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Luis Harold Asturias Méndez

ACCESS FOR ALL: Linking Learning

and Language Tuesday, February 3, 2015

English Learner Leadership Conference 2015

How are mathematics and language connected?

What are the implications for our work?

Born in Guatemala. Raised in El Salvador.

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Guatemala

El Salvador

Now live in USA: California.

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California

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Golden Gate Bridge

WHY? Discuss the five dimensions of a Mathematically Powerful Classroom

WHAT? Content and Practices

HOW? Propose a theory of action Discuss academic language

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TRU MATH: http://map.mathshell.org/materials/trumath.php

SERP MATH: http://serpinstitute.org/index.php/areas/public-products/

UNDERSTANDING LANGUAGE: http://ell.stanford.edu

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Sy hll t yr lbw prtnr—sh r h s yr thnkng prtnr fr tdy.

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Say hello to your elbow partner—she or he is your thinking partner for today.

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What happened?

Did you get to a higher number?

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FRAMING

WHY?

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Competencies

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Culture Conditions

Necessary for a

mathematical powerful

classroom

…race, class, culture, and language all play key roles in teaching and

learning mathematics…

NCSM 2009Improving Student Achievement in Mathematics

by Addressing the Needs of English Language Learners

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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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Let’s use some academic

language…

Let’s do some math…

Travieso

SOLO

PARTNER

TABLE

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?

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Mathematical Character

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Productive Struggle

Mathematical Reasoning

Academic Language

by connecting math & language through productive struggle

Providing ALL Students Access and Opportunity to

Wrestle With, Make Sense of, and

Communicate About Important Mathematics

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THEORY OF ACTION

• Understand why it is important to have students explain their thinking to each other,

• Support teachers’ learning about how to hold students accountable for explaining their thinking to each other, and

• Conduct frequent classroom observations looking for students’ explanations of each other’s thinking.

• Hold students accountable for producing explanations that their classmates can understand,

• Help students revise their explanations to make them easier to understand by their peers, and

• Reflect, with peers, on pedagogical decisions that help students improve their explanations

• Develop the habit of reasoning about mathematics,

• Communicate their own thinking and understand each others’ way of thinking, and

• Hold each other accountable for making sense of the mathematics they are learning.

Shifts in students’ practices

Shifts in teachers’ practices

Shifts in leaders’ practices

• Develop the habit of reasoning about mathematics,

• Communicate their own thinking and understand each others’ way of thinking, and

• Hold each other accountable for making sense of the mathematics they are teaching.

professional learning group inside the classroom

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A FRAMEWORK

Where students develop a robust understanding of important mathematics.

MathCognitive

Demand

Acce

ss

Agency, Authority, & Identity

Uses of

Assessment

mathematically powerful classroom

Where students develop a robust understanding of important mathematics.

MathCognitive

Demand

Acce

ss

Agency, Authority, & Identity

Uses of

Assessment

Chunky Problem

What are the challenges and

opportunities for language

development? (in support

of each of the five

dimensions?)

These are the five general dimensions of a mathematically powerful classroom

What is the academic language students need to communicate their reasoning on this chunky problem?

How does the development of academic language preserve the cognitive demand of the task?

What differentiated scaffolds give all [EL] students access to the mathematics of the task?

How does developing academic language support students development of their mathematical identity?

How do we use students’ language use as formative assessment to decide what they need next?

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MATH

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Focus Coherence

Rigor

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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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LANGUAGE

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

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

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

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

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

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

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

HOW?

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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?

I spent last evening

evening out a pile of dirt.

EVEN

Social Register

Got even

To be even

Even out

Break even

not even

Even Steven

Mathematics Register

multiple modes multiple representations different types of written texts different types of talk different audiences

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sounds words phrases sentences

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grammar syntax function self-correction

non-temporal—math just is non-emotional precise definition-theorem-proof format

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Academic English…

must describe exactly the thing being defined—nothing more, and nothing less.

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Definitions

GOOD: A rectangle is a quadrilateral all four of whose angles are right angles.

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POOR: A rectangle is a parallelogram in which the diagonals have the same length and all the angles are right angles. It can be inscribed in a circle and its area is given by the product of two adjacent sides.

POOR: A rectangle is a parallelogram whose diagonals have equal lengths.

BAD: A rectangle is a quadrilateral with right angles.

UNACCEPTABLE: rectangle: has right angles.

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

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“It depends on what the meaning of the words 'is' is.”

—Bill Clinton

5 = √25 5 < 10 P (5)

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One should NOT aim at being possible to understand, but at being

IMPOSSIBLE to misunderstand. Quintilian

circa 100 AD

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