Facilitators Guide to the Workshop Series

Transcription

FACILITATOR’S
GUIDE
to
WORKSHOP SERIES
© Copyright 2009 Center for Collaborative Education/Turning Points
Teaching High‐Level Mathema2cs to English Language Learners in the Middle Grades was developed by Turning Points, a project at the Center for Collabora;ve Educa;on in Boston, MA. This tool is part of the Mathema2cs Improvement Toolkit, a project of the Na;onal Forum to Accelerate Middle Grades Reform, and was supported by the U.S. Department of Educa;on’s Comprehensive School Reform Ini;a;ve, grant #S332B060005. Opinions expressed are those of the authors and are not necessarily those of the Department. © Copyright 2009 Center for Collaborative Education/Turning Points
Prepared for
Turning Points
by
Dr. Sara Freedman, Project director
Dr. Dan Lynn Watt, Math consultant
Table of Contents
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
in the MIddle Grades
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 to
Facilitators and Math Teams
General Overview
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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.
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 conceptual
understanding
• 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.
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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-level
mathematics.
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 support
English language learners to
•
Work in small groups, taking turns to explain and clarify their thinking;
•
Ask each other questions to help develop accurate and complete
explanations;
•
Use mathematical vocabulary and syntax to discuss mathematical
concepts 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 makes
sense.
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 highlevel mathematics before being enrolled in these classrooms to those who
entered 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.
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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 English
language learners;

Concrete resources for planning math lessons that incorporate these
practices;

Multiple video examples of best practices for English language learners as
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 language
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' prior
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.
Resources provided include:
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners

An annotated facilitator’s guide for each workshop;

A PowerPoint presentation for each workshop;

Video examples of middle grades teachers using best practices to
teach high-level mathematics to English language learners;

Video examples of English language learners discussing
mathematics;

Math problems for teachers to solve and analyze;

Model lesson plans that incorporate the linguistic, cultural and
content-based needs of English language learners to teach highlevel mathematics in the middle grades;

Multiple ways to assess English language learners’ understanding of
key 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 as
springboards for teacher discussion

Resources and references that can be used to supplement the
workshop series.
Intended Audience
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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 home
countries 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 teaching
mathematics to middle school and high school English language
learners;

Math department chairs in middle schools and high schools; and

Central office math curriculum coordinators.
Logistics
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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
Layout of Facilitatorsʼ Notes
for Each Slide
☛
☟
Handout for slide
ACTION
Suggested
actions to take
☚
☟
Number of slide
Picture of slide
TALKING POINTS
This is where you will
find TALKING POINTS
to use with each slide.
As the facilitator, you can decide
when to change each slide and when
to change the text of each slide. The
ACTION section leaves the pacing of
each slide to the discretion of the
facilitator.
☚
SLIDE 1
How to Implement
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
Who should facilitate this tool?
This tool should be facilitated by a team consisting of an experienced teacher of
English language learners and an experienced math teacher, math coach, or math
curriculum specialist. Having co-facilitators, one with experience in teaching
mathematics and one with experience in teaching English language learners, will
ensure that both aspects of teaching mathematics to English language learners –
the math and the language and cultural issues – will be addressed thoroughly. The
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 two 6‐
hour 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 - try
out these practices in their classrooms on a regular basis, observe each other as
they practice new approaches, debrief their practice publicly, and continue to
refine and improve their teaching – we suggest that the workshops be scheduled
several weeks apart.
How do facilitators prepare to lead the workshops?
Each workshop has an extensive facilitator's guide, which includes talking points
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 preparation
should include a first review, second more in depth review and a final review to get
everything ready. Facilitators will also want to familiarize themselves with the
Participant’s Packet, which includes many resources teachers can use with their
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 critical
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 make
sure that all the elements including the video and sound are functioning properly.
To what extent should facilitators follow the time suggestions for each
activity found in the facilitator’s guide?
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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. We
encourage facilitators to use their experience as teachers, coaches and workshop
presenters and adjust to the needs of the group.
It 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 the
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 (often
from 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 is
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 section
within the slide and practice doing so before each workshop. Each slide is different
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 the
slides?
Facilitators can
•read the slides themselves, deciding on the pacing of each slide and section or
•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 is
written on the slide, with any additions that facilitators feel would help clarify what
participants need to do. The text for directions is written as a model of how to give
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 for
successfully teaching mathematics to English language learners.)
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
How should facilitators use the TALKING POINTS for each slide that appear in
the facilitators’ guide?
The TALKING POINTS in the facilitators’ guide provide a script that facilitators’ can
use as they display each slide. They include a number of key points that are not
found in the text of the slide itself, as well as more explicit directions participants
will need to follow for a particular activity.
We encourage facilitators to adapt the TALKING POINTS to fit their own style of
speaking if they wish to do so while incorporating their key points. Avoid simply
reading through the slides or the TALKING POINTS - practice walking through the
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 made
with 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 - to
create 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.
Why is so much time devoted in the workshop series to discussion?
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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 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 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.
For many teachers, this represents a paradigm shift in their own understanding of
how to teach mathematics and the kind of mathematical reasoning required for
success 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 likely
to 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 are the directions for discussions so explicit and exact?
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. Saying “Turn to your partner and talk” does not do
the job! The facilitators should guide the use of the protocol and adjust the timing
and guidelines as needed by the group.
The Participant’s Packet has a handout that provides guidance on giving directions
to English language learners.
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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 highlevel 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 English language
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.
It is our experience that some teachers may take a good bit of time to be
comfortable writing but that with patience, with time and with persistence they will
all do so - and use writing regularly in their own classrooms with English language
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. Suggestions
for 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 what
students are saying so that they, and every other student in the class, has
equal access to the information and can contribute to that information.
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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 HighLevel Mathematics to English Language Learners in the Middle Grades.
Please send us your comments on the tool so that we can continue to improve
it and make it available to schools and teachers throughout the country.
Please email sfreedman@ccebos.org 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 attended
the workshop: type of school, subject area and grades of teachers, number
of participants attending, role of facilitator in district or school, % of English
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
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
Ways to Sustain the Work
between and
After the Workshops
Abundant research has demonstrated that one or two day workshops do not,
by themselves, change teacher practice. The real work comes when teachers
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 approach
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.
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
Answers to Frequently Asked
Questions
Does this tool address the needs of English language learners who enter
middle grades without mastery of basic computational skills?
English language learners, as well as native speakers of English, are very
divergent in terms of their mastery of computational skills and mathematical
facts. All of the strategies have been used in classrooms with English language
learners entering with a great range of facility in mathematical and
computational understanding and knowledge.
This tool focuses on providing all of these students with assess to high-level
mathematics in the middle grades, whether or not they are weak in
computational skills and their knowledge of mathematical facts. The tool is
designed therefore not to supplant support in these areas but to ensure that all
English language learners are provided the opportunity to learn the high-level
middle grades mathematics they need to move forward in school.
English language learners are a highly diverse group. Is access to highlevel 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 language
learners from those in the beginning levels of English language acquisition to
those in more advanced levels and entering speaking many different languages
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 to
work in a particular state or group of states?
The tool does not take a stand on any of the laws and regulations governing the
teaching and assessment of English language learners. It can be used in a
broad variety of classroom settings, including bilingual, ESL and SIOP settings.
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 been
used in settings which use different types of texts. The approaches modeled by
the tool are effective in any middle grade mathematics classroom in which
English language learners are enrolled.
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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 of
research based approaches successful in teaching English language learners,
including SIOP and CALLA, as well as those that are effective in teaching highlevel 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 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
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.
There is a far amount of writing in the workshops. Why?
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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 English
language 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 are
saying so that they can, and every other student in the class, has equal
access to the information and can contribute to that information.
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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 indistrict 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 sfreedman@ccebos.org if you are interested
in pursuing this type of support.
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
in the Middle Grades
PROTOCOLS
USED IN
WORKSHOP 1*
DISCUSSION PROTOCOLS
Think/Write/Pair/Share
Final Word
Numbered Heads
Speak/Respond/Follow-up
Question/Respond
* Protocols originally developed by
National School Reform Faculty
www.nsrfharmony.org
and
Project Zero
www.pzharvard.edu
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
BEST PRACTICE:
USE DISCUSSION PROTOCOLS
Discussion protocols are designed
•to provide clear guidelines and
expectations for class discussions
that are accessible to all students,
•to ensure that English language
learners have the time they need to
process what they hear and
formulate their ideas in a new
language,
•to make sure that all students,
including English language
learners, are equal contributors to
the discussion as speakers and
listeners, and
•to allow for alternative ways of
thinking 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 learners
entry points to every lesson
•All “big ideas” in
mathematics can be linked
to the prior knowledge of
all English language
learners
•Open ended, higher order
thinking questions are
excellent ways of
accessing this knowledge
Think/Pair/Share
Adaptations for English Language Learners
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
Think
Write
Pair
Share
✎
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
Simplified Steps
1.
Announce a discussion topic, one that is meaty enough for a good, rich
discussion.
2.
Give THINK time. Give WRITING time.
3.
Ask students to PAIR with an assigned partner to discuss their ideas. At
times, PAIR English language learners with other English language
learners so that they can participate no matter what their lalevel of
English.
4.
Call on students to SHARE their ideas with the class.
Steps of Think-Write-Pair-Share
1.
Have students sit in pairs. Ask all #1s to raise their hands, check to
make sure every pair has a hand raised, then ask for all #2, check to
make sure every pair has a hand raised.
2.
Announce a rich discussion topic or problem to solve. (Example: Which
room in our school is larger, the cafeteria or the gymnasium and how
could 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 up
significantly when you allow "think time.") Give them another 30
seconds to WRITE their responses - long enough to write but not too
long that the pace slows down. Encourage them to come up with
several responses.
4.
Ask students to PAIR with their partner to discuss the topic or solution.
Direct all #1s that they have one full minute (adjust the time to the
complexity of the question) to tell their partner the answer to the posed
question, 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 is
given one minute to tell #1 how s/he answered the question. #1 listens
quietly the entire time, recalling what s/he heard in the next 30 seconds.
5.
#1 then responds to the comments of #2, using sentence stems such
as “I agree because….”
“I disagree because….” I wonder …..” “ Do you think that …?” “Could
you explain ….. to me. That isn’t clear to me. “ #2 responds to #1’s
comments, then has 30 seconds to ask her/his own questions to #1’s
comments.
6.
Finally, randomly call on a few students to SHARE their ideas with the
class.
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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 of
equity and inclusiveness in classrooms. It’s particularly useful for English
language learners as it gives them a chance to try out their thinking and
practice talking over an idea in a safe structure before they speak to the
entire class. It can be used throughout a class, especially when only a
few students raise their hands in response to a question or when it is
clear that students need a chance to explore a topic before speaking in
front of the entire class.
The structure is extremely versatile but is particularly suited for
generating higher order thinking. The steps are simple, but it's important
to follow the steps exactly to avoid the "groupwork" pitfalls. Sometimes
teachers are tempted to skip some steps and just say, "Turn to a partner
and talk it over." Read on to find out why those words don't necessarily
result thoughtful responses from each student or an equitable classroom
culture.
Before you ask students to use think/write/pair/share on their own, make
sure you model it for students, telling them exactly what step you are
modeling 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 than
just saying "Turn to a partner and talk it over." When you don't assign
partners, students frequently turn to the most popular student and
leave the other person out. You may want to pair an English language
learner with another English language learner or with a native speaker
of English, depending upon the situation.
•
Change Partners - Switch the discussion partners frequently. With
students seated in teams, they can pair with the person beside them
for one discussion and the person across from them for the next
discussion.
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
•
Monitor Discussions - Walk around and monitor the discussion
stage. You will frequently hear misunderstandings that you can
address during the whole-group that discussion that follows.
•
Rallyrobin - If students have to list ideas in their discussion, ask them
to take turns. (For example, if they are to name all the geometric
shapes they see in the room, have them take turns naming the shapes.
This allows for more equal participation.) The structure variation name
is Rallyrobin (similar to Rallytable, but kids are talking instead of taking
turns writing).
•
Randomly Select Students - During the sharing stage at the end, call
on students randomly. The first time you do this, expect them to be
quite 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 to
their partner.
•
Math Problem-Solving - Place a complex problem on the overhead
Ask students to think about the steps they would use to solve the
problem, but do not let them figure out the actual answer. Without
telling the answer to the problem, have students discuss their
strategies for solving the problem. Then let them work out the problem
individually 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 responses
and encourages more thoughtful, fully developed responses.
•
Students become actively involved in thinking about the concepts
presented in the lesson.
•
Research tells us that we need time to mentally "chew over" new ideas
in order to store them in memory. When teachers present too much
information all at once, much of that information is lost. If we give
students time to "think-write-pair-share" throughout the lesson, more
of the critical information is retained.
•
When students talk over new ideas, they are forced to make sense of
those new ideas in terms of their prior knowledge. Their
misunderstandings about the topic are often revealed (and resolved)
during this discussion stage.
•
English language learners are more willing to participate since they
don't feel the peer pressure involved in responding in front of the
whole class.
Final Word
Turning Points Tool
Teaching
High-Level
Mathematics
to 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 of
issues important to group
• provides entry point into discussion
for those who have not been able to
read or absorb entire document
• English language learners can
choose the part of the text they
understand best.
Final Word
#1
#2
➟
➟
➟
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
➟
#4
#3
#1
➟
#2
➟
➟
➟
#4
#3
Final Word
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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. Make
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 have a
“back up” phrase, a second choice in case someone else chooses your
first 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 it is
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 is
important? Or why do they disagree with the excerpt or what important
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 discussion,
gets the “FINAL WORD.” S/he responds to what the others said and
discusses what s/he thinks after hearing everyone else discuss the
excerpt.
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 discussing
their 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. Each
student can choose a phrase or fact in the word problem that s/he thinks is
important for solving the problem.
Remind students to have more than one phrase or fact ready to discuss in
case another student who goes before has already chosen that phrase.
Numbered Heads
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
BEST PRACTICE:
NUMBERED HEADS ASSESSMENT
STRATEGY
• encourages all students to hold each
other accountable
• encourages all students to
collaborate in creating a thoughtful
and thorough response
• ensures that all students are given a
chance to respond publicly
• efficient way to check for
understanding with entire class and
immediately address misconceptions
and misunderstandings
Numbered Heads
Small Group
discussion
#1
#2
#1
➟
#2
➟
➟
➟
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
➟
#4
#4
#3
➟
#4
#4
#1
#1
#3
All #4s
SHARE
Share
out to class
All #1s
SHARE
Numbered Heads
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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 their
teams for a set amount of time (30-90 seconds).
4. Teacher calls a number (1-4). All students with that number
raise their hands, ready to respond.
5. Teacher randomly calls on students with specified number to
answer on behalf of their team.
6. Teacher continues asking questions until the brainstorming or
review session is finished.
Overview
Numbered Heads is a simple and efficient strategy to check for student
understanding throughout a lesson so that any misunderstandings or
partial understandings can be immediately addressed. Since errors and
misunderstandings can be flushed out and resolved as soon as they
arise, this formative assessment strategy is a very good strategy for
ensuring 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 math
classroom: It lets students know that every person in the class is
capable of and will be held accountable for discussing their own
answers and explanations to the class. It also sends the strong message
to all students that they are all responsible for making sure that their
partners or team members can adequately explain what the team or pair
has discussed in their group. This supports the actively listening that
they are required to do throughout the lesson as well as well as
encourages them to ask each other good questions, to make sure that
they check for understanding, and that they learn how to develop a
good explanation for each response they give.
Numbered heads should be used after students have explored critical
concepts 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.
Numbered Heads
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
p.3
Numbered heads does not guarantee, nor should it guarantee, that
students be especially perceptive and accurate in their initial responses.
Rather, it gives teachers a clear picture of what and how the students are
thinking at the moment they are thinking it.
Once the teacher has that critical data on student understanding, s/he
can ask “just the right question,” redirect the discussion through think/
pair/share of other cooperative learning strategies, provide a new activity
to address the misconception or error or any other type of scaffolding
that will lead to more accurate and mature understanding by the
students.
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 pacing
guides and other directives are the every day facts of life in today’s
schools.
However, it paradoxically ensures that students move through the
curriculum at a good speed since the strategy, and all other forms of
formative assessment, make sure that when students are in the math
classroom, they are actually learning important concepts. Time is not
wasted later on in the unit or the year when teachers discover that
students never really understood the subject matter and precious time is
needed for review.
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
Speak/Respond/Question/Respond
BEST PRACTICE:
RESPONSE/FOLLOW-UP
QUESTION/RESPONSE
• gives English language learners
several opportunities to use the
language of mathematics
• models a typical discussion for
• encourages students to go
deeper in understanding the
problem
• provides pattern language as
entry points for English language
learners
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
Speak/Respond/Question/Respond
➟
SPEAK
I notice that...
➟
RESPOND
I agree because ....
I disagree because...
QUESTION
➟
What else do you notice?
Why do you think that is
important?
RESPOND
It is important
because...
Turning Points Tool to
Teaching
High-Level
Mathematics
to English Language
Learners
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-Level
Mathematics to English Language Learners*
• Answers to Frequently Asked Questions about
Turning Points Tool
• Additional Resources*
• References
* see separate handout
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
Visual Cues
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-tofollow routines, and
•allow English language learners
to participate quickly and actively
in lesson.
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
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 learners to participate
quickly and actively in a lesson.
Visual cues can be used
1) when giving directions to English language learners.
#4
For example:
#4
All #4s
SHARE
2) as a mnemonic device to remind English language
learners of important discussion protocols
For example:
3) as a reminder of strategies English language learners can use
to solve problems (see next page)
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
Visual Cues: Choosing a strategy to solve a
problem
Draw a picture
Make a list, table or chart
!
Use easier numbers 1, 2, 3
10, 20, 30
Write an equation
a2 + b2 = c2
Look for a pattern
Work backwards
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
BEST PRACTICE:
SENTENCE FRAMES/
PATTERN LANGUAGE
•provide a clear scaffold for
which they can use to
participate in discussions
•are practiced with students
before they are asked to
use them individually
•allow students to have
some choice in their
responses
•encourage higher order
thinking.
GIVING DIRECTIONS to
ENGLISH LANGUAGE LEARNERS
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 the
students 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. Use
one 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 to
speak 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 for
understanding.
Set a purpose for listening. If the students are the listeners, they should be told exactly why they are
listening and what will be expected of them after the speaker finishes. Each student must know exactly
what s/he is supposed to do and how s/he will be held accountable for doing it well. Model appropriate
responses 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 is
required to really think throughout the time they are in that role. Without that, students are not able to
hold meaningful or extended discussions.
Encourage every student to actively participate and structure their roles so that they all must actively
participate as speakers, as doers, and as listeners.
Encourage risk taking and collaborative thinking. Tell them explicitly that any thoughtful idea counts as long
as 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….” “I
have 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 learn
how to reflect and demonstrates the difference between telling what happened and reflecting on what
happened.
INTRODUCING
PATTERN LANGUAGE
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 used
appropriately.
************************************************************************************************
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.
QUESTIONS to ASK in
MATH 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 you
prove/justify it?
Will this strategy work every time you are trying to figure out a
problem 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 illustrate
your solution?
SENTENCE STARTERS
to 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 conclude
that....
When computing ...... and ...., I noticed that both _____ had the
same _______, while they had different _______.
We noticed that..... We know that..... Therefore, we can conclude
that ...
If the _______ changes, then the _________ changes at the same
______.
If the_______ changes, then the _________ changes at a
different______.
The number of _____ remains constant, while the number of
_______ varies in the following way:...
QUESTIONS to ASK in
MATH CLASS
when someone is working on a problem
??
??
??
What do you think you know about this problem? What do you
know for sure?
What questions do you have? What confuses or puzzles you?
Look at the problem carefully. Can you write down everything you notice
that 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 that is
involved.
What else do you notice? Keep looking/thinking.
What strategy will you try to solve this problem? What will be the first step?
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 a
special 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 stays
the same?
SENTENCE STARTERS
to 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 about
is...
I notice that ..... I wonder/I think that might mean that....
This problem is similar to the ____ problem in the following
ways:
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 problem
because... The first step I will do is to ...
QUESTIONS TO ASK
when you don’t understand or are not sure you understand
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...?
??
??
??
RESPONSES
when someone is giving their ideas
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 question about...
SCAFFOLDING
student responses/gaining fluency in reading and
understanding the language of word problems
• 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.
A certain construction job
usually takes four
kitchen task any #
office
project cleaning painting
Today,
Yesterday
one worker
any # employee
cook
chef
painter
For example:
Today,
two employees
workers
employees
cooks
chefs
painters
six
any #
called in sick, so
didnʼt come
therefore
quit
got another job
there are only
only
didnʼt come,
there are only four
therefore
hours
minutes
days
weeks
seconds
three workers.
any # employees
cooks
chefs
painters
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?
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 long
should it take to finish the project?
CHOOSE a STRATEGY
to solve a problem
Draw a picture
Make a list, table or chart
!
Use easier numbers 1, 2, 3
10, 20, 30
Look for a pattern
Write an equation
a2 + b2 = c2
Work backwards
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
BEST PRACTICE:
PROVIDING an ORGANIZING
TEMPLATE/GRAPHIC
ORGANIZER
•saves time
•focuses English language
learners’ attention on the
mathematical concepts rather
than copying in a new language
• models how to organize
information
•provides clear way students can
organize information
•creates expectations about # and
quality of responses
Organizing Template/Graphic Organizer
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
Example: Double Entry Journal
How the teacher structures the
lesson to encourage
discussion among all students
How the English language
learners use language to talk
about the mathematical
concepts in the lesson
Handout 1-25
Date: ______________________________
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
Best instructional practice for English language learners on which I
am working:
Changes I have noticed in my
________________________________________________________
Changes I have made in my
students’ depth of
practice
understanding and engagement
Content
Content
Instruction
Instruction
Using mathematical language
appropriately and accurately
Using mathematical language
appropriately and accurately
Other
Other
© Enid Lee Consultants www.enidlee.com/modified by Center for
Collaborative Education/Turning Points
Three Essential Lesson Planning Questions
Turning Points Tool
Teaching
High-Level
Mathematics
to English Language
Learners
1. How does this lesson ensure that English
language learners are engaged in highlevel mathematics:
• solving challenging problems,
• using mathematical reasoning, and
• explaining their thinking?
2. How does this lesson ensure that all
English language learners are engaged at
all times throughout the lesson?
3. How does this lesson support English
language learners learning mathematics in
the middle grades
• without simplifying the problem,
• telling them what to do, or
• telling them the answer?
Questions
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 grades
students who do not understand and cannot apply the basic concepts of middle grades mathematics to a
wide range of situations are at great risk of dropping out of high school, not attending college, and being
unemployed or underemployed throughout their adult lives.
Far too many of these students are English language learners.
This tool is designed to help math teachers in the middle grades provide English language learners with the
opportunities all students deserve: access to and support in successfully learning high-level mathematics
and the critical life skills and opportunities it provides.
How does this tool define “high-level mathematics in the middle grades”?
Learning and mastering high-level mathematics in the middle grades, as defined in the tool, includes the
following characteristics:
• Complex challenges, multi-step problems allowing for more than one solution path, different strategies,
different entry points for different students
• Believable contexts that illustrate how mathematics is useful in everyday life, in science, in business
and students’ communities and families
• Collaborative work with other students, where all students are accountable for what the group (small
working group or the whole class) is learning
• “Meaty” problems that encourage discussing the reasons for different approaches, stating and
clarifying ideas, developing academic language to describe the problem, solution strategies and
results, 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 how
they know when their answers make sense.
High-level mathematics in the middle grades emphasizes mathematics as a process in mathematical
reasoning, a process in which students are engaged in understanding and accurately applying the critical
concepts of middle school mathematics identified by the National Council of Teachers of Mathematics
(NCTM).
High-level middle school mathematics problems are challenging for middle grades students. Students work
in groups on problems that are slightly—but not too far—out of their comfort zone. Students make their own
plans for how to proceed, and are required to explain their discoveries and their process through speaking
and 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
such classrooms is “doing mathematics.” This term was coined to distinguish high-level mathematics from
rote learning and/or following formulas to solve problems that research has shown is used in many
classrooms throughout the United States, including those that enroll English language learners.
Questions (continued)
How is “high-level mathematics” different from “mathematics” in the middle grades? Aren’t they the
same?
The goals listed above for “high-level” mathematics have always been among the goals of mathematics
education, but “traditional” mathematics education has often put them in separate compartments, based on
the premise that students must master basic skills and algorithms by rote before they can apply them to
challenging problems. The result—most students learn to think of mathematics as a series of unrelated skills
with no rhyme or reason, no connection to their own lives.
In addition, recent research has indicated that many teachers routinely lower the cognitive demand of
problems 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 example,
teachers may tell students the steps they should take to solve a problem or give them algorithms or tricks to
reach an answer without helping students develop their own understanding of how and why certain strategies
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 are
active through every step of the learning process; not by telling the students what to do or giving them the
answers but by planning lessons that pose rich mathematical questions, by asking just the right questions, by
listening 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 the
lesson. Teachers encourage students to actively participate in mathematics lessons by introducing and
practicing the language structures and vocabulary they need to do so and making sure they use them
consistently 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 Series
for 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-level
mathematics to English language learners, and all other students in the middle grades, takes advantage of
these key developmental traits of adolescence. Lessons that focus on high-level mathematics build in these
traits by requiring all students
• to 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 can
explain with accuracy and clarity and
• to apply this new knowledge to real life solutions that are meaningful to them and important
to the community at large.
Aren’t these the same strategies and approaches that are successful with all students? Are there
any strategies that are unique to English language learners?
All middle grades students need the kind of support outlined above in order to learn the language of
mathematics and master high-level mathematics. The strategies listed above can and should be used
with middle grades students in general.
There are some challenges, however, that are unique to English language learners. Mastering middle
grades mathematics means beginning to learn how to think as mathematicians. Thinking requires talking,
listening, responding, reflecting and rethinking; it is by is nature language based. Middle grades students
need support in mastering the language of mathematics, which is essentially a foreign language to almost
every student who enters a math classroom.
Teachers, however, need to be especially vigilant in planning lessons for English language learners since
these students are learning not just the language of mathematics but English as well. Teachers need to
listen to and talk to English language learners in ways that take into consideration the specific and
individual language and cultural needs of each language learner. They need to make sure that every
English language learner learns how to express himself/herself so that they can actively participate in the
lessons and develop the thinking strategies they need to master high-level mathematics.
This tool provides many different strategies that provide support so that a broad range of English
language learners have access to and master high-level mathematics. This tool also provides information
and encourages teachers to learn how to identify and access the needs of the individual English language
learners 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’s
Packet and the Facilitator’s Guide to Workshop 1 for a detailed discussion of the important language
issues English language learners face in mathematics classrooms.)
Does this tool address the needs of English language learners who enter middle grades without
mastery of basic computational skills?
English language learners, as well as native speakers of English, are very divergent in terms of their
mastery of computational skills and mathematical facts. All of the strategies in this tool have been used in
classrooms with English language learners entering with a great range of facility in mathematical and
computational understanding and knowledge.
This tool focuses on providing all of these students with access to high-level mathematics in the middle
grades, whether or not they are weak in computational skills and their knowledge of mathematical facts.
This tool is designed therefore not to supplant support in these areas but to ensure that all English
language learners are provided the opportunity to learn the high-level middle 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?
This tool is designed to provide access to a broad range of English language learners from who enter the
classroom in the beginning levels of English language acquisition to those in more advanced levels. The
strategies demonstrate how to use the diversity of students’ background knowledge, language of origin, and
ways in which they were taught mathematics.
The laws and regulations governing the teaching and assessment of English language learners differ
from state to state. Is the tool designed to work in a particular state or group of states?
This tool does not take a stand on any of the laws and regulations governing the teaching and assessment of
English language learners. It can be used in a broad variety of classroom settings, including bilingual, ESL
and SIOP settings.
Is the tool designed to be used with a specific textbook?
This tool is designed to be used with a broad range of textbooks and has been used in settings which use
different types of texts. The approaches modeled by the tool are effective in any middle grade mathematics
classroom in which English language learners are enrolled.
Does the tool follow a particular model of training such as SIOP (Sheltered Instruction Operational
Protocol) or CALLA (Cognitive Academic Language Learning Approach)?
This tool integrates the knowledge base and experience of a broad range of research 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 and in the model lessons to language based
activities - talking, listening, writing and responding?
Middle grades students need careful and continuous support as they move from the basic computation and
arithmetic of elementary school to the more complex topics of the middle grades: ratios and proportion,
geometry, graphing and data analysis, functions and algebra. They also need explicit instruction 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 mathematics and beyond. Providing such support is
especially critical for English language learners learning high-level mathematics.
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.
Additional Resources
Selected 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 ‐ BeneWits 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, 9, No.1, 2008.
•www.ncela.gwu.edu/Wiles/uploads/3/mathforELLs.pdf
References
Selected References
•August, S. (2006). Developing Literacy in Second‐Language Learners: Report of the National Literacy Panel on 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 on 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 Education.
• Kieffer, M., Lesaux, N. & Snow. C. (2008) Promises and Pitfalls: Implications of No Child Left Behind for DeWining, 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 Learning.
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 Learners Simultaneously. 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. International
Journal of Bilingual Education and Bilingualism 9(2),159-180.
For additional information
contact:
Dr. Sara Freedman, Project director
sfreedman@ccebos.org

Facilitators Guide to the Workshop Series

Transcription

Similar documents

Ben Vaske – Unique approach of basic skills

Sin título-1

abiators learning style test 1

Drawing Math Stories: Linking Language, Art, and

LEARNER`S DIARY vienna

NCCTM Central Region Conference - NC Mathematics

What-Z-Up Glenstantia - Glenstantia Primary School

Mathematical Modeling as a Means to Demonstrate the

Multiple Intelligences and Technology

ENERGY AND HEAlth - Wisconsin Energy Institute