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Promoting Mathematical Discourse?

Math Summit 2014

Sidney Fox

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Overview of Session

Introduction to Mathematics Discourse

Engagement with Discourse Strategies

Consider implications of the work for your own school/district context

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Common Core • Emphasize a change in which students engage with

and communicate about important mathematics content

• CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others.

• Demonstrate the importance of productive mathematical conversations

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Connecting Literacy and Mathematics

In language arts, it is not enough that students can read the words—they must comprehend the message. Likewise, in mathematics, it is not enough that students can manipulate numbers and symbols and read math words. To be proficient, students must draw connections between these symbols and what they represent. The standard for math should be the same as the standard for reading—bringing meaning to the printed symbols.

- Marilyn Burns

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Critical Question

• How do elementary grade teachers promote and support student engagement in high quality mathematics discourse?

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Three Components Discourse: understand what high quality discourse

for all is and how it supports conceptual understanding

Instruction: understand how certain discourse strategies support the design and implementation of lessons that promote high quality discourse for all

Content: understand the importance of knowing mathematics for teaching for supporting high quality discourse

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What is high quality mathematics discourse?

When you think about high quality mathematics discourse, what feature(s) do you consider most important?

How does high quality mathematics discourse relate to our focus on the Common Core Standards for Mathematical Practice?

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Mathematics Discourse StrategyALL TALK◦ Quick strategy that allows each

student to share a brief idea

◦ Gives everyone a voice

◦ Begins with a prompt

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Sharing our Ideas about High Quality Mathematics Discourse

ALL TALK

BRIEFLY…

One important feature of high quality mathematics discourse is…

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Definition of High Quality Mathematics Discourse

Patterned ways of using questioning, explaining, listening and various modes of communication in the classroom to promote conceptual understanding in mathematics.

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Mathematics Discourse Matrix(Project AIM, 2012)

Dimensions of Discourse

Questioning

Explaining

Listening

Modes of Communication

Types of Discourse

Correcting

Eliciting

Probing

Responsive

Based on Levels of a Math-Talk Learning Community (Hufferd-Ackles, Fuson, Sherin, 2004)

Beyond Good Teaching: Advancing mathematics education for ELLs. Ch. 9 (Driscoll, Heck, & Malzahn, 2012)

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Types of Discourse

• Correcting – what

• Eliciting – what and how

• Probing – what, how, and why

• Responsive – what, how, why, and connections(Project AIM, 2012)

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DO NOT DISTRIBUTE OR QUOTE WITHOUT PERMISSION

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WHAT DOES IT MEAN TO THINK ALOUD?

• Literacy: model the thought processes that take place when difficult material is read

– Making predictions – Developing images – Sharing analogies to make connections– Monitoring and regulating comprehension

• Mathematics: model the thought processes that take place when solving mathematics problems

– Defining unknown vocabulary – Creating images/representations of the situation– Making connections to similar situations– Determining important/unimportant information– Checking if a solution is reasonable

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“Jason put 4 large plates and 8 small plates on the table. How many plates are on the table in all?” (Fuson, 2009,

pg. 208).

What are some differences between Think Aloud 1 and Think Aloud 2?

What does each Think Aloud set students up to do while solving problems?

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Draft & Final Copy‣ Adapted from Literacy ‣ Students think through and discuss solutions to

a problem and create a well-organized representation of their thinking for sharing and publishing.

‣ Purpose: ‣ Organize and prepare to share mathematical thinking ‣ Make mathematical thinking available to others

‣ Tied to explaining and modes of communication

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Important Considerations for Draft & Final Copy

‣ Directions and expectations for the final sharable product should be clearly communicated to students.

‣ Materials should be made available. ‣ Students should have the opportunity to rehearse

explaining their answers.‣ The selection and sequencing of presentations

matter.

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THE CHOCOLATE PROBLEM

• Think Aloud• Draft and Final Copy• Then Talk Chain

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Ferrero Rocher Chocolates ProblemA store buys chocolate from the Ferrero Rocher factory in boxes. Each box has 3 wraps in it. And each wrap has 3 candies. The store sells chocolate candies individually, in wraps, or boxes. At the beginning of August, the store had run out of candies and bought 8 boxes of Ferrero Rocher. By the end of August, 2 boxes and 1 individual candy were left.

Assuming no other shipment came in, use TWO DIFFERENT METHODS for finding out how many total boxes, wraps and candies the store sold.

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Draft and Final Copy Rules• Work independently to solve the problem

and create your draft.• Share your thinking and solution with your

group.• Collaborate to create a final copy that

includes two different strategies.

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TALK CHAIN “RULES”• Begins with the teacher posing a question

about the mathematical work students have done, asking students to share mathematical ideas

• Each person who speaks must respond to the comment made immediately before them

• If someone breaks the chain or the conversation gets off track, the teacher can re-direct the talk chain

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SENTENCE FRAMES TO SCAFFOLD THE TALK CHAIN

• You just said that ________. I (agree/disagree) with it because _____________.

• I understand that you ____________ and I want to (add to/change) what you said by saying ______________.

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Talk Chain Question• How was your understanding deepened

by sharing drafts and working together to create a final copy?

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Supporting All Students• Have open-ended sentence frames to help students get

started with their presentations• Provide a word bank with mathematical terms students

can use in their presentations• Allow the use of graphic organizers, diagrams, visual

aids for student presentations• Have students write a sentence with teacher/peer

support before presenting in front of the whole class

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Final Thoughts• How can the use of discourse strategies

increase student conceptual understanding in mathematics?

Use the Talk Chain Again!

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Contact Info

Sidney FoxAIG teacher at Powell GT Elementary

sfox@wcpss.net@learnwithfoxwww.msfoxaig.weebly.com

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Acknowledgements

• This material is based upon work supported by the National Science Foundation under Grant No. DRL-1020177. Any opinions, findings, and conclusions or recommendations are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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