Protocols and Procedures for Fostering
Mathematics Discourse - Secondary
Sep 16, 2013
(1:00 pm - 1:50 pm)
Outcomes
• Participants will deepen their
understanding of mathematics
discourse, including some background
and rationale.
• Participants will experience Number
Talks and consider how they might be
used as part of a daily routine.
Mathematics Discourse
Agenda
• Background and rationale
• Experience a variety of Number Talks
• Consider implications for
implementation of mathematics
discourse.
• Closing
Mathematics Discourse
Enhancing Instruction for CCSSM
“FAL”
MiniUnit
with
Formative
Assessments
Number Talks
Upgrading Units
Mathematics Discourse
Hand Signals
•
•
•
•
•
•
•
Solution
Strategy
Question
Comment
I agree
Integers
Fractions
Mathematics Discourse
Hand Signals
• Solution
• Agree
• Strategy
• Integers
• Question
• Fractions
• Comment
REASONING AND EXPLAINING
1. Make sense of problems and persevere in
solving them
6. Attend to precision
OVERARCHING HABITS OF MIND
CCSS Mathematical Practices
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
MODELING AND USING TOOLS
4. Model with mathematics
5. Use appropriate tools strategically
SEEING STRUCTURE AND GENERALIZING
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Mathematics Discourse
Four Goals for K-2 Number Talks
• Developing Number Sense
• Developing fluency with small
numbers
• Subitizing
• Making Fives and Tens
• Number Conservation
Number Talks
-Sherry Parrish
Mathematics Discourse
Mathematical Thinking
•
•
•
•
Counting All
Counting On
Known Facts
Derived Facts
– Decomposing
– Recomposing
Duality, Ambiguity, and Flexibility in Successful Mathematical Thinking
Research by Eddie Gray and David Tall, 1994
Mathematics Discourse
Understanding Math Discourse
• Talk Formats
– Whole-Class Discussion
– Small-Group Discussions
– Partner Talks
Classroom Discussions: Using Math Talk to Help Students Learn
-S. Chapin, C. O’Connor, N Anderson (2003)
Mathematics Discourse
Understanding Math Discourse
• Talk Moves
– Revoicing
• So you’re saying the top number in a fraction
is called the numerator.
– Repeating
• Can you repeat what Miguel said in your own
words?
Classroom Discussions: Using Math Talk to Help Students Learn
-S. Chapin, C. O’Connor, N Anderson (2003)
Mathematics Discourse
Understanding Math Discourse
• Talk Moves (continued)
– Reasoning
• Do you agree or disagree and why?
– Adding On
• Please add onto Jimena’s strategy.
– Waiting
• Please take some quite think time.
Classroom Discussions: Using Math Talk to Help Students Learn
-S. Chapin, C. O’Connor, N Anderson (2003)
Mathematics Discourse
Number Talks
• A planned daily routine for whole‐class
instruction
• Number Sense (efficiency, accuracy &
flexibility)
• Generalized Arithmetic-conceptual
understanding
• Reasoning and Problem Solving
• Mental Mathematics
• Preview-Review-Conceptual
Understanding
Mathematics Discourse
Number Talks and Time
• Number Talks (about 10 minutes)
• Mini-Lesson (10 to 20 minutes)
• Lesson (more than 20 minutes)
Mathematics Discourse
Number Talk Examples
–
–
–
–
–
–
–
–
Dot Patterns
Mental Math
Number Strings
True/False Statements
Dilemmas
Spatial Reasoning
What’s My Rule?
Error Analysis and Coaching
Mathematics Discourse
Norms
“No one is as smart as all of us are together.”
• Respect
• Individual think time
• Everyone participates
• Everyone helps
• Leave no one behind
• Be positive
• Technology courtesy
Mathematics Discourse
Socio-mathematical Norms
• Errors are gifts, they promote discussion.
• Share a second sentence to connect your
thoughts.
• The answer is important, but it is not the math.
• Build on the thinking of others.
• Ask questions until ideas make sense.
• Think with language and use language to
think.
Mathematics Discourse
REASONING AND EXPLAINING
1. Make sense of problems and persevere in
solving them
6. Attend to precision
OVERARCHING HABITS OF MIND
CCSS Mathematical Practices
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
MODELING AND USING TOOLS
4. Model with mathematics
5. Use appropriate tools strategically
SEEING STRUCTURE AND GENERALIZING
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Mathematics Discourse
Lenses to Consider During
Professional Development Sessions
Learner Lens
Teacher Lens
Mathematics Discourse
Dot Talk
How many dots do you see?
How did you see them?
Mathematics Discourse
Mental Math
After a 20% discount, the price is
80% of the original price. So 80% of
the original price is $140. What is the
original price?
Mathematics Discourse
Mental Math
Mathematics Discourse
Number String (Mental Math)
35 x 8
70 x 4
140 x 2
Mathematics Discourse
Number String (Mental Math)
3 x 50
3 x 100
3 x 149
Mathematics Discourse
True/False
11
0.44
=
1100
44
True or False?
Why?
Mathematics Discourse
True/False Number Talk
Mathematics Discourse
Dilemma Number Talk
David says that
10xy-5xy + 4xy
equals 9xy
Kirsten says that
10xy-5xy + 4xy
equals xy
Explain the mathematical reasoning that both
David & Kirsten used to simplify the expression
above.
Mathematics Discourse
Order of Operations
Grouping
Symbols
( ), { }, [ ], I I
Exponents
Multiplication/Division
Division/Multiplication
Addition/Subtraction
Subtraction/Addition
Mathematics Discourse
Spatial Reasoning
How many cubes? How do you see them?
What is the surface area?
Mathematics Discourse
Transformations
Rotate the figure 90˚ clockwise.
What are the new coordinates of point A?
Mathematics Discourse
What’s My Rule?
In
Out
1
5
3
2
5
21
13
9
Mathematics Discourse
What’s My Rule?
Input
Output
1
5
3
2
1
25
9
8
Mathematics Discourse
What’s My Rule?
X
Y
1
5
3
2
2
26
10
5
Mathematics Discourse
What’s My Rule?
Domain
Mathematics Discourse
Range
Number Talk Examples
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–
–
–
–
–
–
–
Dot Patterns
Mental Math
Number Strings
True/False Statements
Dilemmas
Spatial Reasoning
What’s My Rule?
Error Analysis and Coaching
Mathematics Discourse
Number Talks and Time
• Number Talks (about 10 minutes)
• Mini-Lesson (10 to 20 minutes)
• Lesson (more than 20 minutes)
Mathematics Discourse
Table Talk
• Have you implemented Number Talks
as part of your daily routine? What
were some of the benefits and
challenges?
• When in your daily routine could you
incorporate the use of Number Talks?
Mathematics Discourse
Questions Teachers Might Ask
• Who would like to share their thinking?
• Did someone solve it a different way?
• Who else used this strategy to solve the
problem?
• How did you figure it out?
Mathematics Discourse
Questions Teachers Might Ask
•
•
•
•
What did you do next?
What did you need to know?
Why did you do that? Tell me more.
Which strategies do you see being used?
Mathematics Discourse
Outcomes
• Participants will deepen their
understanding of mathematics
discourse, including some background
and rationale.
• Participants will experience Number
Talks and consider how they might be
used as part of a daily routine.
Mathematics Discourse
Closing
• Thank you!
• Cecilio_Dimas@sccoe.org
• The best source for Number Talks is
student work (errors, strategies, and
solution pathways).
– Inside Mathematics
– Mathematics Assessment Project
Mathematics Discourse