13 th Annual Academic Success Institute Presented by Kirsten Sarginger Mathematics Coordinator 1...

13th Annual Academic Success Institute

Presented byKirsten Sarginger

Mathematics Coordinator1

Academic Discourse in the Mathematics ClassroomMarch 14, 2015

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


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

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)


Socio-mathematical Norms• Errors are gifts, they promote discussion..• The answer is important, but it is not the math.


Understanding Math Discourse

• Talk Formats– Whole-Class Discussion– Partner Talks

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• Solution

• Strategy

• Agree


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


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


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

15 x 24 = 30 x 12

True or False?Why?


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


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


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


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?


What would this look like in a designated ELD block?


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


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


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]

mailto:[email protected]

13 th Annual Academic Success Institute Presented by Kirsten Sarginger Mathematics Coordinator 1...

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