math talk deepens student mathematical understanding with carla kozak

Math Talk Deepens

Student Mathematical Understandingwith Carla Kozak

Developed by ERLC/ARPDC as a result of a grant from Alberta Education to support

implementation

Where do you work?Using the text tool, type your name and the name of school district where you work?

Carla Edmonton Public School Board

AgendaGOAL: Today’s session will focus on why communication in mathematics is integral to building students’ understanding and how teachers can encourage worthwhile math talk among their students.

• What is Math Talk? What does it look like? • Why is communication important?• How can teachers encourage worthwhile

Math Talk?• Where are those rich mathematical tasks?

Definition of Discourse

NCTM (1991) - a way of representing, thinking, talking, agreeing and disagreeing.

Ball (1991) adds that discourse is the how [process] student knowledge is constructed and exchanged in the classroom.

Just like Me

What does communicating mathematically look like in your math class?

Think about your students and respond with:

Yes, this is just like my classroomOR

No, this is not like my classroom

Just like Me

My students work in pairs and small groups.

Just like Me

My students know that everyone’s idea is accepted and discussed.

Just like Me

My students use manipulatives to support the math concepts they are learning.

Just like Me

My students draw pictures to show their thinking.

Just like Me

My students use words or numbers to explain their thinking.

Just like Me

My students share more than one way to solve a problem.

Just like Me

My students explain and model personal strategies for solving problems and learn from each other.

“Communication elevates math to a thinking skill rather than a rote skill. It allows us to move beyond just doing the math and push students to understand, to explore, and to explain math ideas.” (O’Connell & O’Connor, 2007)

Show me how you solved it!

Math Talk

Watch the short clip and please click on the when you have finished viewing the video.

http://teachertube.com/viewVideo.php?video_id=129790

Does Megan have a strong understanding of number sense?

Respond with a or

1000 – 899 = ?

Solve this problem.

How does this demonstrate students’ understanding of NUMBER?

110 10 10- 8 9 9

0 9 9

1 0 1

Tom Lehrer- New Math342- 173= ?

Watch the short clip and please click on the when you have finished viewing the video.

http://www.youtube.com/watchv=SXx2VVSWDMo&feature=related

Enter most elementary classrooms in Canada today and you will find a room filled with the

sounds of learning - students talking.

Preparing the FutureStudents must be able to: • reason about quantitative information,• possess number sense, • check for the reasonableness of solutions,• communicate (both orally and in writing) their

solutions to problems.

Principles and Standards for School Mathematics (NCTM, 2000)

All students to should be able to:• organize and consolidate their mathematical

thinking through communication,• communicate their mathematical thinking

coherently and clearly to peers, teachers, and others,

Principles and Standards for School Mathematics (NCTM, 2000)

All students to should be able to:• analyze and evaluate the mathematical

thinking and strategies of others, and• use the language of mathematics to express

mathematical ideas precisely.

Alberta K-9 Mathematics Program of Studies (Alberta Education, 2007)

Communication is one of the seven mathematical processes that permeate the teaching and learning of mathematics; “communication is important in clarifying, reinforcing and modifying ideas, attitudes and beliefs about mathematics”.

“Using math talk in your classroom requires a different lesson format than the lesson in which the teacher demonstrates a technique or skill and follows up with student practice.”

(Sullivan and Lilburn, 2002)

How do you see this working in your math class?

“The teacher needs to be “receptive to all students’ responses, the teacher must acknowledge the validity of the various responses while making clear any limitations, drawing out contradictions or misconceptions, and building class discussion from partial answers. ” (Sullivan and Lilburn, 2002)

Four Things for Teachers to Consider

1. Create safe, supportive environment,

2. Provide engaging mathematical tasks,

3. Manage Math Talk, and

4. Ask good questions.

1. Create safe, supportive environment

How do you create a safe, supportive environment for your students?

Click on the text box and type a phrase.

1. All ideas accepted whether right or wrong. 2. Student ideas will be respected and not be judged

negatively by the teacher or their peers. 3. All student contributions are worthwhile and valued. 4. Students are not afraid to take risks or to make

mistakes.5. Mistakes are seen as opportunities to learn 6. Students learn that other classmates may hold

different views and that everyone has the opportunity to argue their case or re-assess their thinking.

Create safe, supportive environment

Together, the teacher and students build “a safe intellectual environment, one where it is alright to be wrong, to challenge another, to correct another, and, more important, to correct oneself” (Leinhardt & Steele, 2005).

2. Provide engaging mathematical tasks

• Interesting problems that ‘go somewhere’ mathematically can often be catalysts for rich Math Talk.

• Students need to “formulate, grapple with, and solve complex problems that require a significant amount of effort and should then be encouraged to reflect on their thinking.”

(NCTM, 2000)

60-45=61-46=59-44=62-47=107-39=201-79=1001-899=

60-45=61-46=59-44=62-47=107-39=201-79=1001-899=

45 50 60

+5 +10

60-45=61-46=59-44=62-47=107-39=201-79=1001-899=

45 50 60

+5 +10

46 56 61

+10 +5

3. Manage Math Talk

• Provide opportunities to talk during the lesson.• Consider a variety of ways to organize

students to encourage sharing- pairs, small groups or whole class discussions.• Listen to students’ responses in order to

guide the conversations.

4. Ask good questions

By asking good questions, teachers engage students in meaningful dialogue, “…not just any kind of student talk is expected to be productive for supporting or challenging students’ thinking.” (Franke et al., 2007)

Ask good questions

• Different types of questions:oprobing (What do you mean by…), ojustifying (Can you solve it another

way?), ofactual (How many were there?)

• Use levels in Blooms Taxonomy to ask more higher level questions.

“The more teachers know about students’ thinking, the more effectively they can adapt their own instructional practices to uncover and address students’ misconceptions and the gaps in their knowledge and understanding, and so support student learning” (Webb et.al., 2008).

Resources

See attached list

Final Thoughts

Using the text tool, write a word or two that stood out for you from today’s session.

Thank you

Contact me at Carla.Kozak@epsb.ca