Classroom Discussions

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Excerpts from Classroom Discussions: Using Math Talk to Help Students Learn, by Suzanne Chapin

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  • Revoicing – “So you’re saying. . .” Restate someone else’s reasoning – “Can you repeat what he just said in your own words?” Apply their own reasoning to someone else’s reasoning – “Do you agree or disagree and why?” Prompting students for further participation – “Would someone like to add on?” Using wait time – “Take your time…we’ll wait.”
  • … supportive environment Set up ground rules for respectful talking, as well as listening Know that this will take time – students must feel safe in order to take risks Focus talk…mathematics Goal is to help students understand the mathematics they are studying, as well as your own … equitable participation Two components – Making it possible for all students to participate actively in the talk & how to make certain that all students are listening actively Explain your expectations… Make sure to let students know what you are expecting them to do & to tell them why you think talk is a good idea Try one …at a time When introducing a new talk format, make sure that the mathematical concepts/procedures you are talking about are familiar to all of the students in the class (FROM CHAPTER 9)
  • Most teachers already use these two strategies - Practice using them with your students BEFORE you formally introduce them Revoicing Try using with several different students during a lesson for several days until are comfortable using it REMEMBER – It’s important not just to repeat what the student said , but, rather, must repeat/rephrase and then ask the student whether that is the correct interpretation of what he/she was trying to say Wait Time Whole Class - Decide how long you will wait (20 seconds) & let students see that you are willing to wait Individual Student – Give extra time to students who may need it without making them feel embarrassed
  • Begin with asking a student to repeat what another student has said in his/her own words – maybe even ask several students to repeat what one student has said – this lets them know that each student’s listening and speaking is important Ask young students to support their own reasoning from early on After children are comfortable talking about their own thinking and listening to others, begin asking them whether they agree/disagree with another student’s idea See pp. 112-114 for some strategies for introducing math talks to K-2 and 3-6 students
  • Starting Off Begin with a problem that lends itself to being solved by several different strategies, or that can have multiple correct answers After the students have discussed and understood the solution methods, let them practice both the talk and the mathematics by introducing a slightly harder version of the same problem Slow it down… As students make their contributions, take the time to ask them to clarify their ideas so that they are as understandable as possible Ask students to repeat what others have said Encourage many… Encourage students to share as many different strategies as possible If this takes longer than anticipated, don’t consider it to be wasting time - Are building the foundation
  • Begin with a problem that lends itself to being solved by several different strategies, or that can have multiple correct answers When students tell you how they are solving the problem, repeat their solutions back to them to check if you understand it. Remember, your focus should be promoting understanding, not necessarily on whether or not they have the right answer. If a group finishes early, ask them to try solving the problem another way. When sufficient time has passed for most groups to solve the problem, you can now begin a whole-class discussion based upon the solutions & discussions held in each small group.
  • Many teachers already use this talk format & often ask their students to “turn and talk” or “talk to your neighbor” Benefits Allows students to practice putting their ideas into words before they face the entire class Allows students to hear how another student is thinking about the problem, perhaps boosting their confidence level Listening to partners as they share strategies/solutions helps you identify students who have hit on the solutions that you think are mathematically important or interesting You can use this information to call on particular students to push the content of the whole-class discussion
  • All teachers are good at asking questions, calling on individual students, and then evaluating whether the answer is right or wrong This method is useful in many circumstances, it has its limits The focus is on the right answer & not the thinking process & there is no opportunity for other students to agree/disagree With older students, you may be able to adopt this practice almost from the beginning – with younger students, or with those who are less used to this kind of discussion, it may take longer
  • This is not the time to focus on whether students have the right or wrong answer – the focus is on developing reasoning skills Much can be learned by listening to students’ explanations of solutions and reasoning to help guide future instruction
  • Might be easiest to begin monitoring Principles 1 & 2 – Did your class follow the guidelines for respectful discussion and was the talk consistently about mathematical reasoning, with an emphasis on understanding Next, did you follow Principle 4 – providing a clear and explicit discussion of what you expected from students in their discussions Some aspects of the process are best observed weekly rather than daily – For example, Principle 3, providing for equitable participation One suggestion when starting out, is to keep a class list on which you can spend one minute each day, adding a check mark for each student who participates – At the end of the week, review the list for patterns and reflect Discuss attached checklist for self-evaluation
  • Discussed mathematical concepts & computational procedures in the fall (tie in nicely with K. Richardson assessments) Barbara will present on problem-solving methods & strategies Keep in mind which Classroom Discussion strategies will work in conjunction with problem-solving
  • Classroom Discussions

    1. 1. Classroom Discussions Using Math Talk to Help Students Learn
    2. 2. Reviewing the Five Strategies <ul><li>Revoicing </li></ul><ul><li>Asking students to restate someone else’s reasoning </li></ul><ul><li>Asking students to apply their own reasoning to someone else’s reasoning </li></ul><ul><li>Prompting students for further participation </li></ul><ul><li>Using wait time </li></ul>
    3. 3. Three Formats for Class Discussions <ul><li>Whole Class Discussion </li></ul><ul><li>Small Group Discussion </li></ul><ul><li>Partner Talk </li></ul>
    4. 4. Getting Started…Principles of Productive Talk <ul><li>Establish and maintain a respectful, supportive environment. </li></ul><ul><li>Focus talk on the mathematics. </li></ul><ul><li>Provide for equitable participation in classroom talk. </li></ul><ul><li>Explain your expectations about new forms of talk. </li></ul><ul><li>Try one challenging new thing at a time. </li></ul>
    5. 5. First Steps…Practicing On Your Own <ul><li>Revoicing </li></ul><ul><ul><li>Practice for several days until you feel comfortable </li></ul></ul><ul><li>Wait Time </li></ul><ul><ul><li>Asking a question of the whole class </li></ul></ul><ul><ul><li>Calling on an individual student </li></ul></ul>
    6. 6. First Steps…Introducing Students to Talk-Centered Instruction <ul><li>Introduce students to the idea that talking about mathematics can help them become better mathematical thinkers. </li></ul><ul><li>Discuss conditions that have to be in place for this kind of talk to succeed. </li></ul><ul><li>Introduce specific talk moves, explaining to students why each is worth doing. </li></ul>
    7. 7. First Steps…Beginning With a Whole-Class Discussion <ul><li>Start off by introducing the class to what you expect them to do. </li></ul><ul><li>Slow it down and ask for repetitions. </li></ul><ul><li>Encourage many contributions. </li></ul><ul><li>Keep the discourse respectful and keep everyone focused. </li></ul>
    8. 8. First Steps…Revoicing in Small-Group Discussion <ul><li>Assign a problem to students to solve in a small-group setting. </li></ul><ul><li>Circulate around the room, listening. After 5 minutes or so, interact with different groups. </li></ul><ul><li>Focus on understanding, not correcting. </li></ul>
    9. 9. First Steps…Using Partner Talk <ul><li>Give students a chance to “practice” describing their solution with one other person before talking with the whole class. </li></ul><ul><li>During the 3-5 minutes </li></ul><ul><li>students are talking, </li></ul><ul><li>circulate and listen to </li></ul><ul><li>their strategies. </li></ul>
    10. 10. First Steps…Building & Supporting an Argument <ul><li>Select a problem that offers rich potential for different solutions and complex reasoning. </li></ul><ul><li>Focus on the development of arguments and connected reasoning. </li></ul>
    11. 11. First Steps…Developing Reasoning Skills <ul><li>Students need to: </li></ul><ul><ul><li>Talk through the problem & make their thinking clear to others. </li></ul></ul><ul><ul><li>Get into the habit of giving reasons for their answers & evidence for their claims. </li></ul></ul><ul><ul><li>Get into the habit of listening to & evaluating one another’s contributions. </li></ul></ul><ul><ul><li>Reason aloud so the teacher can gain information about the mathematical beliefs & understandings of individual students. </li></ul></ul>
    12. 12. Evaluating Your Progress <ul><li>Implementing a new instructional practice takes time </li></ul><ul><li>Keep track of your use of the Principles of Productive Talk </li></ul>
    13. 13. The Mathematics: What Do We Talk About? <ul><li>Mathematical Concepts </li></ul><ul><li>Computational Procedures </li></ul><ul><li>Solution Methods & Problem-Solving Strategies </li></ul><ul><li>Mathematical Reasoning </li></ul><ul><li>Mathematical Terminology, Symbols, & Definitions </li></ul><ul><li>Forms of Representation </li></ul>

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