Math Talk
Deepens
Student Mathematical Understanding
with 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
Agenda
GOAL: 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 classroom
OR
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.
Show me
how you
solved it!
“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)
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?
0 9 9
110 10 10
- 8 9 9
1 0 1
Tom Lehrer- New Math
342- 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 Future
Students 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=
+5
45
+10
50
60
60-45=
61-46=
59-44=
62-47=
107-39=
201-79=
1001-899=
+5
45
+10
50
60
+10
46
+5
56
61
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