Academic Language & English Language

Development

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Sy hllo t yr lbw prtnr—sh or h s yr thnkng prtnr fr tdy.

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Say hello to your elbow partner—s/he is your thinking partner for today.

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TODAY: Discuss three big ideas Propose a re-definition of language Expose you to the three reads and problem stem strategies

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“The basis of all human culture is language, and mathematics is a

special kind of linguistic activity.” !

Yu, Manin Mathematics as profession and vocation,

in Mathematics: Frontiers and Perspectives, (V. Arnold et al, ed), AMS, 200, p. 154.

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Three big ideas

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My belief…

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Provide ALL Students Access and Opportunity to

Wrestle With, Make Sense of, and

Communicate About Important Mathematics

©2010 UC Regents©2010 UC Regents©2012 UC Regents

National Research Council. (2001) Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.)

©2010 UC Regents©2010 UC Regents©2012 UC RegentsNational Research Council. (2001) Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.)

Procedural Fluency: Recall,

automatically, and

accurately

Conceptual Understanding: Explain,

represent in multiple ways, and

apply to solve problems

Strategic Competence: Formulate,

Implement, and

Conclude/Generalize

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Relationships and Convergencesfound in the Common Core State Standards in Mathematics (practices), Common Core State Standards in ELA/Literacy (student portraits), and the Next Generation Science Standards (science & engineering practices)

EDUCATIONGRADUATE SCHOOL OF

M1. Make sense of problems & persevere in solving them

M2. Reason abstractly & quantitatively

M6. Attend to precision

M7. Look for & make use of structure

M8. Look for & express regularity in repeated reasoning

S1. Ask questions & define problems

S3. Plan & carry out investigations

S4. Analyze & interpret data

S6. Construct explanations & design solutions

E1.Demonstrate independence in reading complex texts, and writing and speaking about them

E7. Come to understand other perspectives & cultures through reading, listening, and collaborations

E6. Use technology

& digital media strategically & capably

M5. Use appropriate tools strategically

S8. Obtain,

evaluate & communicate

information

E3. Obtain, synthesize, and report findings clearly

and effectively in response to task and purpose

S2. Develop and use models

M4. Model with mathematics

S5. Use mathematics & computational thinking

E2. Build a strong base of knowledge through content rich texts

E5. Read, write, and speak grounded in evidence

M3 and E4. Construct viable arguments & critique reasoning

of others

S7. Engage in argument from evidence

Sources:

Common Core State Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects, p7.

Common Core State Standards for Mathematical Practice p6-8.

Next Generation Science Standards & A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas, Chapter 3: 41-82.

Credit: Tina Cheuk, tcheuk@stanford.edu

These student practices and portraits are grouped in a Venn diagram. The letter and number set preceding each phrase denotes the discipline and number designated by the content standards in ELA/Literacy, Mathematics, and Science.

Language: Social vs Academic

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What is Language?

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What is Academic Language?

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You write to ask me for my opinion of X, who has applied for a position in your department. I cannot recommend him too highly nor say enough good things about him. There is no other student of mine with whom I can adequately compare him. His thesis is the sort of work you don’t expect to see nowadays and in it he has clearly demonstrated his complete capabilities. The amount of material he knows will surprise you. You will indeed be fortunate if you can get him to work for you.

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!

How do we develop language?

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Sy hllo t yr lbw prtnr—sh or h s yr thnkng prtnr fr tdy.

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Let’s do some math…

Travieso

Socio-mathematical Norms

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Errors are gifts…they promote discussion and learning The answer is important, but not the only math! Ask questions…until it makes sense. Think with language…use language to think. Use multiple representations.

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SOLO

PARTNER

SMALL GROUP

WHOLE GROUP

How did it feel to have to solve a problem in language different from yours?

Did you feel you had access to the problem? …to the language? …to the mathematics?

What is Language?

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Language: Understanding language as a complex adaptive system of communicative actions to realize key purposes rather than primarily as form or even as function.

Language: Access and Production

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So… !

What do English learners need in mathematics?

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ell.stanford.edu

Judit Moschkovich

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Judit Moschkovich

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Language: Communication and

Thinking

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So… !

How do we give English learners access to mathematics and language?

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‣ ACCESS: Receptive Language Functions • Three Reads • Problem Stem ‣ PRODUCTION: Productive Language

Function • Think-Pair-Share or Turn & Talk • Sentence Frames or Starters

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Three Reads (& Problem Stem)

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First Read: What is the situation about?

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‣ What is this situation about?

‣ What are the quantities in this situations and how are they related?

‣ What questions could we ask of this situation?

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A dragonfly flies 50

meters in 2 seconds

‣ How far in a given time? ‣ How long it takes to go a

given distance? ‣ How fast is it going? ‣ Proportionality: Understanding

how these three questions are related mathematically.

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‣ a situation without a question is a problem stem!

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A dragonfly flies 50

meters in 2 seconds

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In a geometry context?

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Listen for: 1. What is the situation about?

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A high tech company has designed a new company logo using three squares.

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2. What is the important information? (quantities, units, and relationships)

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A high tech company has designed a new company logo using three squares.

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3. What questions could we ask about this situation?

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A high tech company has designed a new company logo using three squares. What is the relationship among the of three squares?

Why is English so hard?

I could not disagree with

you less.

Free gifts with every purchase.

I personally feel better

advanced planning never before past history tired cliches sworn affidavit final ultimatum

“the whole piece”

The soldier decided

to desert his dessert

in the desert.

If a vegetarian eats vegetables, what does a

humanitarian eat?

invariant, pre-image, isometry, vector,

!reflection symmetry

geometric constructions synthetic geometry Euclidean geometry reflection in a line

reflection against an axis coordinate rotations

coordinate reflections !

Dilaltion: center of dilation

moved away from the center by a factor of three

each point is three times as far the distance from the center is only

1/2 !

Translation: the vector of translation

Rotation: Rotation has a center

center of rotation rotate 72 degrees

!“it looks congruent and every point shifted along a line; the

orientation is the same” !

“It is a glide reflection as long as the vector is parallel to the

mirror” !

“isometries are the kinds of transformations where size and shape are not changed”

!“a line segment has length

and direction”

EVEN

Social Register

Got even

To be even

Even out

Break even

not even

Even Steven

Mathematics Register

"It depends on what the meaning of the words 'is' is." –Bill Clinton

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is101

5 is the square root of 25. 5 is less than 10. 5 is a prime number.

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5 = √ 25 5 < 10 P (5)

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even, odd, and function

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add, and, plus, sum, and combine

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How many are left?

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Avoid over-trusting technology

(like when we started using calculators)

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Eye halve a spelling chequer It came with my pea sea It plainly marques four my revue Miss steaks eye kin knot sea. Eye strike a key and type a word And weight four it two say Weather eye am wrong oar write It shows me strait a weigh.

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As soon as a mist ache is maid It nose bee fore two long And eye can put the error rite Its rarely ever wrong. Eye have run this poem threw it I am shore your pleased two no Its letter perfect in it's weigh My chequer tolled me sew.

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