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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, [email protected]
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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