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Developing student talk to promote mathematical thinking

Julia Crawford

jcrawford@cognitioneducation.com

www.tiny.cc/MathsTalk

Cognitioneducation.co.nz

cognitioneducation.com

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Take a quick look … what do you see?

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What did you see?

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Dots

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Effective Pedagogy in Mathematics

Best Evidence Synthesis (BES) 2007
Summary 2009

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10 Principles of effective pedagogy

Best evidence synthesis of mathematics

An ethic of care
Arranging for learning
Building on students’ thinking
Worthwhile mathematical tasks
Making connections
Assessment for learning
Mathematical communication
Mathematical language
Tools and representations
Teacher knowledge

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What is mathematics?

Our answer for this effects how we approach teaching /learning

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Two main themes

Mathematical discussion and talk

How do teachers manage class discussion?
Supporting children to talk and grow their thinking
Equitable participation

Worthwhile learning tasks

What is a worthwhile tasks?
High cognitive demand
Low threshold, high ceiling

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Student discourse

An essential component of students’ mathematics learning
When students share and exchange ideas, both the students and their teachers benefit
Creating a discussion rich class environment:

Choose tasks which allow rich discussion and a variety of approaches
‘Orchestrating’ opportunities for students to discuss and present their thinking (teacher moves)
Giving students tools to learn about how to discuss and listen to mathematics thinking (talk moves)

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Mathematical discussion

5 Practices for Orchestrating Productive Mathematics discussions
What are the ‘teacher moves’ to support building on students’ thinking and making connections

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5 Practices for Orchestrating Productive Mathematics Discussions

Anticipating likely student responses to challenging mathematical tasks
Monitoring students’ actual responses to the tasks (while students work on the tasks in pairs or small groups)
Selecting particular students to present their mathematical work during the whole-class discussion
Sequencing the student responses that will be displayed in a specific order
Connecting different students’ responses and connecting the responses to key mathematical ideas.

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Talk moves

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Talking = Learning

The person doing the talking is often the one doing the learning.

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Productive talk

Four principles to guide us:

Discussions should achieve a mathematical goal
Students need to know what and how to share to share so their ideas are heard and are useful to others
Teachers need to orient students to each other and the mathematical ideas (so everyone is involved)
Teachers need to communicate that all students are sense makers and that their ideas are valued.

Intentional Talk: Stenhouse, 2014

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Students are afraid to be wrong

Half Dome, Yosemite – ‘Thank God Ledge’

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Encouraging student discourse

What do you notice? What do you wonder?
Which one doesn’t belong?
What is the same? What is different?
Tell me everything you know about…
Estimation
Predict
Why is this solution incorrect? (error analysis)
Invent and tell a story

From: Safe ways to enter math tasks. Sara van der Werf

Examples to follow…

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Goal

Students will see it before I show them
Students will say it before I tell them.

How will I help students see what I want them to say?

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Encouraging student discourse

What do you notice? What do you wonder?
Which one doesn’t belong?
What is the same? What is different?
Tell me everything you know about…
Estimation
Predict
Why is this solution incorrect? (error analysis)
Invent and tell a story

From: Safe ways to enter math tasks. Sara van der Werf

Examples to follow…

^{©Cognition Education 2018}

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What do you notice? What do you wonder?

What else? What else? What else?

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What do you notice? What do you wonder?

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Math animations�

What do you notice?�What do you wonder?

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Choral Counting

What do you notice?

What do you wonder?

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Notice and wonder tips

Temporarily remove details
Add visuals

Students shut down before even trying.

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Add visuals!

Temporarily remove details

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Starter: Edwards Compass Rose

A massive compass rose is painted onto dry lake bed at Edwards Air Force Base in Kern County, Southern California. With a diameter of more than 4,000 feet (1,220 meters), the compass is almost perfectly aligned with magnetic north and is used by aircraft to test navigation equipment. At the top of this Overview is the Neil A. Armstrong Flight Research Center, NASA’s premier site for aeronautical research.

34.954060°, -117.873340°

What do you notice? What do you wonder?

What else? What else?

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Encouraging student discourse

What do you notice? What do you wonder?
Which one doesn’t belong?
What is the same? What is different?
Tell me everything you know about…
Estimation
Predict
Why is this solution incorrect? (error analysis)
Invent and tell a story

From: Safe ways to enter math tasks. Sara van der Werf

Examples to follow…

^{©Cognition Education 2018}

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Which one doesn’t belong?

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Which one doesn’t belong?

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Move across the room

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Encouraging student discourse

What do you notice? What do you wonder?
Which one doesn’t belong?
What is the same? What is different?
Tell me everything you know about…
Estimation
Predict
Why is this solution incorrect? (error analysis)
Invent and tell a story

From: Safe ways to enter math tasks. Sara van der Werf

Examples to follow…

^{©Cognition Education 2018}

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What’s the same? What is different?

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Same but different Math

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What is the same? What is different?

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Encouraging student discourse

What do you notice? What do you wonder?
Which one doesn’t belong?
What is the same? What is different?
Tell me everything you know about…
Estimation
Predict
Why is this solution incorrect? (error analysis)
Invent and tell a story

From: Safe ways to enter math tasks. Sara van der Werf

Examples to follow…

^{©Cognition Education 2018}

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Tell me everything you know about

0.4

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Tell me everything you know about…

red

axes

numbers

graph

curve

‘crosses y-axis’

y-intercept

‘crosses x-axis’

x-intercepts

‘U-shape’

parabola

THE 1^ST 5 THINGS STUDENTS SAY:

‘high point’

maximum

& vertex

(5,0)

(-1,0)

(0,5)

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Tell me everything you know about

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Encouraging student discourse

What do you notice? What do you wonder?
Which one doesn’t belong?
What is the same? What is different?
Tell me everything you know about…
Estimation
Predict
Why is this solution incorrect? (error analysis)
Invent and tell a story

From: Safe ways to enter math tasks. Sara van der Werf

Examples to follow…

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Estimation

Bout how many cheese balls will fit in the bowl?

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Estimation

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Encouraging student discourse

What do you notice? What do you wonder?
Which one doesn’t belong?
What is the same? What is different?
Tell me everything you know about…
Estimation
Predict
Why is this solution incorrect? (error analysis)
Invent and tell a story

From: Safe ways to enter math tasks. Sara van der Werf

Examples to follow…

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Which fraction is in the wrong location?

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Convince me!?

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From MCAT

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Encouraging student discourse

What do you notice? What do you wonder?
Which one doesn’t belong?
What is the same? What is different?
Tell me everything you know about…
Estimation
Predict
Why is this solution incorrect? (error analysis)
Invent and tell a story

From: Safe ways to enter math tasks. Sara van der Werf

Examples to follow…

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Tell a story

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Invent and tell a story

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Goal

Students will see it before I show them
Students will say it before I tell them.

How will I help students see what I want them to say?

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Support students to practice listening and talking through their thinking.

Teacher moves:

Listening

Prompting

Evaluating progress

Being quiet

Half Dome, Yosemite – ‘Thank God Ledge’

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Encouraging student discourse

What do you notice? What do you wonder?
Which one doesn’t belong?
What is the same? What is different?
Tell me everything you know about…
Estimation
Predict
Why is this solution incorrect? (error analysis)
Invent and tell a story

From: Safe ways to enter math tasks. Sara van der Werf

Examples to follow…

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Where to find resources

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Let me know if I can help

Julia Crawford

jcrawford@cognitioneducation.com

I work with you to develop a plan to meet your needs

Brainstorm needs, evidence, and hunches
Complete the journal application with evidence to align to the national priorities, achievement challenges, faculty goals
Develop a delivery plan
Work with you and your team to implement your plan