CreatinganEnvironmentforELLsto) SucceedinCCSSContentand ...assets.pearsonschool.com/asset_mgr/current/20136/pdf_102907.pdf · CreatinganEnvironmentforELLsto) SucceedinCCSSContentand)

ì

Creating an Environment for ELLs to Succeed in CCSS Content and

Mathematical Practices to Succeed in CCSS Content and

Mathematical Practices Jennifer M. Bay-Williams College and Career Readiness Symposium

Honolulu, Hawaii February 1, 2013

Warm - Up

With a someone at your table:

• Your Name

• A double-meaning word

[means something different in math than in other settings, for example, similar]

AGENDA

ì  Overview

ì  Culturally Responsive ì  Content (Importance and Relevancy) ì  Students (Identity and Power)

ì  Language Considerations

AGENDA



Reflec>ve Planning Guide for Teachers

1. The content of the lesson is about the importance of mathema5cs, and the tasks performed by students communicate high expecta5ons.

•  Does the content include a balance of procedures and concepts? •  Are students expected to engage in problem solving and

generate their own approaches to problems? •  Are connec5ons made between mathema5cs topics?

2. The content is relevant.

•  In what ways is the content related to familiar aspects of students’ lives?

•  In what ways is prior knowledge elicited/reviewed so that all students can par5cipate in the lesson?

•  To what extent are students asked to make connec5ons between school mathema5cs and mathema5cs in their own lives?

•  How are student interests (events, issues, literature, or pop culture) used to build interest and mathema5cal meaning?

Culturally Responsive Mathematics Instruction

Van de Walle, J., Karp, K. & Bay-Williams, J. (2013). Elementary and Middle School Mathematics: Teaching Developmentally [PROFESSIONAL DEVELOPMENT EDITION]. New York, NY: Pearson.

Reflec>ve Planning Guide for Teachers (Con’t)

3. The instruc5onal strategies communicate the value of students’ iden55es.

•  In what ways are students invited to include their own experiences within a lesson?

•  Are story problems generated from students and teachers? •  Do stories reflect the real experiences of students? •  Are individual student approaches presented and showcased so that each

student sees their ideas as important to the teacher and their peers? •  Are alterna5ve algorithms shared as a point of excitement and pride (as

appropriate)? •  Are mul5ple modes to demonstrate knowledge (e.g., visuals, explana5on,

models) valued?

4. The instruc5onal strategies model shared power.

•  Are students (rather than just the teacher) jus5fying the correctness of solu5ons?

•  Are students invited to (expected to) engage in whole-‐class discussions where students share ideas and respond to each other’s ideas?

•  In what ways are roles assigned so that every student feels that they contribute to and learn from other members of the class?

•  Are students given a choice in how they solve a problem? In how they demonstrate knowledge of the concept?


AGENDA

ì  Overview

ì  Culturally Responsive

ì  Students (Identity and Power)


Making Relationships Explicit


Which shapes are partitioned to show fourths?

What will come out of the magic pot?

Hairpin Purse Coins Coats Coins2

Coins 3

Coins 4

In

Out

In the pot

Out of the pot












AGENDA

ì  Overview

ì  Culturally Responsive ì  Content (Importance and Relevancy)

(Identity and Power)


Algorithms Compare the following two division problems from a 4th grade classroom (Midobuche, 2001):

Order of Operations?!

In Kenya:

B: Brackets

O: Of

D: Division (before any multiplication)

M: Multiplication

A: Addition

S: Subtraction







models) valued?







What w

ill come out of the pot?

Groups that Support ELLs (and all learners)

TASK

TASK

Shared Responsibility

Individual Accountability

AGENDA

ì  Overview


•  Many everyday words have multiple meanings when used in mathematics

•  Some vocabulary is only encountered in math class

•  Many words may be used to signal the same concept/topic

•  Meaning is often related to the context

•  Logical connectors can pose problems

Attend to Precision: Mathematics Language

What does it mean to

accommodate? What does it mean to modify instruction?

ADAPTATIONS (INTERVENTIONS)

Accommodations

ì  Change the environment or circumstances to meet the needs of particular students

ì  Adapt typical instructional strategies to meet individual student’s needs

ì  Maintains the task (and high expectations)

Accommodations

The teacher might: •  Write instructions instead of just saying them •  Include opportunities to practice new

vocabulary •  Provide visuals •  Be strategic in setting up groups •  Read task; •  translate task •  Many others…

Modifications

ì  Modifications are changes made to the problem or task itself

ì  Modifications do change what the students are expected to do but do not lower the expectations

Modification #1

Van de Walle, Karp, & Bay-Williams, 2013

Rather than have three different contexts, ELLs use the same context. Still include three different fraction models Use Cars: line of cars (linear) collection (set) parking lot (area)

Reduce Linguistic Load

Modification #2: Original Task

Task: Eduardo had 9 toy cars. Erica came over to play and brought 8 cars. Can you figure out how many cars Eduardo and Erica have together? Explain how you know.

Implementa>on: The teacher distributed cubes to students to model the problem and paper and pencil to illustrate and record how they solved the problem. He asked students to model the problem and be prepared to explain their solu5on.

Van de Walle, Karp, & Bay-Williams, 2013

Modification #2: Modified Task Task: Eduardo had some toy cars. Erica came over to play and brought her cars. Can you figure out how many cars Eduardo and Erica have together? Explain how you know.

Implementa>on: The teacher asked students: What is happening in this problem? What task are you going to do? Then he distributed Task Cards that explained how many cars Eduardo and Erica had.

He varied the difficulty of the numbers: he gave numbers less than ten to students who are struggling, and he gave numbers greater than ten to students who are more advanced.

How does such a modifica>on to the task support ELLS?

Comprehensible Input

Modification #3: Original Task

Original Text: Raphael wants to make posters for his sale by enlarging his 8 1.2” by 11” ad. Raphael thinks big posters will get more attention, so he wants to enlarge his ad as much as possible. The copy machines at the copy shop have cartridges for three paper sizes: 8 1/2” by 11”, 11” by 14”, 11” by 17”. The machines allow users to enlarge or reduce documents by specifying a percent between 50% and 200%. For example, to enlarge a document by a scale factor of 1.5, a user would enter 150%. This tells the machine to enlarge the document to 150% of its current size. A. Can Raphael make a poster that is similar to his original ad on any of the three paper sizes - without having to trim off part of the paper? Why or why not?

(Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004, p. 44)

Modification #3: Modified Task

Modified Text:

Raphael is having a sale. He made an ad on paper that is 8 1/2” by 11”, but he wants to make it as big as possible.

There are three sizes of paper: 8 1/2” by 11”, 11” by 14”, or 11” by 17”. He can make the copy machine change the size of the paper by choosing a percent between 50% and 200%. For example, to make the ad bigger by a scale factor of 1.5, Raphael would choose 150%. This will make the ad 150% bigger than it is now.

Guarded Vocabulary

When Should We Focus on Vocabulary?

A.  Before engaging in an activity?

B.  During the activity?

C.  After the activity is complete?

Before?

J Can equip students with tools that will increase participation

L Takes away time that students have to explore the problem, and may, inadvertently, lower the cognitive demand of the problem


Preview Vocabulary

Preteach Content

During?

During?

J Can make it more meaningful

L Could bog down the activity, using more time



After?

After?

J Good to review, apply in other contexts

L If vocabulary was needed in the lesson, might have lost kids along the way; lost opportunity to practice new words.

(Adapted from Bay-Williams, & Livers, 2009, pp. 238–246)


Developing Meaning of Words

Definition

versus

Description

Definitions are more precise than in other domains, and unique in that:

–  They are based on the least amount of information needed

–  There is “nesting” within definitions (relationships are implied, but not stated)

Definitions in Mathematics

Rectangle Square Polygon

Quadrilateral

Description/Concept

Symbols/Procedure Example

Visual Representation

Mean

What does MEAN mean?

The mean is the average of the numbers: adding up all the numbers and dividing by how many numbers there are.

8 + 12 + 3 + 5 + 7 + 1 6

What is the average length of the names at your table?


















models) valued?







In Reflection

Creating an Environment for ELLS to Succeed in CCSS Content and Mathematical Practices

Documents

CreatinganEnvironmentforELLsto) SucceedinCCSSContentand ...assets.pearsonschool.com/asset_mgr/current/20136/pdf_102907.pdf · CreatinganEnvironmentforELLsto) SucceedinCCSSContentand)