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Protocols and Procedures for Fostering Mathematics Discourse - Elementary
Sep 16, 2013(2:00 pm - 2:50 pm)
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
Agenda
• Background and rationale• Experience a variety of Number
Talks• Consider implications for
implementation of mathematics discourse.
• Closing
Mathematics Discourse
Enhancing Instruction for CCSSM
Upgrading UnitsNumber Talks
“FAL”Mini-Unit with
Forma-tive
Assess-ments
Mathematics Discourse
Hand Signals
• Solution• Strategy• Question• Comment• I agree• Integers• Fractions
Mathematics Discourse
CCSS Mathematical PracticesO
VER
AR
CH
ING
HA
BIT
S O
F M
IND
1. M
ake
sens
e of
pro
blem
s an
d pe
rsev
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solvi
ng th
em6.
Atte
nd to
pre
cisio
nREASONING AND EXPLAINING2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others
MODELING AND USING TOOLS4. Model with mathematics5. Use appropriate tools strategically
SEEING STRUCTURE AND GENERALIZING7. Look for and make use of structure8. 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 ThinkingResearch 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– Rekenreks– Five and Ten Frames– Mental Math– Number Strings– True/False Statements– Dilemmas– Spatial Reasoning– What’s My Rule?
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
CCSS Mathematical PracticesO
VER
AR
CH
ING
HA
BIT
S O
F M
IND
1. M
ake
sens
e of
pro
blem
s an
d pe
rsev
ere
in
solvi
ng th
em6.
Atte
nd to
pre
cisio
nREASONING AND EXPLAINING2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others
MODELING AND USING TOOLS4. Model with mathematics5. Use appropriate tools strategically
SEEING STRUCTURE AND GENERALIZING7. Look for and make use of structure8. 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
I saw ______dots.
I grouped the dots….
I also saw ___ dots, but I grouped the dots differently. I …
Mathematics Discourse
Dilemma
Explain the mathematical reasoning that both Kirsten & David used to simplify the expression above.
Kirsten says that 9 is the missing number in
5 = - 4
David says that 1 is the missing number in
5 = - 4
Mathematics Discourse
Dilemma10-5+4
Explain the mathematical reasoning that both Kirsten & David used to simplify the expression above.
Kirsten says that 9 is the missing number in
5 = + 4
David says that 1 is the missing number in
5 = + 4
Mathematics Discourse
Dilemma
Kirsten says that 10-5+4
is equal to 1
David says that 10-5+4
is equal to 9
Explain the mathematical reasoning that both David & Kirsten used to simplify the expression above.
Mathematics Discourse
Order of Operations
Grouping Symbols (
), { }, [ ], I IExponents
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
Spatial Reasoning Math TalkHow many cubes? How do you see them?
What is the surface area?
Mathematics Discourse
Number Talk Examples– Dot Patterns– Rekenreks– Five and Ten Frames– Mental Math– Number Strings– True/False Statements– Dilemmas– Spatial Reasoning– What’s My Rule?
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!• [email protected]
• http://goo.gl/ylgKi for K-2 Resources
• http://goo.gl/F58uB for 3-5 Resources