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.

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.

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

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

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

Hand Signals Solution Strategy Question Comment Agree Integers Curriculum Leadership Council 2011-2012 CLC December 6, 2011 Hand Signals Solution Strategy Question Comment Agree Integers Fractions *

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

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

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

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? Classroom Discussions: Using Math Talk to Help Students Learn -S. Chapin, C. O’Connor, N Anderson (2003)

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)

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

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? Cecilio

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

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 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

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

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.

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.

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.

Dot Talk Cindy will model Dot Talk

Rekenrek DVD K.2 Fosnet

Five Frames

Ten Frames

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

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

Mental Math 26 + 27

Mental Math 32 x 15

Number String (Mental Math) 7+6 8+7 14+13 25+26

Number String (Mental Math) 3 x 50 3 x 100 3 x 149

Number String (Mental Math) 35 x 8 70 x 4 140 x 2

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

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

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

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

True/False   Cecilio

Dilemma Kirsten says that 9 is the missing number in David says that 5 = - 4 Kirsten says that 9 is the missing number in 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. 39

10-5+4 Dilemma Kirsten says that 9 is the missing number in David says that 1 is the missing number in 5 = + 4 Kirsten says that 9 is the missing number in 5 = + 4 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

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

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

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?

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

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

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

What’s My Rule? X Y 1 5 3 2 4 Cecilio

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

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? 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.)

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.)

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.

Closing Thank you! Cecilio_Dimas@sccoe.org http://goo.gl/ylgKi for K-2 Resources http://goo.gl/F58uB for 3-5 Resources