Outcomes

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.


Agenda• Background and rationale• Experience a variety of Number

Talks• Consider implications for

implementation of mathematics discourse.

• Closing


Enhancing Instruction for CCSSM

Upgrading UnitsNumber Talks

“FAL”Mini-Unit with

Forma-tive

Assess-ments


Hand Signals• Solution• Strategy• Question• Comment• I agree• Integers• Fractions

Hand Signals• Agree

• Integers

• Fractions

• Solution

• Strategy

• Question

• Comment


CCSS Mathematical PracticesOV

ERAR

CHIN

G HA

BITS

OF

MIN

D1.

Mak

e se

nse

of p

robl

ems

and

pers

ever

e in

so

lving

them

6. A

ttend

to p

recis

ion

REASONING 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


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


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


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)


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?



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.



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


Number Talks and Time• Number Talks (about 10 minutes)• Mini-Lesson (10 to 20 minutes)• Lesson (more than 20 minutes)


Number Talk Examples– Dot Patterns– Rekenreks– Five and Ten Frames– Mental Math– Number Strings– True/False Statements– Dilemmas– Spatial Reasoning– What’s My Rule?


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


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.


CCSS Mathematical PracticesOV

ERAR

CHIN

G HA

BITS

OF

MIN

D1.

Mak

e se

nse

of p

robl

ems

and

pers

ever

e in

so

lving

them

6. A

ttend

to p

recis

ion

REASONING 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


Lenses to Consider During Professional Development Sessions

Learner Lens Teacher Lens


Dot TalkHow many dots do you see?

How did you see them?


Dot Talk

I saw ______dots.

I grouped the dots….

I also saw ___ dots, but I grouped the dots differently. I …


Dot TalkHow many dots do you see?



Dot Talk


Rekenrek

DVD K.2


Five Frames


Ten Frames


Ten FramesHow many dots do you see?



Ten FramesHow many dots do you see?



Mental Math

26 + 27


Mental Math

32 x 15


Number String (Mental Math)

7+68+7

14+1325+26



3 x 503 x 1003 x 149



35 x 870 x 4140 x 2


True/False

7 = 4 + 3

True or False?Why?


True/False

17-16= 9-8

True or False?Why?


True/False

8 x 7= 8 x (5+2)

True or False?Why?


True/False

15 x 24 = 30 x 12

True or False?Why?


True/False•


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


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


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.


Order of OperationsGrouping Symbols ( ), { }, [ ], I I

Exponents

Multiplication/Division Division/Multiplication

Addition/Subtraction Subtraction/Addition


Spatial ReasoningHow many cubes? How do you see them?

What is the surface area?


Spatial Reasoning Math TalkHow many cubes? How do you see them?

What is the surface area?


What’s My Rule? In Out

1532

3754


What’s My Rule? Input Output

1532

5251510


What’s My Rule? X Y

1532

0421


Number Talk Examples– Dot Patterns– Rekenreks– Five and Ten Frames– Mental Math– Number Strings– True/False Statements– Dilemmas– Spatial Reasoning– What’s My Rule?


Number Talks and Time• Number Talks (about 10 minutes)• Mini-Lesson (10 to 20 minutes)• Lesson (more than 20 minutes)


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?


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?


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?


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.


Closing

• Thank you!• [email protected]

• http://goo.gl/ylgKi for K-2 Resources

• http://goo.gl/F58uB for 3-5 Resources

http://goo.gl/ylgKi

http://goo.gl/ylgKi

http://goo.gl/ylgKi

http://goo.gl/F58uB

http://goo.gl/F58uB

Documents

Outcomes