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June 27, 2014 10:00 - 11:15 a.m. Kirsten Sarginger, Mathematics Coordinator Sylvia Solís, Multilingual Education Services Project Specialist Academic Discourse in the Mathematics Classroom

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Mathematics Discourse Outcomes Participants will deepen their understanding of mathematical discourse and how it supports student learning Participants will experience Number Talks and learn how they support all students, including EL students, given the increased language demands of the CCSS-M Participants will see the connection between the CCSS-M and the ELD Standards using an integrated approach with reference to the dedicated ELD block

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Mathematics Discourse Agenda CCSS-M and ELD Standards Integration Academic Discourse: Number Talks Implications for implementation of mathematics discourse

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Mathematics Discourse Common Core State Standards As the CA CCSS-M are implemented, students will face increased language demands during mathematics instruction. Students will be asked to engage in discussions on mathematics topics, to explain their reasoning, to demonstrate their understanding, and to listen to and critique the reasoning of others. The increased language demands may pose challenges for all students and even greater challenges for English learners. -CA Mathematics Framework Universal Access Chapter Page 9

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Mathematics Discourse Students are expected to… Communicate their understanding of mathematical concepts Provide and receive feedback Progress to a deeper understanding -Mathematics Framework, Instructional Strategies Chapter Page 14

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Mathematics Discourse Common Core State Standards: Mathematical Practices 1.Make sense of problems and persevere in solving them 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

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Mathematics Discourse Common Core State Standards Content Standards: 2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. A.REI.1 Explain each step in solving a simple equation.

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Mathematics Discourse New CCSS Paradigm : language is central to all academic areas MATH SCIENCE History Social Studies LANGUAGE ARTS * instructional discourse expressing and understanding reasoning Olsen, 2013

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Mathematics Discourse

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ELD Standards Part I: Interacting in Meaningful Ways Provides grade level CA ELD Standards that set expectations for ELs to participate in meaningful, relevant, and intellectually challenging ways in various contexts and disciplines in three modes: A. Collaborative: engagement in dialogue with others B. Interpretive: comprehension and analysis of written and spoken texts C. Productive: creation of oral presentations and written texts -CA ELD Standards Overview Pages 16,19

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Mathematics Discourse Academic Language To support students’ ability to express their understanding of mathematics, teachers need to explicitly teach not only the language of mathematics but also academic language for argumentation (proof, theory, evidence, in conclusion, therefore), sequencing (furthemore, additionally), and relationships (compare, contrast, inverse, opposite). - Math Framework Universal Access Page 10

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Number Talks

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Mathematics Discourse Number Talks A planned daily routine for whole ‐ class instruction Number Sense (e ﬃ ciency, accuracy & ﬂexibility) Generalized Arithmetic-conceptual understanding Reasoning and Problem Solving Mental Mathematics Preview-Review-Conceptual Understanding

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

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Mathematics Discourse Enhancing Instruction for CCSSM Upgrading Units Number Talks “FAL” Mini- Unit with Forma- tive Assess- ments

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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.

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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

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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

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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)

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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)

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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)

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Mathematics Discourse Lenses to Consider During Professional Development Sessions Learner Lens Teacher Lens

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Hand Signals Agree Solution Strategy Question Comment

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

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Mathematics Discourse Dot Talk How many dots do you see? How did you see them?

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Mathematics Discourse Dot Talk I saw ______dots. I grouped the dots…. I also saw ___ dots, but I grouped the dots differently. I …

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Mathematics Discourse Dot Talk

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Mathematics Discourse Five Frames How many dots do you see? How did you see them?

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Mathematics Discourse Ten Frames

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

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

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Mathematics Discourse Mental Math 70-34

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Mathematics Discourse Mental Math Sentence Frames I would like to defend _____________. First I____________________________. Then I ____________________________. Next I_____________________________. Last I____________________________. I agree/disagree with_______________ because_________________________.

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Mathematics Discourse Number Talk Classroom Example Third grade students solving the same problem.

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Mathematics Discourse Mental Math 32 x 15

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

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Mathematics Discourse Number String Sentence Frames I would like to defend _____________. First I____________________________. Then I ____________________________. Next I_____________________________. Last I____________________________. I agree/disagree with_______________ because_________________________.

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Mathematics Discourse Looking for Patterns (Sentence Frame) The pattern is __________________.

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

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

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Mathematics Discourse True/False

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Mathematics Discourse True/False Sentence Frames I would like to defend_________________. I believe it is ___true/false______ because________________.

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Mathematics Discourse True/False 7 = 4 + 3 True or False? Why?

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

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

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

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Mathematics Discourse Dilemma Julie says that 10-5+4 is equal to 1 David says that 10-5+4 is equal to 9 Who is correct and why?

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Mathematics Discourse Dilemma Sentence Frame I would like to defend __________because ____________________.

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Mathematics Discourse Spatial Reasoning How many cubes? How do you see them? What is the surface area?

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Mathematics Discourse Spatial Reasoning Sentence Frame I would like to defend ________________ because ____________________.

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Mathematics Discourse What’s My Rule? InOut 15321532 37543754

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Mathematics Discourse What’s My Rule? InputOutput 15321532 5 25 15 10

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Mathematics Discourse What’s My Rule? XY 15321532 04210421

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Mathematics Discourse What’s My Rule Sentence Frame I believe its ______________ because_________________________. I agree with ___________ because_____________.

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Mathematics Discourse Questions Teachers Might Ask Share your thinking with your partner. How did you solve it differently? Who else used this strategy to solve the problem? How did you figure it out?

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Mathematics Discourse Questions Teachers Might Ask Share the steps you took to solve the problem. What information was helpful? Explain why you took those steps? Tell me more. What strategies are being used?

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Mathematics Discourse Common Core State Standards: Mathematical Practices 1.Make sense of problems and persevere in solving them 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

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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?

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Mathematics Discourse Evidence Based Practices recommended for engaging upper elementary and older students in high quality discussions Carefully prepare for the discussions Ask follow up questions Provide a task or a discussion format Develop and practice the use of specific “discussion protocols” -ELA/ELD Framework Chapter 5, Page 26

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Mathematics Discourse Academic Language To support students’ ability to express their understanding of mathematics, teachers need to explicitly teach not only the language of mathematics but also academic language for argumentation (proof, theory, evidence, in conclusion, therefore), sequencing (furthemore, additionally), and relationships (compare, contrast, inverse, opposite). - Math Framework Universal Access Page 10

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Mathematics Discourse How To Support ELs ∙Provide protocols for effective discussions ∙Ensure equity in participation ∙Provide a positive learning environment that encourages all voices to be heard ∙Promote the acceptance of diverse view points - ELA/ELD Framework Chapter 5, Page 26

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Mathematics Discourse What would this look like in a designated ELD block?

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Mathematics Discourse Learning About How English Works Mathematics text is informational text that requires different skills than narrative texts. Students may... – Need specific instruction on how to read and comprehend mathematics texts (text, diagrams, tables, symbols) which may not necessarily be read from left to right – Instruction in writing informational/explanatory text which requires facility with the symbols of mathematics and graphic representations in addition to understanding of mathematical content and concepts - Math Framework Universal Access Page 10

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Mathematics Discourse Factors To Consider for Success Limited prior and/or background knowledge Cultural differences Linguistics Polysemous words – have same spellings and pronunciation but meanings are different based on context (ex. table) - Math Framework Universal Access Pages 13-17

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Mathematics Discourse Factors To Consider for Success Semantic features

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Mathematics Discourse Factors To Consider for Success Syntactic features of word problems – The arrangement of words in a sentence (phrases, clauses, sentences) Text analysis – Word problems are challenging because they require reading and comprehension of the text, identifying the question, creating a numerical expression, and solving that equation

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Mathematics Discourse

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Resources http://goo.gl/ylgKihttp://goo.gl/ylgKi for K-2 Number Talk Resources http://goo.gl/F58uBhttp://goo.gl/F58uB for 3-5 Number Talk Resources California English Language Development Standards http://www.cde.ca.gov/sp/el/er/eldstandards.asp http://www.cde.ca.gov/sp/el/er/eldstandards.asp Mathematics Framework http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp

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Mathematics Discourse Outcomes Participants will deepen their understanding of mathematics discourse and how it supports student learning Participants will experience Number Talks and learn how they support all students, including EL students, given the increased language demands of the CCSS-M Participants will see the connection between CCSS-M and ELD Standards using an integrated approach with reference to the dedicated ELD block

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Mathematics Discourse Closing Kirsten Sarginger, Mathematics Coordinator kirsten_sarginger@sccoe.org kirsten_sarginger@sccoe.org Sylvia Solís, Multilingual Education Services Project Specialist sylvia_solis@sccoe.org

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