june 27, 2014 10:00 - 11:15 a.m. kirsten sarginger, mathematics coordinator sylvia solís,...

June 27, 201410:00 - 11:15 a.m.

Kirsten Sarginger, Mathematics CoordinatorSylvia Solís, Multilingual Education Services Project Specialist

Academic Discourse in the Mathematics Classroom

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


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

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


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


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


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.


New CCSS Paradigm: language is central to all academic areas

MATH

SCIENCEHistorySocial

Studies

LANGUAGEARTS

*• instructional discourse • expressing and understanding reasoning

Olsen, 2013

Language*


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


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

Number Talks


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)


Enhancing Instruction for CCSSM

Upgrading UnitsNumber Talks

“FAL”Mini-Unit with

Forma-tive

Assess-ments


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.


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?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)


Lenses to Consider During Professional Development Sessions

Learner Lens Teacher Lens

Hand Signals• Agree• Solution

• Strategy

• Question

• Comment


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


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 Talk


Five Frames

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


Ten Frames


Ten FramesHow many dots do you see?

How did you see them?


Mental Math

70-34


Mental Math Sentence Frames•I would like to defend _____________.•First I____________________________.•Then I ____________________________.•Next I_____________________________.•Last I____________________________.

•I agree/disagree with_______________ because_________________________.


Number Talk Classroom Example

Third grade students solving the same problem.


Mental Math

32 x 15


Number String (Mental Math)

7+68+7

14+1325+26


Number String Sentence Frames•I would like to defend _____________.•First I____________________________.•Then I ____________________________.•Next I_____________________________.•Last I____________________________.

•I agree/disagree with_______________ because_________________________.


Looking for Patterns (Sentence Frame)

•The pattern is __________________.



3 x 503 x 1003 x 149



35 x 870 x 4

140 x 2


True/False


True/False Sentence Frames

I would like to defend_________________. I believe it is ___true/false______ because________________.


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?


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?


Dilemma Sentence Frame

I would like to defend __________because ____________________.


Spatial ReasoningHow many cubes? How do you see them?

What is the surface area?


Spatial Reasoning Sentence Frame

I would like to defend ________________ because ____________________.


What’s My Rule? In Out

1532

3754


What’s My Rule? Input Output

1532

5251510


What’s My Rule? X Y

1532

0421


What’s My Rule Sentence Frame

I believe its ______________ because_________________________.

I agree with ___________ because_____________.


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?


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?


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


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?


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


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).



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


What would this look like in a designated ELD block?


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



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


Factors To Consider for Success•Semantic features


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


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

http://goo.gl/ylgKi

http://goo.gl/ylgKi

http://goo.gl/F58uB

http://www.cde.ca.gov/sp/el/er/eldstandards.asp



http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp




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


Closing

Kirsten Sarginger, Mathematics Coordinator [email protected]

Sylvia Solís, Multilingual Education Services Project Specialist [email protected]

mailto:[email protected]

mailto:[email protected]

june 27, 2014 10:00 - 11:15 a.m. kirsten sarginger, mathematics coordinator sylvia solís,...

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