Let’s Talk Math!

Crystal Cabral

ccabral@wcpss.net

Wake County Public School System

Math Talk in the Elementary Classroom

Welcome

• Introductions:

“When I think about discourse in the mathematics classroom, I…….”

• Please feel free to write on your copies as you work together today. I will email you digital files of handouts.

Code of Cooperation & Agenda

• Participate & Ask Questions. You will be asked to “talk about math”.

• Respect & Listen to Others.

• Limit Sidebars.

• Have fun!

Signal for Whole Group Attention: Chimes

My Appointments

Why Are We Here?

Why Are We Here? • For over a decade, NCTM has been urging

teachers to emphasize communication – talk and writing – as a part of mathematics learning and teaching.

• The mathematical thinking of many students is aided by hearing what their peers are thinking.

Chapin, S., C.O’Conner, and N. Anderson. 2003.

Why Are We Here?

• Putting thoughts into words pushes students to clarify their thinking.

• Teachers can identify misconceptions much more easily through discussion.

However…

• Researchers have found that few American classrooms display consistent or even occasional use of student talk.

• Most classroom talk consists of the teacher lecturing, asking students to recite, or posing simple questions with known answers.

Learning the “Talk Moves”

• Revoicing - Teacher repeats some or all of what a student says and then asks the student to verify.

• Asking students to restate someone else’s reasoning – “Can you repeat what he just said in your own words?”

• Asking students to apply their own reasoning to someone else’s reasoning –

“Do you agree or disagree and why?

Learning the “Talk Moves”

• Prompting students for further participation – “Would someone like to add on?

• Using wait time - “Take your time…we’ll wait”.

Talk Formats

Whole Class Discussion

• Teacher is a facilitator and guide.

• Teacher focuses on student thinking and ideas.

• Provides a space for students to practice so they become confident math thinkers.

• Teacher does not reject incorrect reasoning, but uses these mishaps as a way to discover.

Talk Formats Small-Group Discussion

• Teacher gives a question/problem for a group to discuss.

• Teacher circulates as groups discuss and doesn’t control the discussions but observes and interjects.

Talk Formats

Partner Talk

• Teacher asks a question and then gives students a short time, perhaps a minute or two at the most, to put their thoughts into words with their nearest neighbor.

• Initiate by “Turn and talk about this with the person next to you”.

Talk Tasks

• Each person in your group needs 2 “Talk Task” cards.

• As your group works to solve the problem you need to make sure you “play” your talk task card.

Group Problem Solving Roles

The Real Scoop

It was hot at the boardwalk. The Real Scoop was doing very well. Russell had just served up 55 cones, some single scoops, some double scoops, and some triple scoops.

If he served up a total of 103 scoops, how many of the scoops were single scoops, how many were double scoops, and how many were triple scoops?

Let’s Talk Scoops… When your group is finished, discuss the following:

• What strategies/tools did you use to help you solve the problem?

• Why did you choose that strategy(s)?

• How did you reach your conclusion? Does your answer seem reasonable? Why?

• What ideas that you have learned before were useful in helping you solve this problem?

More than Just Talk…

• Goal is to increase the amount of “High-Quality” classroom talk

• Not just the AMOUNT of talk

• Think about it:

• What’s the purpose of the

conversation?

• What do I want to learn or

teach with this conversation?

Aspects of Math Talk

• Social Focus

• Content Focus

• Cognitive Development

Math Talk- Social Focus

The Importance of Classroom Culture

Find your Chess Partner-

What strategies do you use in your classroom to help establish a positive Classroom Culture?

Math Talk Must Haves…

1. Every student is listening to what others say.

2. Every student can hear what others say.

3. Every student may participate by speaking out at some point.

Math Talk - Baby Steps

• Building towards a learning community using math talk is a process.

• The ultimate goal is for the teacher to be a facilitator / guide for the math lesson.

• Building a math talk rich environment takes time.

A Gradual Process

Keep in Mind:

• The development of the community may take several months.

• The classroom will transform as the children and teacher take on new roles and responsibilities.

• Most effective when implemented beyond the math classroom.

Math Talk- Content Focus

• Student Talk- Clarifies for students what they do, and do not understand.

• Brings gaps in student understanding to the surface.

• Helps teachers identify and address misconceptions in student thinking

The Importance of Questioning • 60% of the things said by teachers are questions and most

are not planned.

• These questions can be described as “Open” or “Closed”.

Sullivan, Peter and Pat Lilburn. 2002.

Closed verses Open Questions • Closed Questions simply require an answer to be

given from memory or the reproduction of a skill.

• Open Questions require a student to think more deeply and to give a response that involves more than recalling a fact or reproducing a skill.

Our Mathematics Questions

• In mathematics, closed questions are more common. In the areas such as language arts or social studies, teachers often ask children to interpret situations and justify opinions.

• Partner Talk: Describe how you make decisions on what questions you ask during a mathematics lesson. How do the questions you ask impact student growth and achievement?

The Truth about Questioning

• Questions that encourage students to do more than recall known facts have the potential to stimulate thinking and reasoning.

• To emphasize problem solving, application, and the development of a variety of thinking skills,

it is VITAL that we pay more attention to improving our questioning in mathematics lessons.

Looking at Good Question…

Find the area and

perimeter of the

following rectangle.

5 yd

12 yd

I want to make a garden in the shape of a rectangle. I have 30 meters of fence for my garden. What might be the area of the garden?

Math Talk- Cognitive Development

• Basic components of logical thinking are imbedded in the context of a discussion.

• Student makes a claim

• Teacher asks for evidence to prove that claim

• Use of Examples and Counter-Examples

• Metacognition

Prove It! – 4th Grade

Exploring The Teacher’s Role

In The Beginning

• The teacher models math talk for students and elicits responses.

• The teacher waits patiently and refrains from intervening immediately to correct children’s errors in order to create space and support for children’s voices to emerge.

Continuing to Grow

• The Teacher guides students from the side or back of the classroom so that children can sense that their questions, ideas, and discoveries are the focal point of the instruction.

Math Talk Pro

• Mathematical conversations are the cornerstone of the math lesson.

• Discussions occur between students and feature solid mathematical reasoning.

• Teacher’s role is clearly a guide not a “filter” for mathematical discussions.

Math Talk- Learning Paths

• Let’s look at the levels of Math Talk 0 - 3

Reflection Time

• Take a moment to review each of the 4 levels of Math Talk implementation.

• Where are you currently?

• What are your goals for moving forward?

Let’s Chat!

• Find your Bike Buddy and share where you are at in your Math Talk journey.

• What will your next steps be to increase the level of Math Talk in your classroom?

How the Classroom Changes

Elements of the Gradual Transformation

• A shift from the teacher as sole questioner to both children and teachers as questioners

• Children increasingly explaining and articulating their math ideas

• A shift from the teacher as the source of all math ideas to children’s ideas also influencing the direction of lessons.

Elements of the Gradual Transformation

• Children increasingly taking responsibility for learning and for the evaluation of themselves and others.

• Increasing amounts of child-to-child talk with teacher guidance as needed.

Power Tools • Appropriate Math Vocabulary

• Mathematical Language skills

• Proof Drawings

• Manipulatives

These tools help math become personally meaningful to children and provide a context through which children can share their ideas.

Reflection & Closing

The essence of mathematics is not to make simple things complicated, but to make complicated things simple.

S. Gudder

Let’s Talk Math!

Crystal Cabral

ccabral@wcpss.net

Wake County Public School System

Math Talk in the Elementary Classroom

References

Sullivan, Peter and Pat Lilburn. 2002. Good Questions for Math Teacher: Why Ask Them and What to Ask, K-6. Sausalito, CA: Math Solutions Publications.

Chapin, S., C.O’Conner, and N. Anderson. 2003. Classroom Discussions Using Math Talk to Help Students Learn. Sausalito, CA: Math Solutions Publications.