Let’s Talk Math!
Math Talk in the Elementary Classroom
Crystal Cabral
[email protected]
Wake County Public School System
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 PartnerWhat 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,
VITAL
it is
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!
Math Talk in the Elementary Classroom
Crystal Cabral
[email protected]
Wake County Public School System
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.