1. Protocols and Procedures for Fostering Mathematics Discourse - Elementary Sep 16, 2013 (2:00 pm - 2:50 pm)
Protocols and Procedures for Fostering Mathematics Discourse - Elementary Sep 16, 2013 (2:00 pm - 2:50 pm)
This session will examine some of the protocols and procedures you’ll need to foster meaningful mathematics discourse in elementary school classrooms, including Number Talks.

2. 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.
This session will examine some of the protocols and procedures you’ll need to foster meaningful mathematics discourse in elementary school classrooms, including Number Talks.

3. Agenda Background and rationale Experience a variety of Number Talks
Consider implications for implementation of mathematics discourse.
Closing
Cecilio

4. Enhancing Instruction for CCSSM
“FAL”
Mini-Unit with Forma-tive Assess-ments
Intent: Participants will understand how a unit can be upgraded.
Talking Points:
Explain to participants that a unit normally lasts between 9 and 14 days. It begins with a pre-assessment and instructional decisions are based upon the misconceptions that arise from the pre-assessment. An expert investigation is then given and instructional decisions are made based upon the misconceptions and strengths from the expert investigation. A Formative Assessment Lesson (FAL) is then given to students and instruction is again based upon data from the FAL. A final assessment is given to students at the end of the unit.
This is the big picture of unit design. We will be looking at each one more carefully during the math break-out sessions this year.
Number Talks
Upgrading Units

5. Curriculum Leadership Council 2011-2012
CLC December 6, 2011
Hand Signals
Solution
Strategy
Question
Comment
I agree
Integers
Fractions

6. Hand Signals Solution Strategy Question Comment Agree Integers
Curriculum Leadership Council
CLC December 6, 2011
Hand Signals
Solution
Strategy
Question
Comment
Agree
Integers
Fractions *

7. CCSS Mathematical Practices
REASONING AND EXPLAINING
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
OVERARCHING HABITS OF MIND
1. Make sense of problems and persevere in solving them
6. Attend to precision
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

8. 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
Cecilio

9. 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
Cecilio

10. 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)

11. 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)

12. 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)

13. 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
Cecilio

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

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

16. Curriculum Leadership Council 2011-2012
CLC December 6, 2011
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

17. 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.

18. CCSS Mathematical Practices
REASONING AND EXPLAINING
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
OVERARCHING HABITS OF MIND
1. Make sense of problems and persevere in solving them
6. Attend to precision
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

19. Lenses to Consider During Professional Development Sessions
Learner Lens Teacher Lens 19

20. How many dots do you see? How did you see them?
Dot Talk
How many dots do you see? How did you see them?
Intent: Participants will experience a Dot Talk.
Talking Points:
Explain to participants that we will now model a dot talk.
Please note that this is an animated slide.

21. Dot Talk
I saw ______dots. I grouped the dots…. I also saw ___ dots, but I grouped the dots differently. I …
Intent: Participants will experience a Dot Talk.
Talking Points:
Explain to participants that we will now model a dot talk.
Please note that this is an animated slide.

22. How many dots do you see? How did you see them?
Dot Talk
How many dots do you see? How did you see them?
Intent: Participants will experience a Dot Talk.
Talking Points:
Explain to participants that we will now model a dot talk.
Please note that this is an animated slide.

23. Dot Talk
Cindy will model Dot Talk

24. Rekenrek
DVD K.2
Fosnet

25. Five Frames

26. Ten Frames

27. How many dots do you see? How did you see them?
Ten Frames
How many dots do you see? How did you see them?

28. How many dots do you see? How did you see them?
Ten Frames
How many dots do you see? How did you see them?

29. Mental Math

30. Mental Math
32 x 15

31. Number String (Mental Math)

32. Number String (Mental Math)
3 x 50 3 x x 149

33. Number String (Mental Math)
35 x 8 70 x x 2

34. True/False
7 = 4 + 3
True or False?
Why?
Cecilio

35. True/False
17-16= 9-8
True or False?
Why?
Cecilio

36. True/False
8 x 7= 8 x (5+2)
True or False?
Why?
Cecilio

37. True/False
15 x 24 = 30 x 12
True or False?
Why?
Cecilio

38. True/False
Cecilio

39. Dilemma Kirsten says that 9 is the missing number in David says that
5 =
Kirsten says that
9 is the missing number in
5 =
*Introduce Dilemmas as a type of number talk
*What could come before and after this number talk. Give rationale.
Explain the mathematical reasoning that both Kirsten & David used to simplify the expression above. 39

40. 10-5+4 Dilemma Kirsten says that 9 is the missing number in
David says that
1 is the missing number in
5 =
Kirsten says that
9 is the missing number in
5 =
10-5+4
*Introduce Dilemmas as a type of number talk
*What could come before and after this number talk. Give rationale.
Explain the mathematical reasoning that both Kirsten & David used to simplify the expression above. 40

41. Dilemma Kirsten says that David says that 10-5+4 10-5+4 is equal to 1
*Introduce Dilemmas as a type of number talk
*What could come before and after this number talk. Give rationale.
Explain the mathematical reasoning that both David & Kirsten used to simplify the expression above. 41

42. Order of Operations Grouping Symbols ( ), { }, [ ], I I Exponents
Multiplication/Division Division/Multiplication
Addition/Subtraction Subtraction/Addition

43. How many cubes? How do you see them? What is the surface area?
Spatial Reasoning
How many cubes? How do you see them? What is the surface area?

44. Spatial Reasoning Math Talk
How many cubes? How do you see them? What is the surface area?

45. What’s My Rule? In
Out 1 5 3 2 7 4
Cecilio

46. What’s My Rule?
Input
Output 1 5 3 2 25 15 10
Cecilio

47. What’s My Rule? X Y 1 5 3 2 4
Cecilio

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

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

50. 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?

51. 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?
Cecilio
Intent: Participants will review possible questions teachers may ask of their students during a number talk.
Talking Points:
These questions are just a few questions a teacher would ask.
The teacher could also have sentence stems that students use to share out their solutions and strategies. (Especially helpful for EL students.)

52. 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?
Cecilio
Intent: Participants will review possible questions teachers may ask of their students during a number talk.
Talking Points:
These questions are just a few questions a teacher would ask.
The teacher could also have sentence stems that students use to share out their solutions and strategies. (Especially helpful for EL students.)

53. 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.
This session will examine some of the protocols and procedures you’ll need to foster meaningful mathematics discourse in elementary school classrooms, including Number Talks.

54. Closing Thank you! Cecilio_Dimas@sccoe.org
for K-2 Resources
for 3-5 Resources