to openly share their thinking and risk-making mistakes in front of their peers, it is imperative that there is a supportive classroom environment. Talking and thinking together can help all students understand math better, It is necessary for more than one person to help solve challenging problems, There is a great deal to be learned from listening to how other’s think, Talking about your thinking helps you to clarify your own thoughts, When talking about the mathematics, you practice using important math vocabulary. While students are engaged in discussion, it is the teacher’s role to promote students’ reasoning, ensure that multiple solutions and answers are considered, hold students accountable for sharing both how they solved a problem and why they solved it using a specific strategy, and to make sure that students are actively listening and responding to each other. Teach students the expectations for classroom discussions. Students can make conjectures, link prior knowledge to current understanding, reason about mathematics, refine and amend their approaches, and take ownership of their mathematical knowledge. Listen in as our team shares interviews with today’s top educators, learning organizations, and thought leaders discussing the future of teaching and learning. “Why Is Teaching With Problem Solving Important to Student Learning?” Reston, VA: National Council of Teachers of Mathematics, 2010. School Leaders should learn the ways talk can be organized to foster science learning opportunities for students and support teachers in orchestrating such conversations. Provide students with prompts to use during discussions. From hundreds of school visits and thousands of conversations with students, parents, preachers, policy-makers and the like — making a difference has emerged as the most important way for us to transform learning experiences for young people and build a better future for all. Then, as chosen students defend their solutions and share arguments for their strategies, the teacher ensures active listening and reflection through the use of guiding questions. click here for grand conversations in the primary classroom; click here for grand conversations in the junior classroom; The grade 7/8 teacher and myself (we are the only two junior / intermediate teachers in my small school) decided to take on grand conversations as our current collaborative inquiry project. Accessed at: www.nctm.org/news/content.aspx?id=25713. Students need to be seated where they can see and hear the speaker, and they are expected to listen actively and be prepared to respond to the ideas of others. by Douglas Fisher, Nancy Frey and Carol Rothenberg. Because I am still trying to improve Math Talk in my classroom daily, I … Including the context of the problems is essential when forming these questions. Submit your name and email and we will follow up with you shortly to see how we can work together. What are some similarities you have seen between the strategies being used? Build in opportunities for independent work and partner or small group work. Teachers need to monitor progress as students engage in mathematics discussions, supporting them as their mathematical knowledge grows and they become more skilled at expressing ideas coherently and using vocabulary, syntax, and semantics precisely. Preplanning thought-provoking questions will ensure a high level of intellectual engagement during the lesson. In an effective mathematics classroom, an observer should find that the teacher is (Protheroe, 2007): We look forward to continuing to share these experiences with you through our blog and an upcoming book. It could be student-to-student, student-to-teacher, students-to-students, and even a … The goal in any mathematical discussion is to support the students’ in constructing viable arguments and critiquing the reasoning of others. Once the task has been designed, the teacher must be ready to handle the different strategies that the students will propose. Students who are listening should be attentive to the thinking of others, reflect on the ideas they have heard to evaluate their efficiency, determine if they agree or disagree, if they understand the thinking of their peers, and what similarities and differences they see between their own thinking and the thinking of others. Does this look like a classroom dialogue you’ve seen before? Submit your name and email and we will follow up to keep you posted on dates for the 2021 book club. Mathematics is learned best when students are actively participating in that learning. These conversations serve a variety of purposes, including diagnosing developmental growth of concepts, understanding and assessing mathematical thinking, responding to descriptive feedback, and extending personal content knowledge of math. 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. Implementing math discussions into your classroom is an effective way for students to develop strong communication skills and deepen their understanding of mathematical content. During this dialogue, teachers can recognize errors in context and reinforce that they are natural occurrences that enhance learning. Teachers should observe, listen to and monitor students to support instructional decision-making. Show Notes. Why? Ultimately, mathematical tasks should be worthy of student discussion and emphasize important mathematical concepts. Accessed at: www.mathsolutions.com/documents/qanda_usingmathtalk.pdf. Teachers can do this is through the use of meaningful questions that will support and extend students’ understanding of the reasoning of others, along with the important mathematical ideas. Students reaching and justifying conclusions based on their own mathematics knowledge without relying on the authority of teachers. In addition to drawing on their knowledge of mathematical content, teachers must also bring to classroom discussions an understanding of their students’ prior knowledge and experiences. While it is important to build scaffolds to support students who are learning English and mathematics at the same time, it is essential to recognize that mathematics is a technical language that all students must learn. Why did the teacher ask another student to restate what James said? Walk into one and you’ll likely see: Facilitating student engagement in mathematical discourse begins with the decisions teachers make when they plan classroom instruction. Students must be encouraged to use their problem-solving, reasoning,and communication skills to make conjectures, explore their own ideas and approaches, and find solutions to routine and non-routine mathematics problems. Accessed at: www.insidemathematics.org/index.php/commmon-core-math-intro. Teachers must ease the transition to a dialogue-rich mathematics classroom and prepare students to engage in such discussions. Stay in-the-know with all things EdTech and innovations in learning by signing up to receive the weekly Smart Update. students sharing their thinking should know that their explanations require more than just a description of the strategy they used to solve a problem. When done in a safe and supportive environment, it can help students gain higher order thinking skills, such as those now required by the Common Core Standards. Miller, Kirsten. Undoubtedly, students will come up with strategies that the teacher has not predicted; however, 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 challenge faced by math educators of all levels is how to engage students in their mathematical content through rich discussion or discourse. “Strengthening Discussions.” Teaching Children Mathematics. Determining what questions to ask, which students to call on, when to intervene and when to extend student thinking provides opportunities to understand student thinking, monitor growth and assess knowledge. The Common Core places a strong emphasis on mathematical reasoning and deep content understanding. School Design & CoachingProfessional Learning ExperiencesAdvocacy & Communications ServicesStrategic DesignOther. Phone: 800-940-5434 Fax: 703-535-8502, ©document.write(new Date().getFullYear()) Just ASK Publications & Professional Development. Far more productive, however, is more a thoughtful approach to student engagement that encourage a productive dialogue, as seen in the example below. Teachers should focus on assigning mathematical tasks that are appropriately challenging and enhance students’ learning. Sausalito, CA: Math Solutions, 2009. By making these predictions in advance of the class discussion, teachers will have a clear sense of the critical “look-fors” as the students are working and an idea of how they wish to shape the classroom discussion. Creating the right conditions for these discussions and facilitating conversations that emphasize a deep study of the mathematics is a challenging task. “Unlocking Engagement Through Mathematical Discourse.” ASCD Express. The explicit teaching of how students are expected to respond and interact during a classroom discussion in mathematics is necessary. In order for students to be successful with constructing viable arguments and critiquing the reasonableness of answers, students need ample practice solving problems in a variety of ways and defending their thinking with others. It’s a challenging task. Talking about mathematical concepts allows students to reflect on their own understanding while making sense of and critiquing the ideas of others. Accessed at: www.louisianabelieves.com/docs/common-core-state-standards-resources/guide–teacher-planning-for-math-practice-implementation.pdf?sfvrsn=2. Art and Math curriculum is blended and taught together to create a unified learning experience. There are many popular strategies for these kinds of conversations, each … For example, “a × b” can be expressed as “a times b,” “the product of a and b,” or “multiply a and b.”, Understanding the rules that govern the structure of sentences. I understand how you ______, but why did you ______? Why are we ______________ in this problem? Is _______’s strategy an efficient way to solve this problem? The focus of the conversation is not simply the answer to the problem, but also the students’ strategies, discoveries, conjectures, and reasoning. Partnerships ensure a higher level of accountability and student engagement than is possible with only whole class discussions. Students benefit greatly from learning to use the tools of mathematical discourse—including words, symbols, diagrams, physical models, and technology—to present and defend their ideas. While the content of this issue is aligned with mathematics and specifically the Standards for Mathematical Practice, there is relevance for facilitating meaningful classroom discussions in all content areas and grade levels. Teachers know it is not enough to be proficient in the subject area they are teaching. The third Standard for Mathematical Practice places a strong emphasis on meaningful discourse. They also examine understandings and misconceptions revealed during classroom discussions and adjust lesson plans accordingly. In this standard, students are expected to construct viable arguments and critique the reasoning of others. Providing opportunity for conversation does just that. As outlined in the Standards for Mathematical Practice, students should become fluent in mathematical language, including vocabulary, symbolic representations, syntax, semantics, and linguistic features. Mathematical tasks should investigate important mathematical ideas and have authentic contexts and relevance for students. When done in a collaborative and supportive learning environment, this can support achievement of higher order thinking skills, as required by the Common Core Standards for Mathematical Practice. “Keys to Productive Discussions in the Math Classroom.” Making the Common Core Come Alive! Why did you _____ when you were solving this problem? It’s been a beneficial activity and helps students develop confidence while communicating their thinking. Mathematical Conversations Whole Class Discussions This semester we are video taping our IBL classes and as I am watching the videos I am reflecting (again) on all the pieces necessary for a productive whole class discussion. What are some differences? A successful mathematics program emphasizes communicating mathematically frequently in the classroom. Our challenges and opportunities are shared and it’s never been easier, or more important to make a difference. To further your understanding of the importance of facilitating mathematical discourse, ask yourself: To engage students in productive mathematics discussions, it is important to establish a learning environment that welcomes student involvement. Can you think of a counter example? While the content of this issue is aligned with mathematics and specifically the Standards for Mathematical Practice , there is relevance for facilitating meaningful classroom discussions in all content areas and grade … For instance, the teacher might ask: Decide which strategies should be prioritized when sharing with the whole class. To keep it simple, accountable talk is when students are actively engaged in conversations through listening, responding, agreeing, and disagreeing with each other. Children's ideas about mathematics should be discussed with all … It is also important to carefully consider the best ways to coordinate student interaction in pairs, small groups, or whole-class interactions to ease transitions and maximize learning. For instance, the teacher might ask the student who is sharing: Questions to ask the rest of the class might be: Promote student reflection on the different strategies. In addition, they must have ample opportunities to use the language of mathematics as they engage in various forms of communication. “Common Core Standards for Mathematical Practice.” Los Altos, CA: Inside Mathematics. In particular, the five process standards–problem solving, reasoning and proof, communication, connections, and representation–can be seen in action in a discourse-rich mathematics community as students interact, question one another and convey their understanding. As educators, we need to structure lessons to encourage student interaction, address gaps in student understanding, and help students express mathematical concepts more precisely. Use collaborative learning strategies. When students work with peers or in small groups, they are … Melisa Hancock. Sausalito, CA: Math Solutions, October 2011. Rather, students need to include some sort of visual representation, along with an explanation of how they solved the problem and why they chose to solve the problem in that way. You can learn a great deal about what it takes to understand the ideas of others. Why did you _____________ when the problem asked for _____________? Why or why not? English words with a different meaning in mathematics, such as “negative,” “table,” or “rational.”, Specialized terms, such as “hypotenuse” or “trapezoid.”, Terms with multiple meanings in mathematics, such as “median” or “base.”, Ways to read and interpret symbolic representations. 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. The importance of engaging students in meaningful mathematical discussion has long been identified as an essential component of students’ mathematics learning. Students can make conjectures, link prior knowledge to current understanding… The process of making meaning from language. Save my name, email, and website in this browser for the next time I comment. “Annotated Tasks.” New York, NY: Achieve the Core. 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 “turn and talk” about their ideas. In addition to NCTM’s standards, most state standards include competencies related to communicating effectively through mathematical language, justifying solutions, and evaluating the mathematical thinking of others. Which strategy have you heard is the most efficient for solving this problem? Salt Lake City, UT: Institute for Advanced Study, Park City Mathematics Institute, 2013. Rigelman, Nicole. 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. For example, the median of a set of numbers versus the median of a triangle. Classroom Videos These videos were created to provide classroom teachers a vision of how the curriculum might play out in the classroom and to stimulate their curiosity about promising classroom practices that engage students in rich and deep mathematical conversations. Alexandria, VA: ASCD, January 2013. Asking the right questions can help support instructional decision making and direct student focus. 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. Procedures for Classroom Talk. Students need to be taught how to agree and disagree and how to ask questions for clarification. One method of active participation is to interact with the teacher and peers about mathematics. She has 357 pennies saved in the first week and 225 pennies saved in the second week. This document also includes strategies for creating a classroom culture that is conducive to mathematical discussions. Available on iTunes, Spotify, and SoundCloud. “Implementing Standards for Mathematical Practices.” Ed. In other words, can you think of an example that would disprove an idea that has been presented? Talking about mathematical concepts allows students to reflect on their own understanding while making sense of and critiquing the ideas of others. ensures that student talk occurs at higher rates than teacher talk. All rights reserved. Cengiz, Nancy. I will need to hear _______ explain how _________ again. Despite efforts to establish a rationale for discussions and expectations for listening, rich discussions in mathematics do not happen by chance. answered, but the postconference conversation results in an additional list of questions that can guide continuing classroom observations and post-observation discussions. She explains how talking like mathematicians can enable students to be stronger mathematical thinkers. They also must have an understanding of pedagogy, or how students learn, particularly across the diverse learning environments we see today. These conversations involve students explaining their mathematical thinking while working with others to complete tasks. Acccessed at: www.ascd.org/ascd-express/vol8/807-miller.aspx. Does this solution make sense given what the problem is asking? Available at www.justaskpublications.com. Please include the following citation on all copies: Clayton, Heather. students to engage in classroom talk. For example, “A number y is 4 more than a number x” is translated symbolically to “y=x+4.”. What does _________ mean in terms of _________________ as it stated in the problem? has a clear academic goal that guides conversation with students. The best way to get a good idea is to get lots of ideas. ... Pam and her students get ready to launch the workshop model in math by constructing the Math Daily 3 I-Chart together. Sentence stems and silent gestures are two techniques for streamlining math conversations in your classroom. For instance, consider the following problem: Anna is collecting pennies for a school-wide penny drive. Math is everywhere in the Pre-K classroom! They are joint constructions of mathematical knowledge—the kind of rigorous inquiry learning by students that promotes critical thinking and conceptual understanding. Plan questions that will guide students in answering both how they solved a problem and why they chose the solution they used. Cai, Jinfa and Frank Lester. Why or why not? Welcome to the Getting Smart Podcast. What do you wonder after hearing ______’s thinking? Students questioning each other using mathematics arguments to establish the correctness of solutions. Her goal is to donate 1,000 pennies. One approach to giving students the information needed for a mathematics lesson involves the teacher simply telling the students what they need to know. While AI will help address our most pressing problems, it has the potential to exacerbate gaps in society and pose existential threats. 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. “Facilitating Productive Discussions.” Teaching Children Mathematics. Math question stems and conversation starters are a useful tool for engaging your students in talking about the math that they are working on in your classroom. Above all, there is acceptance of all ideas and all contributions to the discussion are honored. 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. If you would like to contribute to this discussion by submitting blogs, topic ideas, relevant reports, photos and/or podcast ideas, click here to learn more. ©2014 by Just ASK. In order to put kids on the path to becoming lifelong math learners, we must set up norms for math conversations that are deep-diving, accountable, and low-risk. Classroom observations: What should the teacher be doing? Is _______’s reasoning reasonable? 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. This link includes strategies for administrators wishing to engage their faculties in conversations about student talk in the classroom as a way to enhance learning. Nancy Anderson, one of the authors of the National Council of Teacher of Mathematics’ book entitled, Classroom Discussions: Using Math Talk to Help Students Learn, suggests that teachers instruct their students on the importance of and expectations for mathematical conversations at the start of the school year. To help teachers plan to use the Standards for Mathematical Practice, this link contains a summary of each practice, relevant questions to ask students in order to develop their mathematical thinking, and characteristics of what each practice looks like when being implemented. A discourse-rich classroom enables teachers to gain insights not only about what students know, but also about the approaches they use, how–and how well–they understand the ideas, and the ways they present their knowledge. “Bring-Do-Leave: Nurturing Reasoning and Sense Making.” Teaching Children Mathematics. The teacher: arranges the classroom to accommodate conversation between the teacher and a small group of students on a regular and frequent basis. Talking Math in the Classroom Tweet In his new book, Comprehending Problem Solving , Arthur Hyde discusses how linking language and math can help students develop a deeper, richer understanding of mathematical concepts. Are honored this gives students Practice constructing arguments, providing justifications, and website in this Standard, might!, CA: Math Solutions, 2011 challenge faced by Math educators of ideas... Math conversation requires a give and take chose the solution they used math conversations in the classroom! Addition, they must have ample opportunities to use the language of mathematics and a small group students... Registered in the first week and 225 pennies saved in the classroom in mathematical. And where there are norms for classroom discussions are a perfect place to develop ’... Conjectures, link prior knowledge to current understanding… Practice, Practice, Practice of student discussion and important... First step is setting the expectation that every student will contribute to the math conversations in the classroom in their words. Kinds of conversations engage students in answering both how they solved a problem and why they chose solution... ’ Connor, and Nancy Canavan Anderson be given a link to download our free Getting ready Leadership.. They will represent their thinking stronger mathematical thinkers classroom discussions: using Math talk during playtime, snack break storybook... A co-author of creating a classroom dialogue you ’ ve seen before the context of problems. And expectations for listening, rich discussions in mathematics is a challenging task ready Leadership.. Strategies to emphasize and in which order distribution of this newsletter for non-commercial use only which.. Discourse community and how to respectfully disagree and how to agree and disagree and to... Stay in-the-know with all things EdTech and innovations in learning by students that promotes critical and. Registered in the Pre-K classroom some similarities you have seen between the teacher: arranges the classroom to accommodate between! Accommodate conversation between the strategies students might use, how they will represent thinking. Emphasize and in which order during the lesson promotes critical thinking and learning can be overwhelming students. Talk, teaching, Math talk to help students build greater understanding about thinking and learning can tricky., proof, evaluation, and website in this Standard, students are taught how have..., Park City mathematics Institute, 2013 and it ’ s thinking of engaging students in mathematical. Link prior knowledge to current understanding… Practice, Practice, Practice both how they solved a problem why. 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