09.09.09 Facilitator's Guide to Turning Points Tool

8/8/2019 09.09.09 Facilitator's Guide to Turning Points Tool

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FACILITATOR’S

GUIDEtoWORKSHOP SERIES


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Teaching High‐Level Mathema2cs to English Language Learners in the

Middle Grades was developed by Turning Points, a project at the

CenterforCollabora;veEduca;oninBoston,MA.This tool ispartof

the Mathema2cs Improvement Toolkit , a project of the Na;onal

Forum to AccelerateMiddle Grades Reform,and was supported bythe U.S. Department of Educa;on’s Comprehensive School Reform

Ini;a;ve,grant#S332B060005.Opinionsexpressedarethoseofthe

authorsandarenotnecessarilythoseoftheDepartment.

Copyright 2009 Center for Collaborative Education/Turning Points



Prepared for

Turning Points

by

Dr. Sara Freedman, Project director

Dr. Dan Lynn Watt, Math consultant

Copyright 2009 Center for Collaborative Education/Turning Points



Table of Contentsurning Points Tool

eaching

igh-Level

athematics

o English Language

earners

the MIddle Grades

© Copyright 2009 Center for Collaborative Education/Turning Poin

General Overview of Turning Points Tool

What’s Included in the Tool

Intended Audience

Logistics

Layout of Facilitators’ Notes for Each Slide

How to Implement the Workshops

Ways to Sustain the Work between and after the

Workshops

Answers to Frequently Asked Questions

Additional Support Available from Turning Points toFacilitators and Math Teams



Turning Points, a project of the Center for Collaborative Education in

Boston Massachusetts, is pleased to offer you the Turning Points Tool

Teaching High-Level Mathematics to English Language Learners in

the Middle Grades. The Turning Points professional development tool

prepares teachers to make middle grades high-level mathematics

accessible to a wide range of English language learners by focusing on

the key bridging strategies used to support English language learners in

learning high-level mathematics.

rning Points Tool

eaching

gh-Level

athematics

English Language

arnersthe MIddle Grades

© Copyright 2009 Center for Collaborative Education/Turning Points

General Overview

Teaching High-Level Mathematics to English Language Learners, a

professional development resource, is based on the following guiding

principles:

• Mathematics instruction needs to focus on building deeper conceptualunderstanding

• Teachers need resources that enable them to be responsive to the

learning needs of a wide range of English language learners

• Effective professional development includes opportunities for teachers

to reflect on instruction

• Effective professional development occurs across time, includes

implementation, and provides ongoing technical assistance and

support

• English language learners have a right to learn high-level mathematics

in the middle grades

Teaching High-Level Mathematics to English Language Learners

consists of

• two full-day workshops that can be subdivided into four half-day

workshops,

• video examples of teachers introducing best practices to English

language learners in math classrooms,

• handouts to use with English language learners in math classrooms, and• resources for sustaining the professional learning community modeled in

the workshop series.

All the workshop activities model the teaching and learning strategies

that exemplify best practices for teaching high-level mathematics to

middle grades English Language Learners.



urning Points Tool

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athematics

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Workshop 1

Teachers will learn:

• who the English language learners in schools are 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 mathematical reasoning essential to mastering high-levelmathematics.

Workshop 2

Teachers 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.

The workshops promote effective instructional practices that supportEnglish language learners to

• Work in small groups, taking turns to explain and clarify their thinking;

• Ask each other questions to help develop accurate and completeexplanations;

• Use mathematical vocabulary and syntax to discuss mathematicalconcepts and solve problems;

• Use writing to clarify and make explicit their thinking;

• Explain how a concept or skill can be used to solve real life problems;

• Know when and how to use a formula and algorithm; and

• Explain how they are solving a problem and when their answer makessense.

All of the practices included in the tool and demonstrated in the videos that

accompany the tool have been extensively tested in urban classrooms

enrolling high percentages of English language learners. Students enrolled in

these classrooms range from those with little if no formal introduction to high-

level mathematics before being enrolled in these classrooms to those whoentered with a strong background in mathematics.

The demonstration classrooms featured in the video examples include sheltered

English classrooms, English Language Learner math classrooms and

mainstream math classrooms.



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eaching

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What’s Included in the Tool

Teaching High-Level Mathematics to English Language Learners in the

Middle Grades includes:

An overview of best practices for teaching high-level math to Englishlanguage learners;

Concrete resources for planning math lessons that incorporate these

practices;

Multiple video examples of best practices for English language learners a

they are being used in middle grades classrooms.

The two six hour workshops are designed to be used in sequence, with the

second workshop building on the first. The workshops include:

Activities to engage teachers in high-level mathematics on the middle

grades level;

Discussion protocols to ensure that all English language learners are

engaged in high-level middle grades mathematics;

Structured and sequenced cooperative learning activities to support the

active learning of English language learners;

Linguistic structures and pattern language that English language learners

can use to participate actively in math classes;

Examples of sentence frames and probing questions that English languag

learners can use to explain their reasoning and support their peers in

expanding their mathematical explanations;

Activities that demonstrate how to access English language learners' prio

knowledge when introducing key mathematical concepts;

Protocols for analyzing video excerpts of teachers implementing best

teaching practices for English language learners;

Activities that engage teachers in reflecting upon their own practice as

they work to incorporate the lessons of the tool in their own practice.



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Resources provided include:

An annotated facilitator’s guide for each workshop;

A PowerPoint presentation for each workshop;

Video examples of middle grades teachers using best practices toteach high-level mathematics to English language learners;

Video examples of English language learners discussingmathematics;

Math problems for teachers to solve and analyze;

Model lesson plans that incorporate the linguistic, cultural andcontent-based needs of English language learners to teach high-level mathematics in the middle grades;

Multiple ways to assess English language learners’ understanding okey mathematical concepts;

Strategies for encouraging structured cooperative learning and

discussions (including both conversational and academic English); Handouts that can be used by English language learners in

mathematics classrooms

Short articles focused on the main theme of each workshop asspringboards for teacher discussion

Resources and references that can be used to supplement theworkshop series.



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athematics

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Intended Audience

There are several audiences for these workshops. They include:

Middle school math teachers working with a wide diversity of

English language learners, ranging from students with little or no

previous exposure to mathematics education in their homecountries to those enrolling with strong backgrounds in

mathematics;

High school math teachers teaching English language learners

entering high school without a strong background in middle grades

mathematics;

Math content coaches working with mathematics teachers

teaching a wide range of middle grade English language learners;

ESL/Bilingual and Sheltered Immersion teachers teachingmathematics to middle school and high school English language

learners;

Math department chairs in middle schools and high schools; and

Central office math curriculum coordinators.



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Logistics

As far as possible and at least 4 weeks in advance, the facilitators

should:

Establish a date for each of the full day workshops.

Recruit participants. A minimum of 8 and a maximum of 20 is

suggested. Prospective participants could include middle grades

math teachers, bilingual or ESL teachers who teach mathematics

to English language learners, and any other support staff whose job

it is to work with English language learners during math instruction.

Secure a location for the workshop and all of the equipment you

will need - a computer, an LCD projector, good external speakers

and a screen. Additional materials are included in other sections of

this guide. Make sure everything is in working order.

Review the facilitators’ guide and the participant’s packet. Go

through the slide show and be sure you are clear about when to

change the slides and when to click on the text of each slide.

1-2 weeks in advance:

Send reminders to participants

Confirm meeting space and time

Photocopy workshop handouts Practice powerpoint presentation; do all workshop activities.

1-3 days in advance:

Do a test-run with the computer/projector/dvd player and speaker

to ensure you know how to operate each and switch between the

two if needed.

Set up tables or desks to promote small group and partner work Ensure that all workshop handouts and materials are ready

Do a final “test run,” using all of the workshop materials.

Re-read facilitators’ guide to the tool to review essential principles

and approaches



ACTIONSuggestedactions to take

SLIDE 1


☚

☛

Number of slide

TALKING POINTSThis is where you willfind TALKING POINTSto use with each slide.

☟ Picture of slide

☚

☟ Handout for slide

Layout of Facilitatorsʼ Notes

for Each Slide

As the facilitator, you can decidewhen to change each slide and whento change the text of each slide. TheACTION section leaves the pacing ofeach slide to the discretion of thefacilitator.



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athematics

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How to ImplementWho should facilitate this tool?

This tool should be facilitated by a team consisting of an experienced teacher o

English language learners and an experienced math teacher, math coach, or ma

curriculum specialist. Having co-facilitators, one with experience in teaching

mathematics and one with experience in teaching English language learners, wi

ensure that both aspects of teaching mathematics to English language learners the math and the language and cultural issues – will be addressed thoroughly. T

facilitator's guide provides detailed instructions for preparing for and conducting

the workshop.

How are the workshops structured?

The workshop series are face-to-face workshops, designed to be offered in twohour blocks of time with time for breaks and lunch or in four 3 hour segments. In

order to allow teachers to engage in a full cycle of inquiry and implementation -

out these practices in their classrooms on a regular basis, observe each other athey practice new approaches, debrief their practice publicly, and continue to

refine and improve their teaching – we suggest that the workshops be schedule

several weeks apart.

How do facilitators prepare to lead the workshops?

Each workshop has an extensive facilitator's guide, which includes talking poin

and specific directions for each phase of the workshop. The guide also includes

suggested times for each activity, although times should be adjusted to fit the

needs of the group.

Facilitators leading the workshop series will need extensive time to familiarize

themselves with the guides and the workshop materials as a whole, and should

expect to spend several hours in preparation for each workshop. This preparatio

should include a first review, second more in depth review and a final review to g

everything ready. Facilitators will also want to familiarize themselves with the

Participant’s Packet, which includes many resources teachers can use with thei

own students and suggestions for furthering their own study beyond the time

spent in the workshop.

What are the technical requirements?

Technical requirements for the workshops include a computer with Microsoft

PowerPoint™ software, a projector, a good sound system and screen. It is critic

that all participants be able to see the slides and video clips and hear the sound

clearly. Before starting the workshop do a “dry run” with your equipment to mak

sure that all the elements including the video and sound are functioning properly



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athematics

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arnersthe MIddle GradesIt is critically important, however, to make sure that ample time is given to each

activity, particularly time for every participant to think, act, reflect, listen, write,

draw, respond, ask questions, and consider alternative possibilities by

themselves, in pairs, small groups, and with the group as a whole. Such a

process provides time to focus upon the key concept of each activity during th

workshop.

More importantly, it models the critical importance of insuring that every lesson

has a clear and singular focus and that English language learners are given

ample time to concentrate on that focus, to process their understanding (oftenfrom one language to English, back and forth), to be able to express their

thinking about that focus, and to develop a strong understanding of that

concept.

Each activity includes time at the end to debrief its most important points - this

the metacognitive heart of the workshop, and models ways to conduct similar,

and essential debriefs in classrooms with English language learners.

How do facilitators decide when to show each section of the slide?

Each slide is designed to show the text and pictures in one of two ways:

1) all of the text as soon as the slide appears

or

2) different sections of the slide, one at a time.

The facilitator should decide how to pace the timing of each slide and each sec

within the slide and practice doing so before each workshop. Each slide is diffe

so it will take some time to figure out the optimal pacing for each one.

How do the facilitators decide when, how and who should read the text of

slides?

Facilitators can

•read the slides themselves, deciding on the pacing of each slide and section o

•invite participants at random or round robin to read each section.

Some of the slides have text that gives directions. This text should be read as it

written on the slide, with any additions that facilitators feel would help clarify w

participants need to do. The text for directions is written as a model of how to g

directions to English language learners - one at a time, with a clear focus and

rationale. (See Participant’s Packet for more on giving directions, a critical skill

successfully teaching mathematics to English language learners.)

To what extent should facilitators follow the time suggestions for each

activity found in the facilitator’s guide?

The time suggestions listed in the agenda provided in the facilitator’s guide are

based on the field tests conducted in the development of the tool. Facilitators

should adjust them to meet the needs of each group of participants, while

maintaining the sequence of the activities as a whole and within each section. W

encourage facilitators to use their experience as teachers, coaches and worksh

presenters and adjust to the needs of the group.




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How should facilitators use the TALKING POINTS for each slide that appe

the facilitators’ guide?

The TALKING POINTS in the facilitators’ guide provide a script that facilitators’

use as they display each slide. They include a number of key points that are no

found in the text of the slide itself, as well as more explicit directions participan

will need to follow for a particular activity.

We encourage facilitators to adapt the TALKING POINTS to fit their own style o

speaking if they wish to do so while incorporating their key points. Avoid simpl

reading through the slides or the TALKING POINTS - practice walking through

slides so that you can make the presentation your own.

How should the room be arranged for the workshop series?

One of the key strategies emphasized in the workshops is the

importance of ensuring that everyone in the workshop and every student

in a class

• has equal access to all materials,

• can hear everyone easily

• can be heard and seen by everyone easily, and

• can easily see and hear all charts, information, slides and videos.

We suggest that wherever possible, participants be grouped in such a

way as to make sure all of the requirements are met. Furniture that

allows for such flexibility is optimal but even fixed desks can be used

creatively to achieve similar results.

It may help to ask participants, for example, what shape will be madewith their desks (if you are using desks) if a trio sits so that all members

are equidistant from each other, or a group of four, etc. This question

combines thinking about math with the purpose of the seating

arrangement.

It is also helpful to tell participants why the room is arranged as it is - tocreate a professional community of learners and an inclusive classroom

culture in which everyone’s contribution is critical for the learning of all.

It is therefore important that everyone is able to participate fully and

freely during each activity.

This arrangement also replicates the way mathematicians work in real

workplaces - they often solve problems in groups, building on the work

of each other, raising questions, trying out alternatives, revising their

thinking and developing robust solutions that all of them can each

explain and justify to themselves and others.



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athematics

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Clearly, this requires that English language learners have multiple and repeated

opportunities to hear, repeat, and try out their thinking - in a language that is new

to them. All of the strategies in the workshop are designed to provide these

opportunities in multiple ways so that English language learners have the critical

support they need to succeed in mathematics in the middle grades.

For many teachers, this represents a paradigm shift in their own understanding o

how to teach mathematics and the kind of mathematical reasoning required forsuccess in middle grades mathematics and beyond. The workshops in Teaching

High-Level Mathematics to English Language Learners in the Middle

Grades are designed to model how to introduce, use and reflect upon these

strategies as they should be used on a regular and consistent basis during

all math lessons with English language learners. Teachers are far more likelyto use these strategies in their own classrooms if they are given time to practice

learning and using them during the workshops than if the time and persistent

modeling are not provided in the workshops.

Why is so much time devoted in the workshop series to discussion?

Students need to understand the mathematics they are studying. In the middle

grades, all students need to focus on problem solving and conceptual

understanding of complex mathematical concepts. Middle grades students need

support to move from basic computation and arithmetic to more complex topics

ratios and proportion, geometry, graphing and data analysis, functions and algeb

They also need support in learning and using the language of mathematics; with

facility in that language they are unable to discuss, process and understand theconcepts of middle grades mathematics and beyond. Providing such support is

especially critical for English language learners learning high-level mathematics.

In order for English language learners to do so, they need to be able to:

• analyze multi-step mathematical tasks and recognize their constraints,

• make a plan without being given all steps or procedures ahead of time,

• access relevant knowledge and explore a range of possible strategies to deep

understanding of mathematical concepts and arrive at supportable solutions,

• self-monitor the cognitive processes used in solving problems,

• use multiple representations to solve problems and explain their thinking, and

• use mathematical reasoning and language to explain how they solved a probleand why they took the steps they took.


Why are the directions for discussions so explicit and exact?

The workshop series makes extensive use of discussion protocols. These protoc

are carefully structured to ensure that all English language learners become activ

and engaged participants throughout the math lesson. As in all protocols, it is

essential to follow each step of the protocol with fidelity so that every student ga

the depth of understanding built into each activity and has the time to contribute

actively with other students. Saying “Turn to your partner and talk” does not do

the job! The facilitators should guide the use of the protocol and adjust the timin

and guidelines as needed by the group.

The Participant’s Packet has a handout that provides guidance on giving directio

to English language learners.



urning Points Tool

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There is a far amount of writing in the workshops. What are the best ways

facilitators can encourage math teachers to write?

Writing is used in a number of ways throughout the workshops: 1) as writing to

learn [THINK WRITE PAIR SHARE] and 2) as learning to write [Using sentence

starters and pattern language to explain one’s thinking, ask questions and

demonstrate one’s mathematical reasoning].

Both of these approaches help students (and workshop participants) master h

level thinking by giving them

• time to think before answering,

• an opportunity to consider various alternatives that might not occur to them

initially but surface after a few moments after the question or activity is presen

• encourage more thoughtful and expanded ideas than a quick response woul

suggest, and

• provide models for the kind of thinking required to do high-level mathematics

the middle grades.

It may appear counterintuitive to emphasize this practice with English languag

learners. We know, however, that English language learners need consistent an

persistent modeling and support for mastering the academic language of

mathematics in order to be successful students in middle school and beyond.

Writing - with the support of sentence starters, pattern language and the gradu

release of responsibility - provides this kind of support. The workshop gives

English language learners the tools they need to participate in high-level

mathematics in classroom discussions and succeed in standardized tests and

other forms of assessment.

It is our experience that some teachers may take a good bit of time to becomfortable writing but that with patience, with time and with persistence they

all do so - and use writing regularly in their own classrooms with English langu

learners and other students. Wait time in writing works as well as wait time in

discussions.

When should facilitators use charts to make the work of the group

public?

The workshop encourages facilitators and teachers to make their thinking

and their work public - primarily by having the facilitator, the group or

individuals write their responses on chart paper or on stickies. Suggestionsfor doing so appear in the ACTION section that accompanies each slide in

the guide. Notice that facilitators do not write down their own thinking.

They work with the group to co-construct that thinking; the chart paper

records the thinking of the entire group as it unfolds.

This strategy models an important support used in classrooms that

support English language learners. They need to see and hear whatstudents are saying so that they, and every other student in the class, has

equal access to the information and can contribute to that information.



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athematics

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Other supplies needed during the workshops:

• Chart paper

• Screen

• DVD player to play video clips (You may want to have this as back-up

if it is difficult to access the video with the same computer that is

showing the powerpoint.)

• Masking tape

• Name labels

• Pencils

• Markers of various sizes and widths and colors

• Scrap paper

• Calculators, rulers, math manipulatives

• Post-its or Stickies in various sizes, shapes and colors

• Graph paper

Feedback to improve Tool

Turning Points would appreciate your feedback on our tool, Teaching High-

Level Mathematics to English Language Learners in the Middle Grades.

Please send us your comments on the tool so that we can continue to improv

it and make it available to schools and teachers throughout the country.

Please email [email protected] with answers to these questions:

1) What worked? What were the strengths of Workshop 1? Workshop 2?

2) What didn’t work or could be improved?

3) What follow-up occurred in between and after the workshops?

4) Some information on your school or district and the teachers that attendedthe workshop: type of school, subject area and grades of teachers, numbe

of participants attending, role of facilitator in district or school, % of Englis

language learners in school, etc.

5) Additional comments, questions or request for on-site or off-site support

from Turning Points.

THANK YOU, National Turning Points/ the Center for Collaborative Education



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Ways to Sustain the Work

between and

After the Workshops Abundant research has demonstrated that one or two day workshops do no

by themselves, change teacher practice. The real work comes when teacher

and coaches go back to their schools and work together to plan and teach

lessons that use the strategies modeled in the workshop series.

Here are several ways to do such work:

1) provide regularly scheduled time for teachers to meet as a professional

learning community in which each member helps the others continually

improve their practice

2) assign an experienced coach or facilitator to guide the work of the team

and be available to consult, co-teach and otherwise help the teachers as

needed and/or requested

3) use a system of peer observations to observe each other using the

strategies and approaches practiced in the workshop series

4) use discussion protocols designed to supportively give feedback on the

observed lesson to improve instruction

5) use Looking at Student Work protocols to examine how students approac

problems and how best to support their continued learning

The workshop series includes several ways to do such work, all of which are

based on having teachers observe each other and take collective

responsibility for helping the group be highly effective math teachers for

English language learners.

The lesson planning sequence at the end of Workshop 1 is one example.

Teachers observe the work silently, ask clarifying questions to the presenter,

give warm feedback in one round and “I wonders..” in a second round.

Protocols for Looking at Teacher Work and Looking at Student Work are

included in an Appendix at the end of this guide. The appendix at the end of

the Participant’s Packet includes additional protocols used in the workshop

series. They can be used in teachers’ meetings as well.

Turning Points can support this work through conducting “train the trainer”

sessions or facilitating the workshops for districts. Please see “Additional

Support from Turning Points for further information.



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Answers to Frequently AskedQuestions

Does this tool address the needs of English language learners who entermiddle grades without mastery of basic computational skills?

English language learners, as well as native speakers of English, are verydivergent in terms of their mastery of computational skills and mathematicalfacts. All of the strategies have been used in classrooms with English languaglearners entering with a great range of facility in mathematical andcomputational understanding and knowledge.

This tool focuses on providing all of these students with assess to high-levelmathematics in the middle grades, whether or not they are weak incomputational skills and their knowledge of mathematical facts. The tool is

designed therefore not to supplant support in these areas but to ensure that aEnglish language learners are provided the opportunity to learn the high-levelmiddle grades mathematics they need to move forward in school.

English language learners are a highly diverse group. Is access to high-

level mathematics featured in the tool addressed to a particular group or

level of English language acquisition?

The tool is designed to provide access to a broad range of English languagelearners from those in the beginning levels of English language acquisition tothose in more advanced levels and entering speaking many different languag

of origin. The strategies demonstrate how to use the diversity of students’background knowledge and ways of thinking in mathematical classrooms.

The laws and regulations governing the teaching and assessment of

English language learners differ from state to state. Is the tool designed

work in a particular state or group of states?

The tool does not take a stand on any of the laws and regulations governing tteaching and assessment of English language learners. It can be used in abroad variety of classroom settings, including bilingual, ESL and SIOP setting

Is the tool designed to be used with a specific textbook?

The tool is designed to be used with a broad range of textbooks and has beeused in settings which use different types of texts. The approaches modeled the tool are effective in any middle grade mathematics classroom in whichEnglish language learners are enrolled.



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Does the tool follow a particular model of training such as SIOP (Sheltered

Instruction Operational Protocol) or CALLA (Cognitive Academic

Language Learning Approach)?

The tool integrates the knowledge base and experience of a broad range ofresearch based approaches successful in teaching English language learners,including SIOP and CALLA, as well as those that are effective in teaching high-level mathematics to middle grades students. Please see the reference and

research section for further information.

Why is so much time devoted in the workshop series to discussion?

Students need to understand the mathematics they are studying. In the middle

grades, all students need to focus on problem solving and conceptual

understanding of complex mathematical concepts. Middle grades students

need support to move from basic computation and arithmetic to more

complex topics: ratios and proportion, geometry, graphing and data analysis,

functions and algebra. They also need support in learning and using the

language of mathematics; without facility in that language they are unable to

discuss, process and understand the concepts of middle grades mathematicsand beyond. Providing such support is especially critical for English language

learners learning high-level mathematics.

In order for English language learners to do so, they need to be able to:

• analyze multi-step mathematical tasks and recognize their constraints,

• make a plan without being given all steps or procedures ahead of time,

• access relevant knowledge and explore a range of possible strategies to

deepen understanding of mathematical concepts and arrive at supportable

solutions,

• self-monitor the cognitive processes used in solving problems,

• use multiple representations to solve problems and explain their thinking,and

• use mathematical reasoning and language to explain how they solved a

problem and why they took the steps they took.

Clearly, this requires that English language learners have multiple and repeated

opportunities to hear, repeat, and try out their thinking - in a language that is

new to them. All of the strategies in the workshop are designed to provide

these opportunities in multiple ways so that English language learners have the

critical support they need to succeed in mathematics in the middle grades.


The workshop series makes extensive use of discussion protocols. These

protocols are carefully structured to ensure that all English language learners

become active and engaged participants throughout the math lesson. As in all

protocols, it is essential to follow each step of the protocol with fidelity so that

every student gains the depth of understanding built into each activity and has

the time to contribute actively with other students. The facilitator guides the use

of the protocol and adjusts the timing of each step to meet the needs of the

group.



urning Points Tool

eaching

igh-Level

athematics

English Language



There is a far amount of writing in the workshops. Why?

Writing is used in a number of ways throughout the workshops: 1) as writing

to learn [THINK WRITE PAIR SHARE] and 2) as learning to write [Using

sentence starters and pattern language to explain one’s thinking, ask

questions and demonstrate one’s mathematical reasoning].

Both of these approaches help students (and workshop participants) master

high-level thinking by giving them

• time to think before answering,

• an opportunity to consider various alternatives that might not occur to

them initially but surface after a few moments after the question or activity is

presented,

• encourage more thoughtful and expanded ideas than a quick response

would suggest, and

• provide models for the kind of thinking required to do high-level

mathematics in the middle grades,

It may appear counterintuitive to emphasize this practice with Englishlanguage learners. We know, however, that English language learners need

consistent and persistent modeling and support for mastering the academic

language of mathematics in order to be successful students in middle school

and beyond. Writing - with the support of sentence starters, pattern

language and the gradual release of responsibility - provides this kind of

support. The workshop gives English language learners the tools they need

to participate in high-level mathematics in classroom discussions and

succeed in standardized tests and other forms of assessment.

Why do facilitators use charts to make the work of the group public?

The workshop encourages facilitators and teachers to make their thinking

and their work public - primarily by having the facilitator, the group or

individuals write their responses on chart paper or on stickies.

This strategy models an important support used in classrooms that support

English language learners. They need to see and hear what students aresaying so that they can, and every other student in the class, has equal

access to the information and can contribute to that information.



urning Points Tool

eaching

igh-Level

athematics

English Language



Support Available from

Turning Points to

Math Coaches and Teachers

Turning Points can support math coaches, math teachers and ESL/

Bilingual teachers by:

• conducting “train the trainer” sessions to prepare prospective in-

district or in-school facilitators to lead the workshops

• co-facilitating the workshops with school or district staff

• facilitating the workshops for districts, schools, or groups of teachers

and coaches

• conducting a week-long Math Immersion Workshop for Middle Grades

teachers, using the workshops as part of the week’s work

• helping districts use the workshops as an anchor in the development

of a inquiry cycle with math teachers that includes peer observations

and Looking at Student Work, Looking at Teacher Work and analyzing

assessment data to improve classroom instruction.

Contact Dr. Sara Freedman [email protected] if you are interested

in pursuing this type of support.

mailto:[email protected]




Turning Points Tool

Teaching

High-Level

Mathematics

to English Language

Learners

in the Middle Grades

© Copyright 2009 Center for Collaborative Education/Turning P

PROTOCOLS

USED IN WORKSHOP 1*

DISCUSSION PROTOCOLS

Think/Write/Pair/ShareFinal Word

Numbered Heads

Speak/Respond/Follow-up

Question/Respond

* Protocols originally developed byNational School Reform Facultywww.nsrfharmony.organdProject Zero

www.pzharvard.edu

http://www.pz/

http://www.pz/



Turning Points Tool

Teaching

High-Level

Mathematics

to English Language

Learners



BEST PRACTICE:

USE DISCUSSION PROTOCOLS

Discussion protocols are designed

•to provide clear guidelines andexpectations for class discussionsthat are accessible to all students,

•to ensure that English languagelearners have the time they need to process what they hear andformulate their ideas in a newlanguage,

•to make sure that all students,

including English languagelearners, are equal contributors tothe discussion as speakers andlisteners, and

•to allow for alternative ways ofthinking to be aired and evaluated.



Turning Points Tool

Teaching

High-Level

Mathematics

to English Language

Learners



BEST PRACTICE:

USE PRIOR KNOWLEDGE

AS A LINK TO NEW

KNOWLEDGE

•Prior knowledge gives

English language learnersentry points to every lesson

• All “big ideas” inmathematics can be linkedto the prior knowledge ofall English languagelearners

•Open ended, higher orderthinking questions areexcellent ways ofaccessing this knowledge



urning Points Tool

eaching

igh-Level

athematics

o English Language

earners

the Middle Grades

Think

Write

✎Pair

Share

Think/Pair/Share Adaptations for English Language Learners



urning Points Tool

eaching

igh-Level

athematics

o English Language

earners

the Middle Grades

Think/Write/Pair/Share Adaptations for English Language Learners

Steps of Think-Write-Pair-Share

1. Have students sit in pairs. Ask all #1s to raise their hands, check tomake sure every pair has a hand raised, then ask for all #2, check tomake sure every pair has a hand raised.

2. Announce a rich discussion topic or problem to solve. (Example: Whicroom in our school is larger, the cafeteria or the gymnasium and howcould we find out the answer? What does larger mean in this case?)

3. Give students at least 10 seconds of think time to THINK of their own

answer. (Research shows that the quality of student responses goes usignificantly when you allow "think time.") Give them another 30

seconds to WRITE their responses - long enough to write but not toolong that the pace slows down. Encourage them to come up withseveral responses.

4. Ask students to PAIR with their partner to discuss the topic or solutioDirect all #1s that they have one full minute (adjust the time to thecomplexity of the question) to tell their partner the answer to the posequestion, partner #2 listens without talking for the entire time allotted.#2 then has 30 minutes to tell #1 what s/he heard from them. Then #2

given one minute to tell #1 how s/he answered the question. #1 listensquietly the entire time, recalling what s/he heard in the next 30 second

5. #1 then responds to the comments of #2, using sentence stems suchas “I agree because….”“I disagree because….” I wonder …..” “ Do you think that …?” “Coulyou explain ….. to me. That isn’t clear to me. “ #2 responds to #1’scomments, then has 30 seconds to ask her/his own questions to #1’scomments.

6. Finally, randomly call on a few students to SHARE their ideas with thclass.

Simplified Steps

1. Announce a discussion topic, one that is meaty enough for a good, ricdiscussion.

2. Give THINK time. Give WRITING time.

3. Ask students to PAIR with an assigned partner to discuss their ideas. times, PAIR English language learners with other English languagelearners so that they can participate no matter what their lalevel ofEnglish.

4. Call on students to SHARE their ideas with the class.



urning Points Tool

eaching

igh-Level

athematics

o English Language

earners

the Middle Grades


Overview

Think-Write-Pair-Share is one of the most common cooperative learning

structures, it's one of the easiest to implement and it creates a culture ofequity and inclusiveness in classrooms. It’s particularly useful for Englishlanguage learners as it gives them a chance to try out their thinking andpractice talking over an idea in a safe structure before they speak to theentire class. It can be used throughout a class, especially when only afew students raise their hands in response to a question or when it isclear that students need a chance to explore a topic before speaking infront of the entire class.

The structure is extremely versatile but is particularly suited forgenerating higher order thinking. The steps are simple, but it's important

to follow the steps exactly to avoid the "groupwork" pitfalls. Sometimesteachers are tempted to skip some steps and just say, "Turn to a partnerand talk it over." Read on to find out why those words don't necessarilyresult thoughtful responses from each student or an equitable classroomculture.

Before you ask students to use think/write/pair/share on their own, makesure you model it for students, telling them exactly what step you aremodeling and asking them to discuss what they heard and saw during

each step. Chart the steps as you model them . If this is the first time

students have tried out the protocol, have them practice following

the protocol on easy cognitive material before you use it to discuss new material.

For ELLs, provide appropriate pattern language and sentence

starters for them to use during each step.

Hints and Management Ideas

• Assign Partners - Be sure to assign discussion partners rather tha

just saying "Turn to a partner and talk it over." When you don't assipartners, students frequently turn to the most popular student andleave the other person out. You may want to pair an English langualearner with another English language learner or with a native speaof English, depending upon the situation.

• Change Partners - Switch the discussion partners frequently. Withstudents seated in teams, they can pair with the person beside thefor one discussion and the person across from them for the nextdiscussion.



urning Points Tool

eaching

igh-Level

athematics

o English Language

earners

the Middle Grades


• Monitor Discussions - Walk around and monitor the discussionstage. You will frequently hear misunderstandings that you canaddress during the whole-group that discussion that follows.

• Rallyrobin - If students have to list ideas in their discussion, ask themto take turns. (For example, if they are to name all the geometricshapes they see in the room, have them take turns naming the shapes.This allows for more equal participation.) The structure variation nameis Rallyrobin (similar to Rallytable, but kids are talking instead of takingturns writing).

• Randomly Select Students - During the sharing stage at the end, callon students randomly. The first time you do this, expect them to bequite shocked! Most kids don't listen well, and all they know is what

they said! If you keep using this strategy, they will learn to listen totheir partner.

• Math Problem-Solving - Place a complex problem on the overhead Ask students to think about the steps they would use to solve theproblem, but do not let them figure out the actual answer. Withouttelling the answer to the problem, have students discuss theirstrategies for solving the problem. Then let them work out the problemindividually and compare answers.

Benefits of Think-Write-Pair-Share• Think-Write-Pair-Share is easy to use on the spur of the moment.

• Providing "think time" increases quality of student responses.

• Providing “writing time” gives all students time to develop responsesand encourages more thoughtful, fully developed responses.

• Students become actively involved in thinking about the conceptspresented in the lesson.

• Research tells us that we need time to mentally "chew over" new ideasin order to store them in memory. When teachers present too much

information all at once, much of that information is lost. If we givestudents time to "think-write-pair-share" throughout the lesson, moreof the critical information is retained.

• When students talk over new ideas, they are forced to make sense ofthose new ideas in terms of their prior knowledge. Theirmisunderstandings about the topic are often revealed (and resolved)during this discussion stage.

• English language learners are more willing to participate since theydon't feel the peer pressure involved in responding in front of thewhole class.



urning Points Tool

eaching

igh-Level

athematics

o English Language

earners

the Middle Grades

Final Word Adaptations for English Language Learners

BEST PRACTICE:

FINAL WORD

• efficient way to discuss a reading

• provides controlled choice• makes sure all voices are heard

• ensures in-depth discussion ofissues important to group

• provides entry point into discussionfor those who have not been able to

read or absorb entire document• English language learners canchoose the part of the text theyunderstand best.



urning Points Tool

eaching

igh-Level

athematics

o English Language

earners

the Middle Grades


#1 #2

#4 #3

➟

➟

➟ ➟

#4

#1 #2

#3

➟

➟

➟

➟



urning Points Tool

eaching

igh-Level

Mathematics

o English Language

earners

n the Middle Grades


1. Choose a text for students to read and give them time to read.2. Have everyone identify one significant idea or phase from the text. Ma

sure it’s short - one or two sentences.

3. Mark the phrase.4. Think about why you have chosen the phrase. It is a good idea to hav

“back up” phrase, a second choice in case someone else chooses yofirst choice.

5. Get into small groups and have each group choose a facilitator/ timekeeper.

6. 1st person reads his/her phrase, making sure everyone knows where in the text and then has 1 minute (or any other short period of time) to

say why that excerpt struck him or her. Why do they think it isimportant? Or why do they disagree with the excerpt or what importa

issues does it raise for him or her?7. 2nd person says what s/he read 1st person say, responds to the

excerpt briefly .8. Next person in group does the same.9. Person #1, the person who chose the quote and started the discussio

gets the “FINAL WORD.” S/he responds to what the others said anddiscusses what s/he thinks after hearing everyone else discuss theexcerpt.

Continue until everyone gets a chance to share his/her quote, hear the

others in the group respond, and then have the “FINAL WORD.”

Adaptations for English language learners

Give students sentence starters or pattern language to use in discussingtheir excerpt.

I think _____ is important because...

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

(See appendix for additional sentence starters.)

Adaptations for word problems

Instead of a text, choose a word problem for students to read. Eachstudent can choose a phrase or fact in the word problem that s/he thinksimportant for solving the problem.

Remind students to have more than one phrase or fact ready to discuss case another student who goes before has already chosen that phrase.



Numbered Heads

urning Points Tool

eaching

igh-Level

athematics

English Language

earners

the Middle Grades


Adaptations for English Language Learners

BEST PRACTICE:

NUMBERED HEADS ASSESSMENT

STRATEGY

• encourages all students to hold eachother accountable

• encourages all students tocollaborate in creating a thoughtfuland thorough response

• ensures that all students are given achance to respond publicly

• efficient way to check for

understanding with entire class andimmediately address misconceptionsand misunderstandings



Numbered Heads

urning Points Tool

eaching

igh-Level

athematics

o English Language

earners

the Middle Grades



#1 #2

#4 #3

➟

➟

➟

#1 #2

#3#4

➟

➟

➟

Small Group discussion

#4#4

Share out to class

#1#1

All #1s

SHARE

All #4s

SHARE



Numbered Heads

urning Points Tool

eaching

igh-Level

Mathematics

o English Language

earners

n the Middle Grades



Overview

Numbered Heads is a simple and efficient strategy to check for studentunderstanding throughout a lesson so that any misunderstandings orpartial understandings can be immediately addressed. Since errors andmisunderstandings can be flushed out and resolved as soon as theyarise, this formative assessment strategy is a very good strategy forensuring that all students reach mastery of critical mathematical

concepts as quickly and as accurately as possible.Numbered heads also establishes important cultural norms for the mathclassroom: It lets students know that every person in the class iscapable of and will be held accountable for discussing their ownanswers and explanations to the class. It also sends the strong messageto all students that they are all responsible for making sure that theirpartners or team members can adequately explain what the team or pairhas discussed in their group. This supports the actively listening thatthey are required to do throughout the lesson as well as well asencourages them to ask each other good questions, to make sure that

they check for understanding, and that they learn how to develop agood explanation for each response they give.

Numbered heads should be used after students have explored criticalconcepts using think/write/pair/share or other cooperative speaking,

writing and listening strategies. For ELLs, it gives them an opportunity

to rehearse their answers and gain a sense of confidence before

they are required to speak in front of the class as a whole.

p.2

Steps

1. Students number off in teams, one through four.2. Teacher asks a series of questions, one at a time.

3. Students discuss possible answers to each question in theirteams for a set amount of time (30-90 seconds).

4. Teacher calls a number (1-4). All students with that numberraise their hands, ready to respond.

5. Teacher randomly calls on students with specified number toanswer on behalf of their team.

6. Teacher continues asking questions until the brainstorming or

review session is finished.



Numbered Heads

urning Points Tool

eaching

igh-Level

athematics

o English Language

earners

the Middle Grades



Numbered heads does not guarantee, nor should it guarantee, thatstudents be especially perceptive and accurate in their initial responses.

Rather, it gives teachers a clear picture of what and how the students arethinking at the moment they are thinking it.

Once the teacher has that critical data on student understanding, s/hecan ask “just the right question,” redirect the discussion through think/ pair/share of other cooperative learning strategies, provide a new activityto address the misconception or error or any other type of scaffoldingthat will lead to more accurate and mature understanding by thestudents.

Since the strategy provides time for many different students to speak, it

may seem as though it is too slow and cumbersome to use when pacingguides and other directives are the every day facts of life in today’sschools.

However, it paradoxically ensures that students move through thecurriculum at a good speed since the strategy, and all other forms offormative assessment, make sure that when students are in the mathclassroom, they are actually learning important concepts. Time is notwasted later on in the unit or the year when teachers discover thatstudents never really understood the subject matter and precious time isneeded for review.

p.3



Speak/Respond/Question/Respond Adaptations for English Language Learners

Turning Points Tool

Teaching

High-Level

Mathematics

to English Language

Learners

n the Middle Grades


BEST PRACTICE:

RESPONSE/FOLLOW-UP

QUESTION/RESPONSE

• gives English language learnersseveral opportunities to use thelanguage of mathematics

• models a typical discussion forEnglish language learners

• encourages students to go

deeper in understanding theproblem

• provides pattern language asentry points for English languagelearners



Speak/Respond/Question/Respond Turning Points Tool

Teaching

High-Level

Mathematics

to English Language

Learners

n the Middle Grades


I notice that...

SPEAK

RESPOND

I agree because ....

I disagree because...

➟ What else do you notice?

Why do you think that is

important?

QUESTION

It is importa

because...

RESPON

➟

➟



Turning Points Tool to

Teaching

High-Level

Mathematics

to English Language

Learners


© Copyright 2009 Center for Collaborative Education/Turning Po

ADDITIONAL

RESOURCES

• Visual Cues

• Choosing a strategy to solve a

problem

• Giving Directions to English Language Learners

•Using Pattern Language

• Questions to Ask in Math Class

• Sentence Starters to Use in Math Class

• Examples of Organizing Templates/Graphic

Organizers

• Three Essential Lesson Planning Questions

• Best Instructional Practices to Teach High-Leve

Mathematics to English Language Learners*

• Answers to Frequently Asked Questions about

Turning Points Tool

• Additional Resources*

• References* see separate handout



Visual Cuesurning Points Tool

Teaching

High-Level

Mathematics

o English Language

earners

n the Middle Grades


BEST PRACTICE: VISUAL CUES

Easy-to-identify, visual cues •call attention to key points and

critical classroom routines,

•reduce the language load,

•create predictable and easy-to-follow routines, and

•allow English language learnersto participate quickly and activelyin lesson.



Visual CuesTurning Points Tool

Teaching

High-Level

Mathematics

o English Language

Learners

n the Middle Grades


Easy-to-identify, visual cues

• call attention to key points and critical

classroom routines,

• reduce the language load,

• create predictable and easy-to-follow routines,

and

•allow English language learners to participate

quickly and actively in a lesson.

Visual cues can be used

1) when giving directions to English language learners.

For example:

#4#4

All #4s

SHARE

2) as a mnemonic device to remind English languagelearners of important discussion protocols

For example:

3) as a reminder of strategies English language learners can use

to solve problems (see next page)



Draw a picture Make a list, table or cha

!

Use easier numbers Look for a pattern 1, 2, 3

10, 20, 30

Write an equation Work backwards

a2 + b2 = c2

Turning Points Tool

Teaching

High-Level

Mathematics

o English Language

Learners

n the Middle Grades

Visual Cues: Choosing a strategy to solve

problem




urning Points Tool

Teaching

High-Level

Mathematics

o English Language

earners

n the Middle Grades


BEST PRACTICE:

SENTENCE FRAMES/

PATTERN LANGUAGE

•provide a clear scaffold forEnglish language learnerswhich they can use toparticipate in discussions

•are practiced with studentsbefore they are asked to

use them individually•allow students to havesome choice in theirresponses

•encourage higher orderthinking.



GIVING DIRECTIONS toENGLISH LANGUAGE LEARNER


Giving Directions: Supports for ELL students

Provide a general overview of the process, then give the directions one at a time, and only just before thestudents are to do that particular part of the discussion.

Make sure the directions are clear and precise at each stage of the procedure. Reduce language load by using as few words as possible.

Use body language.

Write the steps on the board, emphasizing key words (both nouns and verbs.)

Use symbols or pictures or different colored markers. Don’t crowd the board or the handout. Leave plenty of white space. Speak slowly and enunciate clearly. Model each step of the directions, then ask one or two students to model them for class. Check for

understanding from all students.

Make absolutely sure that students have adequate time to think, plan and carry out the instruction. Useone full minute, timed, as the rule of thumb, for the time needed to think and respond.

Set a purpose for speaking. If the student is a speaker, s/he should know exactly what she is supposed tospeak about, what her audience should gain from her speaking, and what a good contribution sounds like.Model appropriate responses and ask students to list the characteristics of a good response. Check forunderstanding.

Set a purpose for listening. If the students are the listeners, they should be told exactly why they arelistening and what will be expected of them after the speaker finishes. Each student must know exactlywhat s/he is supposed to do and how s/he will be held accountable for doing it well. Model appropriateresponses and ask them to list the characteristics of a good response. Check for understanding.

If students are working in groups, design every role and every group activity so that each student isrequired to really think throughout the time they are in that role. Without that, students are not able tohold meaningful or extended discussions.

Encourage every student to actively participate and structure their roles so that they all must activelyparticipate as speakers, as doers, and as listeners.

Encourage risk taking and collaborative thinking. Tell them explicitly that any thoughtful idea counts as longas each person participates and they all thoughtfully and respectfully consider every response.

Give them the language structure to use in these kinds of discussions. “I agree with you because….” “Ihave another way of thinking about it…. It’s different because…., “etc.

Include a debrief!!! Make sure students are given time to reflect upon what worked and what didn't work,and how you and they can make it better next time. Providing a list of reflective questions helps them learnhow to reflect and demonstrates the difference between telling what happened and reflecting on whathappened.



Here are some important steps to take in introducing pattern language (sentence

starters/sentence frames) to English language learners.

Say the pattern language (sentence starter, phrase, question, etc.)Write the pattern language.

Show students where the phrase appears in the handout.

Have students repeat the phrase in unison.

Model using the pattern language in several different contexts with which they are

already familiar but never introduce it by itself. Always introduce it when it is necessary for the particular rich mathematical discovery on which the students are presently

working.

Ask them to listen for clues about when this phrase is used.

Share those ideas with a partner.

Share them with the class/check for misunderstandings.

Model using it in a few situations when it is appropriate to be used, especially in any

new situations or when introducing new mathematical contexts. Clarify when it is not used.

Ask them to try out the phrase with a partner, each person taking turns.

Ask one person from several pairs to say their phrases outloud/check for understanding.

Require them to use the phrase when it is appropriate, and check that it is being usedappropriately.

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

The following pages show examples of pattern language used in mathematics

classrooms in the middle grades. Copy two or three phrases at a time for

students, never more than a few.

Wait until they master each set, then introduce new ones. Mix up old and new

phrases gradually until their repertoire of phrases becomes larger and larger and

more and more automatic.

INTRODUCINGPATTERN LANGUAGE




QUESTIONS to ASK inMATH CLASS when someone is explaining his/her answer

? ?

? ?

? ?Why do you think that? How do you know that is true?

Why do you think that strategy will work?

Can you explain that in a different way?

Do you see any patterns? Can you describe them?

Will this work with every number? Every similar situation?

What surprised you? Why did that surprise you?

Show us how you did that. Tell us what you did.

You are doing a good job of telling us what you did. Now, can

you explain what you did, tell us why you did each step?

How do you know you have an accurate answer? How can youprove/justify it?

Will this strategy work every time you are trying to figure out aproblem about ___________? When will it work? When won’t it

work?

Can you use a different strategy to figure that out?

Can you give an example to help explain your answer?

What picture, diagram, chart or graph can you show to illustrateyour solution?




SENTENCE STARTERSto USE in MATH CLASS when you are explaining your answer


“... .”

If ..., then...

The ____ is _____ since...

It seems to me that what this ____ really means is .....

It seems to me that what this _____ really is showing is that...

I believe that ...... Consider the following examples: ....

Since .... we know that ..... Also, .... Therefore, we can concludethat....

When computing ...... and ...., I noticed that both _____ had thesame _______, while they had different _______.

We noticed that..... We know that..... Therefore, we can concludethat ...

If the _______ changes, then the _________ changes at the same ______.

If the_______ changes, then the _________ changes at adifferent______.

The number of _____ remains constant, while the number of _______ varies in the following way:...



QUESTIONS to ASK inMATH CLASS when someone is working on a problem

? ?

? ?? ?What do you think you know about this problem? What do youknow for sure?

What questions do you have? What confuses or puzzles you?

Look at the problem carefully. Can you write down everything you noticethat you think might be needed to solve the problem?

In what ways is this problem similar to others we have worked on? Look carefully and notice all the similarities.

In what ways is it different? Look carefully and notice all the differences.

What do you already know about the situation described in this problem?List all of the things you already know about the situation or the math tha

involved.

What else do you notice? Keep looking/thinking.

What strategy will you try to solve this problem? What will be the first st

What is the main question this problem is asking you to figure out?

Are there any words or phrases that are confusing to you, or used in aspecial way in this problem?

Can you draw a picture or create a chart or graph for this problem?

What patterns do you notice? What changes in the pattern and what staythe same?




SENTENCE STARTERSto USE in MATH CLASS when you are working on a problem

“... .”


I know that.... because....

One thing I don’t know is.... or One thing I’m not sure aboutis...

I notice that ..... I wonder/I think that might mean that....

This problem is similar to the ____ problem in the followingways:First,....Next,...Finally,...

This problem is different to the ____ problem in the

following ways:First,....Next,...Finally,...

I am going to try the _______ strategy to solve this problembecause... The first step I will do is to ...



Could you please repeat that?

Will you please explain that again?

Would you mind going over that again a little more slowly?

Can you explain that another way?

I think you are saying.... Is that right?

In other words, you are saying that …

I have a question about that. Do you mean...?

QUESTIONS TO ASKwhen you don’t understand or are not sure you understand

? ?

? ?

? ?




I agree with you because . . .

I disagree with you because . . .

I don't understand, please explain it in a different way.

In other words, you are saying that …

I noticed that...

That reminds me of...

I see a connection to...

You could also ....

I think what they mean is...

I have a uestion about...

RESPONSES when someone is giving their ideas





A certain construction job usually takes four workers six hours

kitchen task any # employees any # minutes

office project cooks days cleaning chefs weeks

painting painters seconds

Today, one worker called in sick, so there are only three workers.Yesterday any # employee didnʼt come therefore only any # employees

cook quit cookschef got another job chefs

painter painters For example:Today, two employees didnʼt come, therefore there are only four cooks.

How long should it take them to do the job?will finish task

complete project

For example:How long will it take them to finish the project?

SCAFFOLDINGstudent responses/gaining fluency in reading andunderstanding the language of word problems

Student created problem: A certain kitchen project usually takes six cooks an hour.Today, two employees didnʼt come, therefore there are only four cooks. How longshould it take to finish the project?

• Start with original problem (in bold).• Provide appropriate alternative choices.

• Model how to make a similar but different problem, using the choices provided.

• Have students orally practice creating several different choices until they gain fluency.

• By doing this process with many different word problems, students will be able to

recognize the way such problems use language in test situations and textbooks.



Draw a picture Make a list, table or chart

!

Use easier numbers Look for a pattern 1, 2, 310, 20, 30

Write an equation Work backwards

a2 + b2 = c2

CHOOSE a STRATEGY to solve a problem




urning Points Tool

Teaching

High-Level

Mathematics

o English Language

earners

n the Middle Grades


BEST PRACTICE:

PROVIDING an ORGANIZING

TEMPLATE/GRAPHIC

ORGANIZER

•saves time

•focuses English languagelearners’ attention on themathematical concepts ratherthan copying in a new language

• models how to organizeinformation

•provides clear way students canorganize information

•creates expectations about # andquality of responses



urning Points Tool

Teaching

High-Level

Mathematics

o English Language

earners

n the Middle Grades


How the teacher structures thelesson to encourage

discussion among all students

How the English language

learners use language to talk

about the mathematical

concepts in the lesson

Organizing Template/Graphic Organizer

Example: Double Entry Journal



Date: ______________________________

Best instructional practice for English language learners on whicham working:

________________________________________________________

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 my

students’ depth of understanding and engagemen

Content

Instruction

Handout 1-25

Turning Points Tool

Teaching

High-Level

Mathematics

to English Language

Learners


© Enid Lee Consultants www.enidlee.com/modified by Center forCollaborative Education/Turning Points

http://www.enidlee.com/modified





urning Points Tool

Teaching

High-Level

Mathematics

o English Language

earners

n the Middle Grades


Three Essential Lesson Planning Questio

1. How does this lesson ensure that Englishlanguage learners are engaged in high-level mathematics:• solving challenging problems,• using mathematical reasoning, and• explaining their thinking?

2. How does this lesson ensure that all English language learners are engaged atall times throughout the lesson?

3. How does this lesson support Englishlanguage learners learning mathematics in

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



Answers to Frequently AskedQuestions


Why does the tool focus on high-level mathematics for English language learners?

Mastering high-level middle grades mathematics is critical to the life chances of all students. Middle gradtudents who do not understand and cannot apply the basic concepts of middle grades mathematics to

wide range of situations are at great risk of dropping out of high school, not attending college, and beingnemployed or underemployed throughout their adult lives.

ar too many of these students are English language learners.

his tool is designed to help math teachers in the middle grades provide English language learners with tpportunities all students deserve: access to and support in successfully learning high-level mathematics

nd the critical life skills and opportunities it provides.

ow does this tool define “high-level mathematics in the middle grades”?

earning and mastering high-level mathematics in the middle grades, as defined in the tool, includes theollowing characteristics:

• Complex challenges, multi-step problems allowing for more than one solution path, different strategdifferent entry points for different students

• Believable contexts that illustrate how mathematics is useful in everyday life, in science, in businesand students’ communities and families

• Collaborative work with other students, where all students are accountable for what the group (smaworking group or the whole class) is learning

•

“Meaty” problems that encourage discussing the reasons for different approaches, stating andclarifying ideas, developing academic language to describe the problem, solution strategies andresults, and confronting gaps in one’s thinking

• Ways to organize information and look for patterns• Explaining – so other students can understand – how they solved (or are solving a problem) and ho

they know when their answers make sense.

igh-level mathematics in the middle grades emphasizes mathematics as a process in mathematical

easoning, a process in which students are engaged in understanding and accurately applying the criticaoncepts of middle school mathematics identified by the National Council of Teachers of MathematicsNCTM).

igh-level middle school mathematics problems are challenging for middle grades students. Students wn groups on problems that are slightly—but not too far—out of their comfort zone. Students make their olans for how to proceed, and are required to explain their discoveries and their process through speakinnd writing – and most important, to defend their methods and conclusions.

Another term used in this tool and by researchers (Smith and Stein) to describe the work students do in

uch classrooms is “doing mathematics.” This term was coined to distinguish high-level mathematics frote learning and/or following formulas to solve problems that research has shown is used in manyassrooms throughout the United States, including those that enroll English language learners.



Answers to Frequently AskedQuestions (continued)


How is “high-level mathematics” different from “mathematics” in the middle grades? Aren’t they t

ame?

The goals listed above for “high-level” mathematics have always been among the goals of mathematicsducation, but “traditional” mathematics education has often put them in separate compartments, based o

he premise that students must master basic skills and algorithms by rote before they can apply them tohallenging problems. The result—most students learn to think of mathematics as a series of unrelated sk

with no rhyme or reason, no connection to their own lives.

n addition, recent research has indicated that many teachers routinely lower the cognitive demand of roblems as initially presented in textbooks, especially those specifically funded by the National Science

Foundation to emphasize a constructive approach to learning mathematics (Smith and Stein). For exampeachers may tell students the steps they should take to solve a problem or give them algorithms or tricks each an answer without helping students develop their own understanding of how and why certain strate

work and what strategies are also possible.

What are the characteristics of teaching high-level mathematics to English language learners?

Teachers who support English language learners, and all other students, to learn high-level mathematics ctive through every step of the learning process; not by telling the students what to do or giving them thenswers but by planning lessons that pose rich mathematical questions, by asking just the right questionsstening carefully to their students’ responses, by redirecting their focus when misconceptions or

misdirections surface, by presenting students with interesting challenges, by offering them a range of materials they can use to solve problems and by requiring students to explain their thinking throughout theesson. Teachers encourage students to actively participate in mathematics lessons by introducing andracticing the language structures and vocabulary they need to do so and making sure they use themonsistently throughout every lesson.

Please see Best Instructional Practices for Teaching High-Level Mathematics to English Language

Learners included in the Participant’s Packet to Workshop 1 and Facilitator’s Guide to the Workshop Seor a fully developed description of the characteristics.

How is this approach to teaching mathematics particular for middle grades students?Middle grades students seek challenges and a chance to express their own ideas. Teaching high-levelmathematics to English language learners, and all other students in the middle grades, takes advantage hese key developmental traits of adolescence. Lessons that focus on high-level mathematics build in thraits by requiring all studentsto choose a method for solving a problem,to discuss these choices with peers,to come up with workable and provable solutions that everyone can agree upon and everyone canexplain with accuracy and clarity andto apply this new knowledge to real life solutions that are meaningful to them and importantto the community at large.





ren’t these the same strategies and approaches that are successful with all students? Are there

ny strategies that are unique to English language learners?

l middle grades students need the kind of support outlined above in order to learn the language ofathematics and master high-level mathematics. The strategies listed above can and should be usedith middle grades students in general.

here are some challenges, however, that are unique to English language learners. Mastering middle

rades mathematics means beginning to learn how to think as mathematicians. Thinking requires talking

stening, responding, reflecting and rethinking; it is by is nature language based . Middle grades studentseed support in mastering the language of mathematics, which is essentially a foreign language to almos

very student who enters a math classroom.

eachers, however, need to be especially vigilant in planning lessons for English language learners sinceese students are learning not just the language of mathematics but English as well. Teachers need to

sten to and talk to English language learners in ways that take into consideration the specific anddividual language and cultural needs of each language learner. They need to make sure that everynglish language learner learns how to express himself/herself so that they can actively participate in thessons and develop the thinking strategies they need to master high-level mathematics.

his tool provides many different strategies that provide support so that a broad range of Englishnguage learners have access to and master high-level mathematics. This tool also provides information

nd encourages teachers to learn how to identify and access the needs of the individual English languagearners in their own classrooms and design individualized support for them throughout their lessons.

See the reading “Learning the Language of Mathematics in the Middle Grades” in the Participant’sacket and the Facilitator’s Guide to Workshop 1 for a detailed discussion of the important languagesues English language learners face in mathematics classrooms.)

oes this tool address the needs of English language learners who enter middle grades without

astery of basic computational skills?

nglish language learners, as well as native speakers of English, are very divergent in terms of theirastery of computational skills and mathematical facts. All of the strategies in this tool have been used inassrooms with English language learners entering with a great range of facility in mathematical andomputational understanding and knowledge.

his tool focuses on providing all of these students with access to high-level mathematics in the middlerades, whether or not they are weak in computational skills and their knowledge of mathematical facts.his tool is designed therefore not to supplant support in these areas but to ensure that all Englishnguage learners are provided the opportunity to learn the high-level middle grades mathematics theyeed to move forward in school.





nglish language learners are a highly diverse group. Is access to high-level mathematics featured

e tool addressed to a particular group or level of English language acquisition?

his tool is designed to provide access to a broad range of English language learners from who enter theassroom in the beginning levels of English language acquisition to those in more advanced levels. Therategies demonstrate how to use the diversity of students’ background knowledge, language of origin, aays in which they were taught mathematics.

he laws and regulations governing the teaching and assessment of English language learners diff

om state to state. Is the tool designed to work in a particular state or group of states?

his tool does not take a stand on any of the laws and regulations governing the teaching and assessmennglish language learners. It can be used in a broad variety of classroom settings, including bilingual, ESLnd SIOP settings.

the tool designed to be used with a specific textbook?

his tool is designed to be used with a broad range of textbooks and has been used in settings which usefferent types of texts. The approaches modeled by the tool are effective in any middle grade mathematiassroom in which English language learners are enrolled.

oes the tool follow a particular model of training such as SIOP (Sheltered Instruction Operational

rotocol) or CALLA (Cognitive Academic Language Learning Approach)?

his tool integrates the knowledge base and experience of a broad range of research based approachesuccessful in teaching English language learners, including SIOP and CALLA, as well as those that arefective in teaching high-level mathematics to middle grades students. Please see the reference andsearch section for further information.

hy is so much time devoted in the workshop series and in the model lessons to language based

ctivities - talking, listening, writing and responding?

iddle grades students need careful and continuous support as they move from the basic computation a

ithmetic of elementary school to the more complex topics of the middle grades: ratios and proportion,

eometry, graphing and data analysis, functions and algebra. They also need explicit instruction in learnin

nd using the language of mathematics; without facility in that language they are unable to discuss, proce

nd understand the concepts of middle grades mathematics and beyond. Providing such support is

specially critical for English language learners learning high-level mathematics.





Clearly, this requires that English language learners have multiple and repeated opportunities to hear,

epeat, and try out their thinking - in a language that is new to them. All of the strategies in the

workshop are designed to provide these opportunities in multiple ways so that English language

earners have the critical support they need to succeed in mathematics in the middle grades.


he workshop series makes extensive use of discussion protocols. These protocols are carefully

tructured to ensure that all English language learners become active and engaged participants

hroughout the math lesson. As in all protocols, it is essential to follow each step of the protocol withdelity so that every student gains the depth of understanding built into each activity and has the time

o contribute actively with other students. The facilitator guides the use of the protocol and adjusts the

ming of each step to meet the needs of the group.



Additional Resources


•Adler, J. B. (2001) Teaching Mathematics in the Multilingual Classroom. Series: Mathematics Education

Library, Vol. 26

• Burns, M. (1990). A Collection of Math Lessons Grades 6‐8. Math Solutions

• Burns, M. (1995). Writing in Math Class. Math Solutions

• Burns, M. (2006) Marilyn Burns on the Language of Mathematics. Instructor Magazine

•Coggins, D., Kraven, D., Coates, G.D. and Carroll, M.D. (2007) English language learners in the mathematics

classroom. Corwin Press.

•Evans, Linda. Building Background ‐ Beneits of Using Sentence Frames to Build Background Knowledge.

http://EzineArticles.com/?expert=Linda_L_Evans

•Heinze, L. (2005). The Language of Mathematics. Presentation at TESOL Conference. http://kathrynheinze.efoliomn2.comhttp://kathrynheinze.efoliomn2.com

• Irujo, Suzanne. (November/December 2007). Putting it All Together: Integrating Academic Math Language

into Math Teaching. The ELL Outlook (online resource)

•Irujo, Suzanne. (March/April 2007). Teaching Math to English Language Learners: Can Research Help? The

ELL Outlook (online resource)

•Irujo, Suzanne. (May/June 2007) So Just What is the Academic Language of Mathematics? The ELL Outlook

(online resource)

•Moschkovich, J. N. Understanding the needs of Latino students in reform‐oriented mathematics classrooms.

In L. Ortiz‐Franco, N. Hernandez, and Y. De La Cruz (Eds.), Changing the Faces of Mathematics (Vol. 4):

Perspectives on Latinos. Reston, VA:NCTM, 5‐12.

•National Council of La Raza (2005) Educating English Language Learners: Implementing Instructional

Practices.

•Slavit, D. and Ernst‐Slavit, G. (2007). Teaching Mathematics and English to English Language Learners

Simultaneously. Middle School Journal, November 2007. Volume 39. Number 2. Pages 4‐11.

•West Ed (2008). Helping English Language Learners acquire the language of mathematics. R&D Alert, Vol, 9No.1, 2008.

•www.ncela.gwu.edu/iles/uploads/3/mathforELLs.pdf

Selected Resources

http://www.ncela.gwu.edu/files/uploads/3/mathforELLs.pd

http://kathryn/

http://kathryn/

http://ezinearticles.com/?expert=Linda_L_Evans



http://kathryn/

http://kathryn/

http://kathryn/

http://kathryn/

http://kathryn/

http://kathryn/





References


•August, S. (2006). Developing Literacy in Second‐Language Learners: Report of the National Literacy Panel

Language‐Minority Children and Youth. Center for Applied Linguistics.

•Brown, C. (2005) Equity of Literacy‐Based Math Performance Assessments for English Language Learners.

http://brj.asu.edu/content/vol29_no2/art5.pdf

• Bruner, J. (1966) Process of Education. Harvard University Press.

•Celeson‐Pattichis, S. (2009) Research Findings Involving English Language Learners and Implications for

Mathematics Teachers. NCTM•Council of Great City Schools. (2003) English Language Learners in the Great City Schools: Survey Results o

Students, Languages and Programs.

•Dolan, S. (2009). Missing Out: Latino Students in America’s Schools. National Council of La Raza.

• Francis. D. (2006). Practical Guidelines for the Education of English Language Learners. LEP Partnership

Meeting Presentation.

• Francis. D. and Rivera, M. (2006). Research‐Based Recommendations for Serving Adolescent Newcomers.

Center of Instruction.

•Heller, R. and Greenleaf, C. (2007). Literacy Instruction in the Content Areas. Alliance for Excellent Educatio

• Kieffer, M., Lesaux, N. & Snow. C. (2008) Promises and Pitfalls: Implications of No Child Left Behind forDeining, Assessing, and Serving English Language Learners. The Regents of the University of California.

•Learning, Institute for. High-Level Algebra and Geometry Tasks: Resources for Both Student and Teacher Learni

Connexions. 2 Apr. 2008 <http://cnx.org/content/m15958/1.2/ >.

•Moschkovich, J. N. Understanding the needs of Latino students in reform‐oriented mathematics classrooms

In L. Ortiz‐Franco, N. Hernandez, and Y. De La Cruz (Eds.), Changing the Faces of Mathematics (Vol. 4):

Perspectives on Latinos. Reston, VA:NCTM, 5‐12.

•National Council of Teachers of English. (2008). ELL Research Brief

• Robertson, Kristina.(2009). Math Instruction for English Language Learners. http://www.colorincolorado.org.

•Slavit, D. and Ernst‐Slavit, G. (2007). Teaching Mathematics and English to English Language LearnersSimultaneously. Middle School Journal, November 2007. Volume 39. Number 2. Pages 4‐11.

Stein, M.K., Smith, M.S., Henningsen, M., & Silver, E.A. (2000). Implementing Standards-based Mathematics

Instruction: ACasebook for Professional Development. Second Edition. New York: Teachers College Press.

Vialpando, J. and Yedlin, J. (2005) Educating English Language Learners: Implementing Instructional Practices.

National Council of La Raza.

Walqui, A.( 2006). Scaffolding instruction for English Language Learners: A Conceptual Framework. Internationa

Journal of Bilingual Education and Bilingualism 9(2),159-180.

Selected References

http://cnx.org/content/m15958/1.2/








For additional information

contact:

Dr. Sara Freedman, Project [email protected]



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