RESPONSIVE TEACHING WITH FRACTIONS

Vicki Jacobs University of North Carolina at Greensboro

Susan Empson Gladys Krause D’Anna Pynes

The University of Texas at Austin Funded by the National

Science Foundation

Responsive Teaching in Elementary Mathematics

University of Texas at Austin Susan Empson (PI) Gladys Krause D’Anna Pynes

University of North Carolina at Greensboro Vicki Jacobs (co-PI) Naomi Jessup Amy Hewitt

Other Partners: SRI & Teachers Development Group

What is Responsive Teaching? • Many ways to be responsive

• Children’s thinking is visible, valued, and used in instruction…before and after correct answers

•  Instruction is continually adjusted on the basis of children’s thinking, rather than scripted in advance •  Teachers elicit and use evidence of children’s thinking (NCTM’s

Principles to Action)

Initial Model of Responsive Teaching

Knowledge of Children’s

Mathematical Thinking

(Empson & Levi, 2011)

Generative Instructional Practices

Noticing Children’s Thinking

(Jacobs et al., 2010)

Enacting Moves to Support and

Extend Children’s Thinking

Children’s Opportunities to Advance Their Thinking

Overview of Study • Goal: organize interactive teaching moves into a framework … usable by teachers and researchers

• Builds on Prior Work (Jacobs & Ambrose, 2008)

• Methods: o  Cases of responsive teaching

ü  3 upper elementary teachers with expertise in responsive teaching

ü  Focus on problem solving, sense making ü  2 types of data

o  Grades 3–5 o  Fractions

4 children are sharing 3 bars of clay equally. How much does each child get?

Rita

Supporting & Extending Children’s Thinking

Exploring details of child’s existing strategy

Encouraging child to consider other strategies Ensuring child is making sense of story context Inviting child to generate symbolic notation Adjusting problem to match child’s understandings

Supporting & Extending Children’s Thinking

Exploring details of child’s existing strategy

Posing starter questions to child Pressing child for detailed explanation problem-solving process Probing child’s representation to highlight connections to problem context Questioning child about quantities and their relationships in the strategy Inviting child to think ahead before executing a problem-solving step

Encouraging child to consider other strategies Ensuring child is making sense of story context Inviting child to generate symbolic notation Adjusting problem to match child’s understandings

Supporting & Extending Children’s Thinking

Exploring details of child’s existing strategy

Posing starter questions to child Pressing child for detailed explanation problem-solving process Probing child’s representation to highlight connections to problem context Questioning child about quantities and their relationships in the strategy Inviting child to think ahead before executing a problem-solving step

Encouraging child to consider other strategies Ensuring child is making sense of story context Inviting child to generate symbolic notation Adjusting problem to match child’s understandings

Supporting & Extending Children’s Thinking

Exploring details of child’s existing strategy

Posing starter questions to child Pressing child for detailed explanation problem-solving process Probing child’s representation to highlight connections to problem context Questioning child about quantities and their relationships in the strategy Inviting child to think ahead before executing a problem-solving step

Encouraging child to consider other strategies Ensuring child is making sense of story context Inviting child to generate symbolic notation Adjusting problem to match child’s understandings

Posing starter questions •  Initiates a conversation

Supporting & Extending Children’s Thinking

Exploring details of child’s existing strategy

Posing starter questions to child Pressing child for detailed explanation problem-solving process Probing child’s representation to highlight connections to problem context Questioning child about quantities and their relationships in the strategy Inviting child to think ahead before executing a problem-solving step

Encouraging child to consider other strategies Ensuring child is making sense of story context Inviting child to generate symbolic notation Adjusting problem to match child’s understandings

ALICE: 8 children want to share 14 cookies so that each child gets the same amount. How much can each child get?

Pressing for Detailed Explanation of Alice’s Process “I see you went on and then you stopped yourself here, why?”

“So I noticed you cut this one into eighths, why did you choose to cut that one into eighths?”

“Here you made this model, how come you didn’t go ahead and make the lines on there?”

Pressing for Detailed Explanation of Alice’s Process “I see you went on and then you stopped yourself here, why?”

“So I noticed you cut this one into eighths, why did you choose to cut that one into eighths?”

“Here you made this model, how come you didn’t go ahead and make the lines on there?”

Supporting & Extending Children’s Thinking

Exploring details of child’s existing strategy

Posing starter questions to child Pressing child for detailed explanation problem-solving process Probing child’s representation to highlight connections to problem context Questioning child about quantities and their relationships in the strategy Inviting child to think ahead before executing a problem-solving step

Encouraging child to consider other strategies Ensuring child is making sense of story context Inviting child to generate symbolic notation Adjusting problem to match child’s understandings

Encouraging Amir to Consider Other Strategies Kenzie loves to go on long hikes. She often hikes with her college friends. She drinks 2/3 cup of water for every mile she hikes. Her water bottle holds 4 cups of water. How many miles can she hike before her water runs out?

18 9 6

Encouraging Amir to Consider Other Strategies Kenzie loves to go on long hikes. She often hikes with her college friends. She drinks 2/3 cup of water for every mile she hikes. Her water bottle holds 4 cups of water. How many miles can she hike before her water runs out?

Encouraging Amir to Consider Other Strategies Kenzie loves to go on long hikes. She often hikes with her college friends. She drinks 2/3 cup of water for every mile she hikes. Her water bottle holds 4 cups of water. How many miles can she hike before her water runs out?

Do you think there is a second way you could check because you’ve thought about 12, you’ve thought about 18, and then you thought 9 and now you’re thinking, wait a minute. Could you make a grid or some other way that you could think about solving it? I just want you to double check so you’re like, ‘Okay this makes sense to me what I’m doing.’

Encouraging Amir to Consider Other Strategies Kenzie loves to go on long hikes. She often hikes with her college friends. She drinks 2/3 cup of water for every mile she hikes. Her water bottle holds 4 cups of water. How many miles can she hike before her water runs out?

Final Thoughts • Framework categories for supporting and extending children’s thinking appear robust

• Power of 1-on-1 interactions in classrooms

• Consistency between 1-on-1 interactions inside and outside of classroom setting

Responsive Teaching

Knowledge of Children’s

Mathematical Thinking

(Empson & Levi, 2011)

Generative Instructional Practices

Noticing Children’s Thinking

(Jacobs et al., 2010)

Enacting Moves to Support and

Extend Children’s Thinking

Children’s Opportunities to Advance Their Thinking