Alexandria, VA: ASCD, January 2013. You'll also get a 20% discount on the book! This strategy is instrum… 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. One approach to giving students the information needed for a mathematics lesson involves the teacher simply telling the students what they need to know. It can be overwhelming for students to hear and understand the reasoning behind too many different strategies at once. 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. 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. What I don’t understand about ______’s explanation is why _______. 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. For instance, students might say: Present meaningful problems. 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. answered, but the postconference conversation results in an additional list of questions that can guide continuing classroom observations and post-observation discussions. In the classroom, a math conversation requires a give and take. As Anderson tells her students: Along with establishing a rationale for mathematical discussions, it is also critical to establish expectations for respectful listening. Implementing math discussions into your classroom is an effective way for students to develop strong communication skills and deepen their understanding of mathematical content. 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. But we all know that setting the groundwork for conversations about thinking and learning can be tricky. 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. 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. Our challenges and opportunities are shared and it’s never been easier, or more important to make a difference. Why are we ______________ in this problem? I understand how you ______, but why did you ______? Sausalito, CA: Math Solutions, December 2013. Sausalito, CA: Math Solutions, October 2011. Once students have had ample time to work on th Use collaborative learning strategies. The following keys can help teachers ensure that the discourse in their mathematics classrooms is rich and extends the learning of students. You can learn a great deal about what it takes to understand the ideas of others. Chapin, Suzanne, Catherine O’Connor, and Nancy Canavan Anderson. School Leaders should learn the ways talk can be organized to foster science learning opportunities for students and support teachers in orchestrating such conversations. 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. In other words, can you think of an example that would disprove an idea that has been presented? Sentence stems and silent gestures are two techniques for streamlining math conversations in your classroom. The single most important thing teachers should do to ensure the success of discussions is to ask meaningful questions and facilitate the dialogue among students. How did these students benefit by sharing what they knew as part of the mathematics discussion? You have entered an incorrect email address! The discussions emphasize reasoning, proof, evaluation, and justification. In classroom discussions, students work with multiple ideas and have to balance new ideas with their original conclusions. She has 357 pennies saved in the first week and 225 pennies saved in the second week. Stay in-the-know with all things EdTech and innovations in learning by signing up to receive the weekly Smart Update. Teachers should focus on assigning mathematical tasks that are appropriately challenging and enhance students’ learning. Sausalito, CA: Math Solutions, 2009. ©2014 by Just ASK. Once the school year is under way, it is important to revisit the established norms in order to maintain the quality of conversations. “Keys to Productive Discussions in the Math Classroom.” Making the Common Core Come Alive! Carefully crafted questions such as the following can help guide these discussions: In summary, how successfully a teacher facilitates a discussion drives how mathematically rigorous the work is for students. Mathematics is learned best when students are actively participating in that learning. The problems posed should have multiple solution strategies, encourage investigation, promote reasoning, and require students to provide justifications for their thinking. Do you agree with ______? For example, “A number y is 4 more than a number x” is translated symbolically to “y=x+4.”. A key strength is the ability to employ instructional strategies that engage students in academic discourse. It could be student-to-student, student-to-teacher, students-to-students, and even a … Students are taught how to respectfully disagree and question one another. 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. 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. Using evidence in discussion strengthens students’ comprehension and confidence. Accessed at: www.insidemathematics.org/index.php/commmon-core-math-intro. Volume III, Issue IV, 2014. Video. Teach students the expectations for classroom discussions. Accessed at: www.mathsolutions.com/documents/qanda_usingmathtalk.pdf. 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. As outlined in the Standards for Mathematical Practice, students should become fluent in mathematical language, including vocabulary, symbolic representations, syntax, semantics, and linguistic features. Because I am still trying to improve Math Talk in my classroom daily, I … Phone: 800-940-5434 Fax: 703-535-8502, ©document.write(new Date().getFullYear()) Just ASK Publications & Professional Development. 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. What are some similarities you have seen between the strategies being used? 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. Above all, there is acceptance of all ideas and all contributions to the discussion are honored. It’s been a beneficial activity and helps students develop confidence while communicating their thinking. 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. Classroom discussions are a perfect place to develop students’ ability to use textual evidence. Her goal is to donate 1,000 pennies. 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. “Introduction to the Common Core State Standards.” Washington, D.C.: National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010. Meaningful math conversations are more than just exchanges of ideas. Hintz, Allison. Teachers must ease the transition to a dialogue-rich mathematics classroom and prepare students to engage in such discussions. Why did the teacher allow students to evaluate the correctness of Julie’s answer? Show Notes. Does this look like a classroom dialogue you’ve seen before? 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. Available on iTunes, Spotify, and SoundCloud. Asking the right questions can help support instructional decision making and direct student focus. Preplanning thought-provoking questions will ensure a high level of intellectual engagement during the lesson. 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. students to engage in classroom talk. 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. 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. This link contains annotated tasks and assessments that are aligned with the Common Core, grades K-2, 3-5, 6-8, and high school. The focus of the conversation is not simply the answer to the problem, but also the students’ strategies, discoveries, conjectures, and reasoning. Is _______’s strategy an efficient way to solve this problem? A challenge faced by math educators of all levels is how to engage students in their mathematical content through rich discussion or discourse. Our #AskAboutAI campaign investigates the implications that AI will have on employment, learning and ethical issues–a conversation around how we can shape a future that works for everyone. Share. 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. 2.) By the time I got home, I was really determined to make it a regular habit to encourage math talk, so I decided to do some research. The Common Core places a strong emphasis on mathematical reasoning and deep content understanding. Why or why not? Teacher’s anticipation of students’ strategies and errors, prior to the discussion. Instead of modeling and assigning several practice examples to introduce a new kind of problem, give students a generous amount of time to solve just one challenging problem with as many strategies as they can. In order to assess what students are thinking, we have to get them talking. Math is everywhere in the Pre-K classroom! 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. Including the context of the problems is essential when forming these questions. This document also includes strategies for creating a classroom culture that is conducive to mathematical discussions. Talking Math: How to Engage Students in Mathematical Discourse, Talking Math: 100 Questions That Help Promote Mathematical Discourse, 6 Strategies For Getting Students to Engage in Mathematical Discourse, Curriculum Associates: Leveraging For-profit Power With a Nonprofit Purpose, 3 Reasons Coding Should Be a Core Subject, Supporting Struggling South African Schools With Online Learning, Addressing the Challenges of Remote Learning for Emergent Bilingual Students, Academic Magnet High School is on a Mission of Excellence through Creating Opportunity for All, Joe Erpelding on Magical Schools and Thrively, How Parents Can Create Dedicated Learning Zones, With Remote Professional Learning, The Opportunities Are Boundless. What does a classroom rich with mathematical discourse look like? 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. We personalize all of our proposals to meet individual partner needs, so just select other and let us know how we can help. Students questioning each other using mathematics arguments to establish the correctness of solutions. 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. We look forward to continuing to share these experiences with you through our blog and an upcoming book. Depending on prior experiences, students might find these new expectations for engagement uncomfortable and may not be ready to plunge into mathematical dialogue feet first. She explains how talking like mathematicians can enable students to be stronger mathematical thinkers. I will need to hear _______ explain how _________ again. Practice, Practice, Practice. Children's ideas about mathematics should be discussed with all … 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. “Bring-Do-Leave: Nurturing Reasoning and Sense Making.” Teaching Children Mathematics. Reproduced with permission of Just ASK Publications & Professional Development (Just ASK). 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. What strategies do you think you could try when solving future problems. How many more pennies will Anna need to reach her goal? All rights reserved. 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. Sausalito, CA: Math Solutions, March 2013. Imparting these new skills on students allows teachers to access, monitor, and evaluate students’ mathematical understanding and development. Partnerships ensure a higher level of accountability and student engagement than is possible with only whole class discussions. 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 … Why? The goal in any mathematical discussion is to support the students’ in constructing viable arguments and critiquing the reasoning of others. “Why Is Teaching With Problem Solving Important to Student Learning?” Reston, VA: National Council of Teachers of Mathematics, 2010. Cai, Jinfa and Frank Lester. “Unlocking Engagement Through Mathematical Discourse.” ASCD Express. For instance, the teacher might ask: Decide which strategies should be prioritized when sharing with the whole class. There are many popular strategies for these kinds of conversations, each … 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. The importance of engaging students in meaningful mathematical discussion has long been identified as an essential component of students’ mathematics learning. Chapter 5. Acccessed at: www.ascd.org/ascd-express/vol8/807-miller.aspx. Permission is granted for reprinting and distribution of this newsletter for non-commercial use only. Mathematical tasks should investigate important mathematical ideas and have authentic contexts and relevance for students. Far more productive, however, is more a thoughtful approach to student engagement that encourage a productive dialogue, as seen in the example below. Classroom Discussions: Using Math Talk to Help Students Learn. A successful mathematics program emphasizes communicating mathematically frequently in the classroom. Why or why not? 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. When entering the discussion, the teacher should have in mind which strategies to emphasize and in which order. 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. Procedures for Classroom Talk. The way ______ solved the problem makes sense to me because…, ______’s strategy was similar to mine because…, ______’s strategy was different than mine because…. “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. Interactions are indeed the heartbeat of the mathematics classroom. What are some differences? Facilitate the sharing of strategies with the whole class. These conversations involve students explaining their mathematical thinking while working with others to complete tasks. Jun 30, 2020 - Explore LANETHA LATIMORE's board "Instructional Conversations" on Pinterest. Plan questions that will guide students in answering both how they solved a problem and why they chose the solution they used. Requiring at least two strategies builds independence in verifying their own solutions and jump-starts students’ ideas for discussion. 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. Establish a safe environment where students can take risks and where there are norms for classroom discussions. Thought-Provoking questions will ensure a higher level of accountability and student engagement than is possible only! Mathematics Institute, 2013 strategies, encourage investigation, promote reasoning, proof, evaluation, and Nancy Canavan..: arranges the classroom, a Math conversation requires a give and take ” making the Common places. See how we can work together their mathematical thinking while working with others to complete.. Developing a deeper understanding of pedagogy, or more important to make a difference and their teachers.. 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