Understanding LanguageDay 2

SUPPORTING ENGLISH LANGUAGE LEARNERS IN MATHEMATICS

Grace Dávila CoatesWriting and Review Team

Understanding Language Initiative Stanford University

gcoates@berke ley.edu510-453-0844

Book List

• EQUALS, University of California, Berkeley• Cooperative Problems: Get it Together• Family Math (Number Line Rectangles)• FM for Young Children• Family Math II• The Journey Through Middle School Math• English Language Learners in the Mathematics

Classroom, Coggins, Coates, et al.

Goals for Today

Apply the Understanding Language guidelines in a variety of structures:

• Examine visual learning models

• Experience a conceptual development lesson

• Apply the ELA standards in mathematics environments

• Revisit Jigsaw with a different purpose

• Discuss the Standards for Mathematics Practice

• Meet with our team in a planning / discussion session

• Work on logic and reasoning problems for grades 4-6

Jobs and Roles

• Recall your job from yesterday

• Pass it (the job) to the person on your left

• Partner up for Recorder, Reporter, Materials, Clean-Up

Bigtown and Smalltown

From 1990 to 2000, Smalltown’s population grew from 10,000 to 20,000. During the same period, Bigtown’s population grew from 100,000 to 130,000.

Alice thinks that Smalltown grew more, while Ben thinks that Bigtown grew more.

Write a paragraph a note on how you would mediate their dispute.

Bigtown and Smalltown

• At your table:

• Discuss

1. What did you think of first as you worked on the task?

2. How did you organize your strategies / work?

3. Be prepared to share at least one thing you shared with the group.

Revisiting Roger’s Rabbits

• Roger’s Rabbits asks students to identify finite sequences of numbers, follow given rules, and to extend them according to those rules.

– Use the four operations to solve problems– Represent these problems using equations with a letter

standing for the unknown quantity– Generate and analyze patterns

Roger’s Rabbit:

The Standards do not require the student to infer or guess the underlying rule… but to generate a pattern from a given rule and identify features of the pattern.

What rules did we generate?How did this affect the patterns?How did we extend the thinking about the rules?

Roger’s Rabbits is more than a day’s work in the classroom.

Roger’s Rabbits

What 4th graders did

• H x 2 = TDoors for any house

• H1 + 1 = Blocks

• D x H = ___ your answer like 2 doors plus 2 doors is Hutch number 2. Then you add 2 more for #3

• Double the doors for each hutch

• Add 1 after the first hutch or…

• I counted by 2’s you get the doors for each one you add, like 1st is added to

Roger’s Rabbits

For any given number of hutches H,• doors: D = H x 2 10,000 X 2 = 20,000 Doors• blocks: B = H + 1 10,000 + 1 = 10,001 blocks

“… I like big numbers so this is like for a company that sells rabbits. Not Roger’s

Cooperative Logic Problems

Today:

• Remember to help others in your group• Illustrate, give clues, partner up

Facilitators: make sure everyone participates

Guidelines for Mathematics Instructional Materials

#1 Focus on Standards for Mathematical Practice

Structure: JigsawResearch: Visual LearningToolkit: Reduction

Materials: Description of the 8 SMPs

Each table will have a copy of 1 of the SMPs

Standards for Mathematical Practice

1. With your tablemates, read the SMP assigned to you.

2. Discuss ways that you could reduce the language and create a poster with a message that visually demonstrates the Standard.

3. Be prepared to share your poster with the class.

You will need a timekeeper to help the

group finish on time

Presentation of Posters

• Supporting the reporter:

– Everyone takes a part in reporting– A partner can co-report– Recorder can write up awesome notes to crib

from– Give props and way-to-go’s

Break

See you in 15 Minutes

Visual Learning for Conceptual UnderstandingNumber Line Rectangles

• Your team will create rectangles that represent their assigned numbers.

• Example: Grace’s numbers are 0, 1, 2, 3, and 4.

Visual Learning for Conceptual UnderstandingNumber Line Rectangles

0 1 2 3 4 5 6

Number Line Rectangles:

• SMPs?

• Mathematics Standard?

Number Line Rectangles

• What about this delivery works for ELLs?

– Experiential

TEAM Planning

• Meet with your team

• Creating A Common Vision

• Next Steps

Sharing Work

• Share ideas from your discussions withthe larger group.

You have the option to pass

Principles

1. Focus on students’ mathematical reasoning, not on accuracy in language use.

2. Focus on mathematical practices, not language as single words or definitions.

3. Recognize the complexity of language in mathematics, and support students in engaging in this complexity.

4. Treat everyday and home languages as resources, not obstacles.

Rosie’s Bears

1. Read Rosie’s Bears and the lesson guide for the task.

2. Analyze the lesson and the lesson design.

3. Decide what can be changed to make it more aligned to the guidelines and principles of a UL lesson.

4. Demonstrate how you would create access for ELL’s academic language development.

Rosie’s Bears

Create a poster that shows your adaptations, changes, or other structures your team creates

Works still under construction will be accepted.

Review the Day

• Examined visual models to develop conceptual understanding

• Applied structures that create access

• Applied the ELA standards in mathematics environments

• Revisited Jigsaw

• Examined and applied the Standards for Mathematics Practice

• Met with our team in a planning / discussion session

• Worked on logic and reasoning problems for grades 4-6

Reflection

• Write a reflection on the last two days in this session.

• If you have further questions and provide a contact number or email address, I will respond to you.