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Math CAMPPP 2012 Breakout 4A

Math CAMPPP 2012 Breakout 4A. Questioning, Listening and Responding to Promote Students’ Mathematical Thinking. 1. Learning Goals. We will develop a deepened understanding of: the types of questioning that elicit and promote mathematical thinking

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Math CAMPPP 2012 Breakout 4A

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  1. Math CAMPPP 2012Breakout 4A Questioning, Listening and Responding to Promote Students’ Mathematical Thinking 1

  2. Learning Goals We will develop a deepened understanding of: • the types of questioning that elicit and promote mathematical thinking • the meaning of fraction as an action (operator & quotient meanings) • the use of the PPQ template as a means to anticipate and identify good questions 2

  3. View with a Purpose http://cooperativelearning.nuvvo.com/lesson/9592-seinfeld-teaches-history • What does it mean to think? • What would you see/hear in a thinking classroom? • What types of questions did the teacher ask?

  4. Evaluative Questioning • Direct answer • Right or wrong • Rehearse known facts or procedures e.g. What is the value of xin this equation? e.g. What is ¾ of 4?

  5. Interpretive Questioning … • Explore mathematical meanings & relationships • Probe student thinking • Generate discussion • Extend thinking e.g. How do you know this makes sense? e.g. Will that work in every situation?

  6. Learn the work by doing the work • Where teachers’ math understanding and the students’ math understanding come together • Conversations should enhance both teachers’ and students’ knowledge

  7. Small Group Activity Imagine you have 7 brownies to share equally among 4 people. How many brownies will each person get?

  8. Questioning, Listening & Responding Students: • talk with each other as they question, agree/disagree, justify, and explain their thinking Teacher: • circulates among the students, observing student interactions, taking note of students’ math thinking, and posing questions to provoke and elicit thinking

  9. Student responses • Provide insight into their thinking • Illuminate ways the students understand concepts • Provide examples of ways of thinking for other students

  10. Fraction as a Quotient (partitive) • A fraction can represent division • e.g. 7 brownies divided among 4 people • Number of groups is known (4) • The amount per group is unknown

  11. Asking Effective Questions

  12. Posing Powerful Questions • Have the lessons in a template with room for participants to include questions of their own from the monograph … • Insert the lesson activity into the PPQ template here ? • Use the AfL template here ?

  13. Fraction as a Quotient (measurement) • You can divide by a fraction • e.g. 7 yards of ribbon, ¾ of a yard to wrap a gift • Number of groups (gifts) is unknown • The amount per group (gift) is unknown (¾)

  14. Questioning to … • playback to student what I see in their work • get kids to reflect on their work and see where they can go next • probe student thinking • develop a student-to-student network of dialogue

  15. Summary … • our questioning can serve to elicit and promote mathematical thinking • a fraction can be a verb – the action of operator & quotient • the use of the PPQ template is an effective means to anticipate and identify good questions

  16. Learning Wall • How might we reconfigure the display of our learning journey thus far?

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