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Enhancing Mathematical Thinking through Effective Questioning and Student Engagement

This resource focuses on developing a deeper understanding of questioning techniques that promote mathematical thinking in students. It emphasizes the meanings of fractions as actions and employs the PPQ (Preparing for Powerful Questions) template to identify effective questioning strategies. The approach includes classroom activities that encourage student collaboration, dialogue, and critical thinking. Viewers will learn to create environments that foster rich mathematical conversations, deepening both student and teacher understanding of mathematical concepts through questioning, listening, and responding.

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Enhancing Mathematical Thinking through Effective Questioning and Student Engagement

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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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