(c) PEBC. Hoffer, 2011 Wendy Ward Hoffer Director of Education, PEBC A recording of today’s...

(c) PEBC. Hoffer, 2011

Wendy Ward HofferDirector of Education, PEBC

Math Discourse:

Talking to

Learn

A recording of today’s webinar will be available at:http://www.carnegielearning.com/webinars

Think about it…

When you hear students talking with one another, what sorts of things do they say?

(c) PEBC. Hoffer, 2011A recording of today’s webinar will be available at:http://www.carnegielearning.com/webinars

Typical Student-to-Student Talk

Gossiping

Playing

Teasing

Making Social Plans

complainingAsking for answers

Tattling


Think about it…

When you talk with students, what kinds of things do you say?


Typical Teacher-to-Student Talk

Socializing

Correcting

Praising

Teasing

DirectingAccounting

Policing


Focus Questions:

What is the value of mathdiscourse?

How can teachers promote and facilitate classroom discourse in math?

(c) PEBC. Hoffer, 2011A recording of today’s webinar will be available at:

http://www.carnegielearning.com/webinars

Learners making meaning of content through accountable, engaged conversations.

What is math discourse?

Why discourse?

Discourse…

• engages learners.

• promotes understanding.

• develops 21st century skills

• supports language development.



Discourse engages learners.

“Learning and succeeding in school requires active engagement—whether students are rich or poor, black, brown, or white. The core principles that underlie engagement are applicable to all students—whether they are in urban, suburban, or rural communities.” - Melzer & Hamman, 2004

Of 171,000 students in 26 states surveyed in 2005, less than a third reported feeling excited about their classes.



Discourse promotes understanding.

“As Socrates well understood, learning is more likely to change through dialogue and reflection than through lecture and imposition.” – Kober, 1993

A 2006 study of 30 industrialized nations ranted US high school students 25th in math.



Discourse develops 21st century skills.

“In order to get good jobs, and to be active and informed citizens in our democracy, economy, today’s students – and tomorrow’s workers – need to learn how to …work in teams and lead by influence, be agile and adaptable, communicate clearly and concisely…” – Tony Wagner, 2008

The top ten jobs of 2015 don’t exist today.


Discourse supports language development.

Between 1995 and

2005, seven states

saw a 300% increase

in the number of

English Language Learners

enrolled in school.

“Language development is an active, not passive process. Teachers must give students opportunities and time to talk, which means teachers must make key shifts: talk less, listen more.” – Klaus-Quinlan & Nathenson-Mejia &, 2010


How can we get there from here?



Discourse

Purpose

Tasks

StructureFacilitation

Accountability

Community


Stepping Stones To Successful Student Discourse

Purpose

• clear academic rationale

• transparent process skills

goal(s)

Work is assigned because it is the next topic in the book.

Learning goals for both content and process are clearly identified, and the task is engineered to support all in attaining those goals.



Tasks

• worthy

• rich

• open endedWorksheet:

6 x 75%

5 x 50%

30 x 25%

8 x 10%

If you drive 12,000 miles annually in a vehicle at 20 mpg, how much carbon dioxide will your car produce each year if one gallon of gas weighs approximately 6 pounds, 75% of its weight is in carbon, and each atom of carbon produces 3.67 times its weight in carbon dioxide?



Structure

• specific tasks

• limited time

• metacognition

Work in groups to solve problems.

After students work independently, they turn and talk for two minutes about whether their answers to #1 were similar or different, and why. Then, as a group, they discuss how that paired sharing helped them to understand.



Facilitation

• open-ended questions

• focus on thinking

• welcome multiple perspectives

• Help us understand your thinking.

• Did anyone else think of this

differently?

• Does everyone have the same idea?

• What questions do you have?

• What is confusing?

• What was the big idea that helped

you make sense of this?

• What are people still wondering?


Community

• shared norms

• interdependence

• supported by modeling

Students work alone, then tell each other their answers.

“I disagree with Adam because I think when you multiply 4.5 by 3.67 you should get a number close to 12, since that is 4 x 3. So I think 165.15 is too big.”



Accountability

• responsibility for learning

• frequent informal assessment

Students are not asked to demonstrate understanding regularly.

“So, now that you have solved these, discussed them with your partners, listened to the whole group share their thinking, take a half sheet of paper and write down what you do and don’t understand now about how to solve these problems.”



Discourse

Purpose

Tasks

StructureFacilitation

Accountability

Community


Stepping Stones To Successful Student Discourse

Small Group Discourse Structures

• Think-Pair – Share• Back to Back• Carousel Critique• Give One – Get One• Reciprocal Teaching• Notice and Wonder



Small Group Discourse Structures

Think – Pair – Share

Reciprocal Teaching

Back to Back

Notice & Wonder

Carousel Critique

Give one – Get one



Large Group Discourse Structures

• Solution Discussion• Peer Critique• Socratic Seminar• Review Games in Teams• Sharing understandings



How will you begin?

What questions do you have?



References

• Daniels School of Business, University of Denver advertisement

• Klaus- Quinlan, Moker and Sally Nathansen- Mejia. Bridging Words And Worlds: Effective Instruction for Culturally & Linguistically Divserse Learners. (PEBC, 2010)

• Program for International Student Assessment, 2006 (OECD)

• Quate, Stevi and John McDermott. Clockwatchers: Six Steps to Motivating and Engaging Disengaged Students Across the Content Areas (Heinemann, 2010)

• Wagner, Tony. The Global Achievement Gap: Why Even Our Best Schools Don't Teach the New Survival Skills Our Children Need--And What We Can Do About It(Basic Books, 2008)

For Further Reading

• Boaler, Jo. What’s Math Got to Do with It? (Viking, 2008)

• Chapin, Suzanne. Classroom Discussions Using Math Talk. (Math Solutions, 2003)

• Hyde, Art. Understanding Middle School Math: Cool Problems to Get Students Thinking and Connecting. (Heinemann, 2009)

Follow Up Questions ?

• [email protected]




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(c) PEBC. Hoffer, 2011 Wendy Ward Hoffer Director of Education, PEBC A recording of today’s...

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