math camppp 2012 breakout 4a

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Math CAMPPP 2012Breakout 4A

Questioning, Listening and Responding toPromote Students’ Mathematical Thinking

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

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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?

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Evaluative Questioning

– Direct answer– Right or wrong– Rehearse known facts or procedures

e.g. What is the value of x in this equation?

e.g. What is ¾ of 4?

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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?

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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

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Small Group Activity

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Imagine you have 7 brownies to share equally among 4 people.

How many brownies will each person get?

Questioning, Listening & Responding

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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

Student responses

• Provide insight into their thinking• Illuminate ways the students understand

concepts• Provide examples of ways of thinking for

other students

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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

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Asking Effective Questions

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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 ?

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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)

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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

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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

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Learning Wall

• How might we reconfigure the display of our learning journey thus far?

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