math for ell students workshop 2 handouts

8/8/2019 Math for ELL Students Workshop 2 Handouts

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Teaching

High-Level Mathematics

to English Language

Learners

in the Middle Grades

Participant’s

Packet

Worksho 2

Copyright 2009 Center for Collaborative Education/Turning Points



Prepared for

Turning Points

by

Dr. Sara Freedman, Project Director

Dr. Dan Lynn Watt, Math Consultant




Teaching High‐Level Mathematics to English Language Learners in the

Middle Gradeswasdevelopedby Turning Points, a project atthe

CenterforCollaborativeEducationinBoston,MA.Thistoolispartof

the Mathematics Improvement Toolkit , a project of the National

Forum toAccelerateMiddleGradesReform, andwas supportedbythe U.S. Department of Education’s Comprehensive School Reform

Initiative,grant#S332B060005.Opinionsexpressedarethoseofthe

authorsandarenotnecessarilythoseoftheDepartment.




Turning Points Tool Teaching

High-Level

Mathematics

to English Language

Learners

n the Middle Grades

© Copyright 2009 Center for Collaborative Education/Turning Poin

Warm-up/Checking In Big Ideas of Workshop 2 – Mathematical

Tasks and Cognitive Demand Comparing the Cognitive Demands of

Two Tasks: Linguistic, mathematical andcultural

Doing Mathematicso Classroom Video #1o Doing Mathematics: Finding the Best

Boxo Reflecting on Doing Mathematics

Keeping Classroom Activities at a High

Level of Cognitive Demand Action Plans: Next Steps in Your Own

Classroom Closing Circle

Handout 2-1

Agenda for Workshop 2



Handout 2-2Overview of Workshop Series

In workshop 1, you learned:

• who are the English language learners in schools

today

• how to support English language learners in

learning the language of mathematics

• how to ensure the active engagement of English

language learners in developing the mathematicareasoning essential to mastering high-level

mathematics

In workshop 2, you will learn:

• how to distinguish high-level from low-level

mathematical tasks in the middle grades• how to create high-level math activities that

engage English Language Learners in the middle

grades.


High-Level

Mathematics

o English Language

Learners

n the Middle Grades




Handout 2-3Best Practices Modeled in

Workshop 1


High-Level

Mathematics

o English Language

Learners

n the Middle Grades

© Copyright 2009 Center for Collaborative Education/Turning Poi

• Using prior knowledge

• Providing time and support for English

language learners to discuss, process and explain

their mathematical reasoning

• Creating predictable routines and signals

• Checking for understanding throughout the

lesson from all students

• Using discussion protocols

• Using structured cooperative learning

• Think/write/pair/share

• Assigning numbers for round robin discussion

• Using visual cues

• Providing and practicing sentence frames

•

Speak/respond/follow-up question/respond• Organizing template/graphic organizer

• Using numbered heads as an assessment and

sharing strategy

• Final word

• One new learning at a time

• Providing concrete representations

• Creating models

• Role playing



Handout 2-4

1. Think about one best practice from the previous workshop that

you have used to change the way you teach English language

learners - a practice that you have added to your personaltoolkit.

(You may use the list of best practices reproduced in Handout 2-

3.)

2. Write it down, explaining how it has changed your teaching and how it hashelped the English language learners in your classroom to learn high-levelmathematics.

(You may use Handouts 1-24 and 1-25 introduced at the last

workshop to help you refresh your memory if you brought themwith you. )


High-Level

Mathematics

to English Language

Learners





Handout 2-6

Notes from the Share Out Turning Points Tool Teaching

High-Level

Mathematics

to English Language

Learners

n the Middle Grades


Why did you choose this particular strategy to try out?

What did you learn by sharing with a partner?

************************************************************

(Your own questions and further notes)



Turning Points Tool

to Teaching

High-Level

Mathematics

to English Language

Learnersn the Middle Grades


The Big Ideasof Workshop 2



Handout 2-7Turning Points Tool Teaching

High-Level

Mathematics

to English Language

Learners


© Copyright 2009 Center for Collaborative Education/Turning Po

The cognitive demand of a task is the sum total of what

a student needs to know, understand and be able todo in order to solve a problem or complete a task

successfully.

The level of cognitive demand depends not only on

the task, but also on the prior knowledge of the

students.

“… students who performed best … were in classrooms in

which tasks were … set up and implemented at high levels

of cognitive demand … For these students, having the

opportunity to work on challenging tasks in a supportive

classroom environment translated into substantial learning

gains on an instrument designed to measure student thinking,

reasoning, problem solving and communication.”*

Key Finding of the Quasar Project:

*A Quote from: Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development .Teachers College Press, 2000, by M. K. Stein, M. S. Smith, M.A. Henningson and E. A. Silver.



Handout 2-8

Final Word Protocol


Pair with another person. Decide who will speak first.

1. Each of you choose a brief excerpt from the quote: a

phrase or short passage to discuss. Take some time to

think about why it is important to you. Take some notes if

you wish.

2. Person#1 reads their phrase and explains what it means tothem and why it is significant. Person #1 has 1 minute to

speak. If they finish before the minute is up, person #2

waits until the minute is over before responding.

3. Person #2 retells what they heard person #1 say and adds

their own comment.

4. Person #1 has the last comment, the Final Word, taking

into account all that has been said.

5. Switch roles and repeat the protocol starting with

’

Adaptations for English language learners

Give students sentence starters or pattern language to use indiscussing their excerpt.

I think _____ is important because...

I heard you say that.... One connection I can make is...

(See appendix for additional sentence starters.)

BEST

PRACTICE:FINAL WORD

efficient way to

discuss a

reading

providescontrolled

choice makes sure all

voices are

heard ensures in-

depth

discussion ofissues

important to

group

provides entry

point intodiscussion forthose who

have not been

able to read or

absorb entire

document

Englishlan ua e

#1 #2 #1




Handout 2-9

Compare two tasks


High-Level

Mathematics

to English Language

Learners


2 cm

2 cm

1 cm

Task 1. Find the surface area and volume of arectangular prism that measures 2” x 4” x 24”.

Task 2. Out of This World Candies plans to sellStarburst candies in a new package containing 24individually wrapped Starbursts. Your challenge is to

find the dimensions of the least expensive box thatcan hold exactly 24 Starbursts. Each wrappedStarburst has a square shape that measures 2 cm on aside and 1 cm high.

Write a report including the dimensions for all thepossible boxes we can use to package 24 Starbursts,the dimensions of the least expensive box, andexplain how you know your answers are correct.



Best Practice:• Ensures both parties

are involvedthroughout theconversation. No one

can dominate.• RETELL rovides a

Handout 2-10 Linguistic Demands


High-Level

Mathematics

to English Language

Learners


Task 1. Find the surface areaand volume of a rectangularprism that measures 2” x 4” x24”.

Task 2. Out of This World Candies plans to sellStarburst candies in a new package containing 24individually wrapped Starbursts. Your challenge is find the dimensions of the least expensive box thacan hold exactly 24 Starbursts. Each wrapped

Starburst has a square shape that measures 2 cm side and 1 cm high.Write a report including the dimensions for all thepossible boxes we can use to package 24 Starbursthe dimensions of the least expensive box, andexplain how you know your answers are correct.

Linguistic demands

Task 1 Task 2


.



Handout 2-11 MathematicalTurning Points Tool to Teaching

High-Level

Mathematics

to English Language

Learners


Task 1. Find the surface areaand volume of a rectangularprism that measures 2” x 4” x

24”.

Task 2. Out of This World Candies plans to sellStarburst candies in a new package containing 24individually wrapped Starbursts. Your challenge is tfind the dimensions of the least expensive box that

can hold exactly 24 Starbursts. Each wrappedStarburst has a square shape that measures 2 cm oside and 1 cm high.Write a report including the dimensions for all the

possible boxes we can use to package 24 Starburststhe dimensions of the least expensive box, and expl

how you know your answers are correct.

Mathematical demands

Task 1 Task 2




Handout 2-12 Cultural Demands Turning Points Tool

Teaching

High-Level

Mathematics

to English Language

Learners



Task 2. Out of This World Candies plans to sellStarburst candies in a new package containing 24individually wrapped Starbursts. Your challenge isfind the dimensions of the least expensive box thacan hold exactly 24 Starbursts. Each wrapped

Starburst has a square shape that measures 2 cm side and 1 cm high.Write a report including the dimensions for all the possible boxes we can use to package 24 Starburst

the dimensions of the least expensive box, and exphow you know your answers are correct.

Cultural demands

Task 1 Task 2



Handout 2-13

JIG SAW ACTIVITY PROTOCOL – TASK 1

Handout 2-13


1. Divide into three expert groups; one each forlinguistic, mathematical and cultural demands. *

2. Each person will share his/her answers, one at atime, with the “expert” group.

Come to consensus on the best responses

• consider all responses respectfully,

• ask each other questions, and

• decide which ones are the best.


High-Level

Mathematics

o English Language

Learners

n the Middle Grades

All members of this group must make sure thateveryone in the group is an expert on the particulardemand being considered by the end of this part ofthe activity.

3. Responses of my expert group on ____________ demands forTask 1. (Copy the information on your groupʼs chart.)

Task 1. Find thesurface area andvolume of arectangular prismthat measures 2” x4” x 24”.




High-Level

Mathematics

to English Language

Learners



* Make sure that English language learners have sentenceframes that they can use to answer the questions and havepracticed the key vocabulary words they will need to use in theirgroups.

Handout 2-14


1. Divide into three expert groups; one each forlinguistic, mathematical and cultural demands. *

2. Each person will share his/her answers, one at atime, with the “expert” group.

Come to consensus on the best responses

• consider all responses respectfully,

• ask each other questions, and

• decide which ones are the best.

urning Points Tool Teaching

High-Level

Mathematics

o English Language

earners

n the Middle Grades

All members of this group must make sure thateveryone in the group is an expert on the particulardemand being considered by the end of this part ofthe activity.

3. Responses of my expert group on ____________ demands fortask 2. (Copy the information on your groupʼs chart.)

Task 2. Out of This

World Candies plans to sellStarburst candies ina new packagecontaining 24individually wrappedStarbursts. Yourchallenge is to findthe dimensions of

the least expensivebox that can holdexactly 24Starbursts. Eachwrapped Starbursthas a square shapethat measures 2 cmon a side and 1 cmhigh.

Write a report

including thedimensions for allthe possible boxeswe can use topackage 24Starbursts, thedimensions of theleast expensive box,and explain how youknow your answersare correct.



Handout 2-15


High-Level

Mathematics

to English Language

Learners



Task 2. Out of This World Candies plans to sellStarburst candies in a new package containing 24individually wrapped Starbursts. Your challenge is find the dimensions of the least expensive box tha

can hold exactly 24 Starbursts. Each wrappedStarburst has a square shape, that measures 2 cm a side and 1 cm high.Write a report including the dimensions for all the possible boxes we can use to package 24 Starburst

the dimensions of the least expensive box, and exphow you know your answers are correct.


Consider the key finding of the Quasar Project:

“… students who performed best … were in classrooms in which task

were … set up and implemented at high levels of cognitive

demand … For these students, having the opportunity to work on

challenging tasks in a supportive classroom environment translated into

substantial learning gains on an instrument designed to measure stude

thinking, reasoning, problem solving and communication.”

If you want English language learners to engage in high-level mathematics abecome successful mathematical thinkers, reasoners, problem solvers andcommunicators, would you use Task 1 or Task 2? Explain why.




High-Level

Mathematics

to English Language

Learners


Doing Mathematics!with

English Language Learners




High-Level

Mathematics

to English Language


Handout 2-16Thinking Geometrically: Finding the best box

This is a classic geometric problem that can help studentsdevelop and consolidate their understandings of basic

concepts of two and three-dimensional geometry, and of hogeometry connects to basic arithmetic.

The Problem Statement:

To: Best Solutions Consulting Company

From: Out of This World CandiesRe: Problem to be solved

Our company, Out of This World Candies , plans to sell our Starburst candies in anew package containing 24 individually wrapped Starbursts. Your challenge is to findthe dimensions of the least expensive box that can hold exactly 24 Starbursts. *

Each wrapped Starburst has a square shape that measures 2 cm on a side and 1 cmhigh.

In your report we want you to tell us:

1. The dimensions in centimeters of all the possible boxes we cause to package exactly 24 Starbursts.

2. The dimensions of the least expensive box for us to produce.3. An explanation of your answers to parts 1 and 2.4. A suggestion to us about which one, of all the boxes, you thin

would be our best choice. We want to know why you think aparticular box is the best choice over all the others.

* Out of This World Candies is an imaginary company. Starburst Fruit Chews are a real product

manufactured by Mars, Inc.


2 cm

2 cm 1 cm



Handout 2-17Classroom Video: Introducing the Starburst Problem to EnglishLanguage Learners


High-Level

Mathematics

to English Language

Learners

n the Middle Grades


How does the teacherengage her students?

What do I wonder?



Handout 2-18Speak, Listen, Question and Respond


High-Level

Mathematics

to English LanguageLearners

n the Middle Grades


Read HANDOUT 2-16 and use HANDOUTS 2-19, 2-20, and 2-21

One at a time, individually, complete each of the three handouts:

2-19: What SPECIFIC INFORMATION is given in the problem

2-20: What PRIOR KNOWLEDGE can we use to solve the problem

2-21: What do we need to FIND OUT that will help us solve theproblem?

Divide into pairs. Use SPEAK, LISTEN, QUESTION and RESPONDwith your partner to share and discuss your responses. When it is youturn to ask questions, you may use the scaffolding questions onHANDOUTS 2-19, 2-20 and 2-21 to question your partner.



Handout 2-19


High-Level

Mathematics

to English Language



Sacffolding questions to ask your partner:

Where does it say that in the problem?Why is that important?How does knowing that help us solve the problem?Please explain or show what [a word or phrase] means.

Statements to make to your partner:

The problem tells us that.....It also tells us that....Another fact included in the problem is that....Finally, the problem tells us that...

What SPECIFIC INFORMATION is given in theroblem?




High-Level

Mathematics

o English Language

Learners

n the Middle Grades



I already know that ...I know how to find ...Finally, I know that ...I know this problem is the like ... because...Therefore, I know that I can use ... to help solve the

problem.

What PRIOR KNOWLEDGE can we use to solve theproblem? (What do we already know that can help us?

Scaffolding questions to ask your partner:

How do you know that?How does that relate to the mathematics of this problem?How will that help us solve the problem?Please explain or show what [a word or phrase] means



Handout 2-21


High-Level

Mathematics

to English Language

Learners

n the Middle Grades


What do we need to FIND OUT that will help solve theproblem?


We need to find out ...We also need to know ... because …Finally, we need to answer the question ... in order tofinally solve the problem.


How will we know if we have solved the problem?Can you explain why we need to know that?How will knowing that help us find the solution?How will we be able to find that out?Please explain what [a word or phrase] means.




High-Level

Mathematics

to English Language

Learners

n the Middle Grades


Draw a picture Make a list, table or cha

Create a model

Use easier numbers Look for a pattern

1, 2, 3

10, 20, 30

Write an equation Work backwards

a2 + b2 = c2

CHOOSE a STRATEGY to solve a problem



Handout 2-23Keeping Track of InformationUse more co ies of this a e if necessar

Turning Points Tool

Teaching

High-Level

Mathematics

to English Language

Learners



DIMENSIONS DIAGRAMS

8 cm x 6 cm x 2 cm



Handout 2-24Evaluating Partial Solutions


High-Level

Mathematics

o English Language

Learners

n the Middle Grades


Look at all the boxes and dimensions posted byever one so far and answer the followin

Statements to make to your partner:no

I think there are … a few more boxes possible because ...many

Do you think we have found all the possible boxes?

How many more do you think there might be: hundreds of

possibilities or just a few?

Explain: give reasons for your answers.


How many of the boxes that people already found are the same?how many are different?

Do you think there could be any more boxes longer (shorter, highthan any of these?

What’s the longest (tallest, shortest ) box we could make?

Can you describe any patterns among the boxes that are listed?

Do you think there are any numbers that cannot be used as one othe dimensions of a box that will hold exactly 24 Starbursts. Whatare some of those numbers? How do you know?



Handout 2-25


High-Level

Mathematics

to English Language



Examine this data gathered by teachers in an earlierworkshop.

What pattern or patterns do you notice in the data?

Can these patterns help you determine whether you have

found all the possible boxes that can hold exactly 24

Starbursts?



rning Points Tool eaching

gh-Level

athematics

English Language

arners

the Middle Grades


Now that you have found all possible boxes that can hold

exactly 24 Starbursts, how can you determine the leastexpensive box?

Handout 2-26Finding the Least Expensive Box

Scaffolding Questions

What calculations do you need to make?

Do you need to make a calculation for every possible box, or just some of them? Explain.

Could there be more than one box that is least expensive?

What argument can you make to convince someone that youhave found the least expensive box?

Pattern Language:

To find the least expensive box I suggest that we ____ because _____.



Handout 2-27aReporting to Out of This World Candies


High-Level

Mathematics

to English Language

Learnersin the Middle Grades


To: Best Solutions Consulting CompanyFrom: Out of This World Candies

Re: Problem to be solved

Our company, Out of This World Candies , plans to sell our Starburst candies in anew package containing 24 individually wrapped Starbursts. Your challenge is to find thdimensions of the least expensive box that can hold exactly 24 Starbursts.

Each wrapped Starburst has a square shape that measures 2 cm on a side and 1 cmhigh.

In your report we want you to tell us:

1. The dimensions in centimeters of all the possible boxes we can useto package exactly 24 Starbursts.

2. The dimensions of the least expensive box for us to produce.3. An explanation of your answers to parts 1 and 2.4. A suggestion to us about which one, of all the boxes, you think

would be our best choice. We want to know why you think aparticular box is the best choice out of all the others.

Here is an excerpt from the Memo from Out of This World Candiesto Best Solutions Consulting Company

Make a list of items to include in your report to Out of This World

Candies. Pay particular attention to items 3 and 4. For item 3, be sure you make a concise and convincing case that you

have found the information requested. For Item 4, you may want to recommend that Out of This World

Candies use a box that is NOT the least expensive box. If you makesuch a recommendation be sure to think about:

o How would it look to shoppers?o What would make it appealingo What kind of visual information should be displayed on the

box?o How would the box look on a shelf with other candies?



Handout 2-27bReporting to Out of This World Candies


High-Level

Mathematics

to English LanguageLearners



Use this page to write down the items you plan to includein your report.



Handout 2-28Debrief: Reflecting on “doing mathematics” in thiworkshop Turning Points Tool

Teaching

High-Level

Mathematics

o English Language

Learners

n the Middle Grades


Think about the following questions within your team and with the entire worksgroup. Answer these questions as workshop participants, not as English langulearners in the middle grades.

1. Mathematical content: Did anything about the mathematics of this problem surprise you

Did you recognize any mathematical misconceptions in your owand your colleague’s work? If so, how were they addressed?

What mathematical questions do you have after solving thisproblem?

What did you learn about the way you and others approachmathematical problems?

2. The Process of Doing Mathematics: Did anything about this process surprise you?

How did group members help every member understand and sothe problem?

How is “doing mathematics” similar and different from the waysthese kinds of mathematical concepts are normally taught?



Handout 2-29Debrief: Reflecting on “doing mathematics” withEnglish language learners in the classroom


High-Level

Mathematics

o English Language

Learners

n the Middle Grades


Three Essential Questions for Lesson Planning

1. How does this lesson ensure that English languagelearners are engaged in high-level mathematics by

solving challenging problems, using mathematical reasoning, and explaining their thinking?

2. How does this lesson ensure that all English languagelearners are engaged at all times throughout thelearning process?

3. How does this lesson support English languagelearners learning mathematics in the middle grades

without simplifying the problem, telling them what to do, or telling them the answer?




High-Level

Mathematics

to English Language

Learners


Keeping Classroom Activitiesat a High Level of

Cognitive Demand for

English Language Learners




Turning Points Tool

Teaching

High-Level

Mathematics

to English Language

Learners

n the Middle Grades


Handout 2-30Rubric for Levels of Cognitive

DemandLevel 1 tasks: Memorizing Facts and Following procedures

Typical activities involve: Memorizing definitions, facts, algorithms and formulas Using memorized definitions, algorithms, facts and formulas, exactly as

learned Using known algorithms to produce correct answers Following steps in a given order Evaluating an expression for a given variable Solving a one-step word problem using a known algorithm Solving problems with unambiguous correct answers Describing procedures without further explanation

Level 2 tasks: Using Procedures and Concepts

Typical activities involve Solving Multi-step problems Using and making connections among multiple representations

(diagrams, concrete models, symbols, formulas) Solving problems requiring conceptual understanding Using procedures to help illustrate or understand concepts Identifying and extending a pattern Justifying the steps in a solution Using a graph, table or figure to solve a problem

Level 3 tasks: Doing Mathematics

Typical activities involve

Solving novel problems Accessing relevant prior knowledge Analyzing multi-step mathematical tasks and recognizing their

constraints Making a plan without being given all steps or procedures ahead of time

Self-monitoring progress, evaluating and revising plans as needed Exploring to deepen understanding of mathematical concepts Using mathematical models and multiple representations to solve

problems and explain thinking Using mathematical reasoning and language, drawings and models to

explain problem-solving strategies and justify (prove) solutions Solving problems in more than one way




High-Level

Mathematics

to English Language



Handout 2-31 Matchin Tasks and Co nitive Levels

Task DescriptionWhich Level do you think it is?Explain.

TASK A:Students at Grayson Middle School areordering school T-shirts. They come in twocolors. A survey of 25 students shows that 10students preferred blue T-shirts and 15students preferred red. Explain how you canestimate how many red and blue T-shirts toorder, if a total of 180 students order shirts.Use diagrams, tables and mathematicalexpressions to make your explanation easier tounderstand.

Task B:3/5 of the students in Ms. Jones’ class of 30students are boys. How many of the studentsare boys and how many are girls?

Task C:The student council has budgeted $300 to buydrinks for the graduation dance. Your job is toorder drinks that most students will like. Asurvey of 40 students shows that 15 prefercola, 5 prefer ginger ale and the rest preferlemonade. Sodas cost $2.00 for a 2-liter bottleand lemonade costs $3.00 for a 2-litercontainer.

To have enough drinks for everyone, you

want to spend as much of the $300 as possiblewithout going over budget. Decide how muchof each drink to order and write a report tothe student council justifying your decision.




High-Level

Mathematics

to English Language



Handout 2-32 Modifying Cognitive Levels

Task Description

Suggestions for enhancing the

cognitive level of the task TASK A:Students at Grayson Middle School areordering school T-shirts. They come in twocolors. A survey of 25 students shows that 10students preferred blue T-shirts and 15students preferred red. Explain how you canestimate how many red and blue T-shirts toorder, if a total of 180 students order shirts.Use diagrams, tables and mathematicalexpressions to make your explanation easier to

understand.

Task B:3/5 of the students in Ms. Jones’ class of 30students are boys. How many of the studentsare boys and how many are girls?

Task C:The student council has budgeted $300 to buydrinks for the graduation dance. Your job is toorder drinks that most students will like. Asurvey of 40 students shows that 15 prefercola, 5 prefer ginger ale and the rest preferlemonade. Sodas cost $2.00 for a 2-liter bottleand lemonade costs $3.00 for a 2-litercontainer.

To have enough drinks for everyone, youwant to spend as much of the $300 as possiblewithout going over budget. Decide how muchof each drink to order and write a report tothe student council justifying your decision.

Suggestions for simplifying thistask:




High-Level

Mathematics

to English Language



Handout 2-33How Tasks Chan e in Classrooms*

Furthermore, when students

ask for help teachers may

simplify the task even moreby giving hints or askingleading questions.

• They may tell students that they

have (or have not) found all the

possible boxes rather than makingthem reason it out for themselves.

• They may tell students to first findthe volume of 24 Starbursts, andthen use the factors of that numberto find dimensions of other boxes..

• They may give “hints” or “remind”students to use formulas they

alread know for volume and

Teachers whomake such

changes meanwell. They

want to helpstudents“succeed” in

solving aparticularproblem with

lessfrustration,

but they deprive themof

Teachers of

Englishlanguage

learners mustguard against

reducing the

cognitivedemands of

mathematicaltasks andmake sure

their students

have access tohigh- levelmathematics

in the middle

However, teachers may decide to

simplify the task for their students.

•They may tell students what to do first,second, third.

•They may tell students, for instance, that theyhave to find the box with the smallest surfacearea.

•They may provide formulas for students touse, give them a table to fill in, etc.

•They may eliminate the requirement forstudents to explain their work both orally

and in writing.

A task – such as Finding the Best Box – may

be set up at the Doing Mathematics level of cognitive demand:•Students are asked to solve a novel problem using knowledge of

mathematical concepts and problem solving strategies

•The are asked to develo their own a roach to the roblem

* Adapted from: Implementing Standards-Based

Mathematics Instruction: A Casebook for Professional

Development . Teachers College Press, 2000, by M.K. Stein, M. S. Smith, M.A. Henningson and E. A.Silver.




High-Level

Mathematics

o English Language

Learners

n the Middle Grades


Handout 2-34Scaffolding the “Best Box” problem

for English language learners

Work with a partner to brainstorm three or more suggestions for scaffoldingFinding the Best Box to support English language learners in your ownclassrooms.

1

2

3

4

5

6




High-Level

Mathematics

to English Language



Handout 2-35Scaffolding the “Best Box” problem

for English language learners

Suggestions for Scaffolding “Finding the Best Box”

for English language Learners

Scaffolding not only helps students solve the problem athand, but also gives them strategies they can use in any

problem-solving situation.

Compare these suggestions with the ones your workshop group came

up with: • Create a context for the problem that students will understand, even enjoy.

In our example, choosing familiar Starburst candies instead of abstract

“blocks” or “cubes” helps motivate students and keep them involved.• Provide students with sets of 24 Starbursts so they can actually construct

rectangular prisms by rearranging the candies.• Ask students to plan their work by identifying their objectives, decide what

they know and what they need to know, and make a plan for the steps theycan take to solve the problem.

• Instruct students to discuss their plans in their groups, using a structuredgroup protocol to make sure that everyone speaks and everyone listens, andcome to agreement about what they are going to do.

• Give students sentence starters (pattern language) so that they can practiceusing mathematical language when they talk in their groups or share with the

class.• Ask “scaffolding questions” that help students think, without “giving hints.”

For example: Have you ever solved a similar problem? What information do you

have to start with? What have you chosen as a first step? Have you found all the

possibilities? How do you know? Please explain your thinking. • Give students lists of scaffolding questions and encourage them to ask them

of each other.• Set up a structure to help the different groups share information so they can

all learn from the work the others have done.• Make sure that all posted work is visible to everyone, so everyone can see

the same information.

• Stop the working groups at several points to share information and learnfrom each other.

• Choose students randomly from each group to report on their group’s

decisions and discoveries. It’s important to choose randomly so that studentsknow that every student in a group is responsible for being able to explain all

the work of the group.




High-Level

Mathematics

o English Language

Learners

n the Middle Grades


Handout 2-36Some Final Thoughts

High-level mathematics in middle school is challenging,

engaging, and enjoyable.

High-level mathematics instruction helps English languagelearners build confidence, develop problem-solvingstrategies, learn and practice basic skills and develop anunderstanding of the language, methods and purposes of mathematics.

To keep mathematics instruction at a high level teachersmust assign challenging tasks, allow students enough time to

work on them, establish classroom procedures andexpectations so that students work together comfortably,build on each other’s ideas and take responsibility for their

own and each other’s learning.

It is challenging for teachers as well as students to maintaina high level of cognitive demand.

Scaffolding by teachers is essential in fostering the learningof high-level mathematics. This takes professional insight,

preparation, and time.

High level mathematics is within the reach of all middlegrades students, of all English language learners.

We hope this challenge will become one that sustains,

guides and focuses your work as a teacher.





High-Level

Mathematics

o English Language

Learners

n the Middle Grades

Handout 2-37

COMMITMENT:

Over the next few weeks I will try out thefollowing best practices for teaching high-levelmathematics to English language learners:

I will collect the following evidence in order todetermine how well it is working in improvingthe access my students have to learning high-level mathematics.



Date: ______________________________

Best instructional practice for English language learners on whicham working:

________________________________________________________

High-level math content:

Instruction

Using mathematical languageappropriately and accurately

Using mathematical languageappropriately and accurately

Other Other

Changes I have made in mypractice

Changes I have noticed in mystudents’ depth of

understanding and engagemen

High-level math content:

Instruction:

Handout 2-38



High-Level

Mathematics

o English Language

earners

n the Middle Grades



Handout 2-39Workshop strengths (information, facilitation, pacing, mix of

activities, etc.):

Suggestions for improvement (information, facilitation, pacing,

mix of activities, etc.):

Questions or concerns I now have:

Most important ideas I will take away from the workshop:

ning Points Tool aching

gh-Level Mathematics

English Language

arners

he Middle Grades

math for ell students workshop 2 handouts

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