Download - Math CAMPPP 2012 Breakout 4A
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Math CAMPPP 2012Breakout 4A
Questioning, Listening and Responding toPromote Students’ Mathematical Thinking
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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?
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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
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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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