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June 27, 201410:00 - 11:15 a.m.
Kirsten Sarginger, Mathematics CoordinatorSylvia 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 StandardsAs 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 quantitatively3. Construct viable arguments and critique the
reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. 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
SCIENCEHistorySocial
Studies
LANGUAGEARTS
*• instructional discourse • expressing and understanding reasoning
Olsen, 2013
Language*
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Mathematics Discourse
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Mathematics Discourse
ELD StandardsPart 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 othersB. Interpretive: comprehension and analysis of written and spoken textsC. Productive: creation of oral presentations and written texts
-CA ELD Standards Overview Pages 16,19
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Mathematics Discourse
Academic LanguageTo 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 (efficiency, 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 UnitsNumber 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 ThinkingResearch 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 TalkHow 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 FramesHow many dots do you see?
How did you see them?
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Mathematics Discourse
Ten FramesHow 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+68+7
14+1325+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 503 x 1003 x 149
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Mathematics Discourse
Number String (Mental Math)
35 x 870 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 ReasoningHow 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? In Out
1532
3754
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Mathematics Discourse
What’s My Rule? Input Output
1532
5251510
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Mathematics Discourse
What’s My Rule? X Y
1532
0421
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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 quantitatively3. Construct viable arguments and critique the
reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. 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 LanguageTo 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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Mathematics Discourse
Resources
http://goo.gl/ylgKi for K-2 Number Talk Resources
http://goo.gl/F58uB for 3-5 Number Talk Resources
California English Language Development Standards http://www.cde.ca.gov/sp/el/er/eldstandards.asp
Mathematics Frameworkhttp://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 [email protected]
Sylvia Solís, Multilingual Education Services Project Specialist [email protected]