Helping ELLs Speak Math…
What’s the Problem and How Can We Solve It?
A Presentation by David Irwin
Language Development Opportunities
with much help from Erynn Torrey
Othello School District
June 19, 2015
Entry Task
• Think back to when you were in school…
• How did you feel about story problems?
• Were you successful solving them?
• Did you understand them? Why or why not?
• Draw a picture to represent how you felt and/or
Write a short phrase to describe this memory
• Be prepared to share your thoughts with an elbow
partner
Learning Targets:
I can explain why math and math problem
solving are such difficult tasks for students,
especially English language learners.
I can identify at least 2 explicit language
strategies I can implement during math
instruction to strengthen ELL students’
problem solving skills and math vocabulary.
Well…What's the Problem?
• Math is NOT a universal language!
• Cultural differences in how math is taught
• Large Emphasis on word problems in USA
• Limited Prior/Background Knowledge
• Word problems require academic reading skills and
knowledge of content-specific vocabulary—CALP
Math & Linguistics
• Multi-meaning (Polysemous) words
• table (chart/furniture), mean (unkind/average), odd (strange/not
even), operation (surgery/math process)
• Synonyms
• add, plus, combine, sum (+)
• Homophones
• sum/some, whole/hole
• Word arrangements & passive structures
• A is 5 less than B (a=b-5), 7 trees were cut down
• Prepositions
• above, over, from, by, near, below, etc.
And There’s More…
• We tend to assume
students who can “do
math” can also “do story
problems” without
explicitly teaching them
specific strategies for
understanding the technical
writing of story problems
• As a result, we inadvertently teach
students to “number harvest,”
which gives them little
understanding of the problem’s
context or vocabulary
• THIS IS NOT WORKING!
Let’s Process This…
• ELLs struggle with story problems because… (choose
ideas from the word bank below to help you finish this sentence)
Academic Language
Abstract Ideas
Number Harvest
Lack of Context
Content-Specific Vocabulary
Technical Language
CALP
Comprehension
Linguistics
NOT Universal
We understand the problem:
So what’s the solution?
By implementing explicit strategies
for language instruction during
math, we can help students from
various cultural and language
backgrounds understand and solve
math story problems, while also
strengthening their receptive &
productive language abilities
The Good News Is…
• We already use many of these strategies during our daily
Literacy instruction…
• By focusing on each of the 5 domains of language during
math, we will provide students with the support they
need to access math story problems
(READING, WRITING, LISTENING, SPEAKING, VISUAL LITERACY)
How do the ELP Standards support math?
Through the Practices and the K-12 Practices Matrix
Go to the Practices Matrix, page 34
Standards 1-7: Content-Area Practice Focus
Standards 8-10: Language Specific Focus
1
Form
Function
2
construct meaning from oral presentations and literary and informational text through
grade-appropriate listening, reading, and viewing
participate in grade-appropriate oral and written exchanges of information, ideas, and
analyses, responding to peer, audience, or reader comments and questions
3
speak and write about grade-appropriate complex literary and informational texts and
topics
4
construct grade-appropriate oral and written claims and support them with reasoning
and evidence
5
conduct research and evaluate and communicate findings to answer questions or solve
problems
6
analyze and critique the arguments of others orally and in writing
7
adapt language choices to purpose, task, and audience when speaking and writing
8
determine the meaning of words and phrases in oral presentations and literary and
informational text
9
create clear and coherent grade-appropriate speech and text
10
make accurate use of standard English to communicate in grade-appropriate speech
and writing
Standards for Mathematical Practice
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning.
Structuring the Practices
Activity
•In teams, divide up the 8 Math Practices
•Highlight the verbs and nouns
•Find the ELP Standard(s) that best support(s)
that Practice
•Make a poster that illustrates the
connections
Not all the practices are connected to an ELPS in the Matrix.
We can connect them anyway.
4 BIG Ideas for Teaching Math Story
Problems:
1. Explicit instruction of vocabulary/keywords
2. Regular use of visuals
3. Provide opportunities for
oral processing
4. Teach strategies for story comprehension
BIG IDEA #1: Vocabulary Instruction
• ELL students need explicit vocabulary instruction and
ample opportunities to use the new language through
multiple domains
• Always connect vocabulary to visuals!
• Linking keywords to operations/categories can also be
helpful for understanding
Vocabulary—Practice, Practice, Practice!
• Repeated exposure!
• Is a process that takes time & intentional teaching
• Has to be ENGAGING and FUN:
• Examples: Games, Chants/Songs, Partner Activities
• Have students record new words in a personal dictionary
• Post words in the classroom for students to reference
• Organize words by CATEGORY (as opposed to alphabetically or randomly)
Grab some words
• Big idea words that are also concepts
• Related to your next (or recent) unit
• Keep them ready for later
BIG IDEA #2: Use Visuals and Activities
to Develop Understanding
• VISUAL LITERACY:
• Receptive: Students can interpret meaning from graphic representations
• Productive: Students can use visuals to communicate understanding
• IDEAS FOR PROMOTING VISUAL LITERACY:
• Introduce new concepts using a KWL chart or other graphic organizers
• Have students connects words and ideas to one another with graphic organizers to
develop understanding
• Have students draw pictures to go with vocabulary words
• WITH YOUR PARTNER:
• Think of another way you can promote visual literacy in your classroom
Nonlinguistic Representations:
Marzano Strategy:
Nonlinguistic Representations
• How the brain stores
information: linguistic
form and imagery form
(nonlinguistic)
• Combining both systems
increase what students
can learn and remember
Examples of Nonlinguistic
Representations:
• Graphic Organizers
• Visual Representations
• Physical Models
• Mental pictures
• Pictures/Pictographs
• Kinesthetic Activities
Linking Keywords to Operations
• T-charts
• CCD Charts
• Venn diagrams
• Part/whole charts
• Chants/motions
• Color-coding
• Webs/mapping
• Word Walls
Organized By operation/concept/idea
Bring from yesterday’s Vocab training…
• Choose 4 math words you will use in a typical lesson
• Create the Marzano 6-step plan for them
• Oh yes, if we didn’t do it yesterday, we will be
singing!
BIG IDEA #3: Partners & Talk Time
• Students should be partnered
based on math AND language
ability
• This is called “Precision
Partnering” (Anita Archer)
*Lower students in each pair
• Partner a higher
will have a model with higher
ability student with a
math and language skills
middle ability student and a
middle ability student with a
lower ability student
*Higher students will strengthen
their skills/build confidence
Precision Partners Example
• How to break students into
precision partners:
• List students in order from
1(high) -20 (low)
• Cut the list in half
• match the middle student
with the highest student
Example Class:
1. Sue (highest)
2. Jeff
3. Bill
4. Maria
5. Bob
6. Katie
7. Alex
8. Steve
9. Tina
10. Ted (middle)
11.Ed(middle)
12. Ben
13. Rob
14. Tom
15. Jose
16. Brock
17. James
18. Sarah
19. Nikita
20. Joe (lowest)
Let’s Partner-up!
• LET’S HAVE SOME FUN!
• Now you will have the
opportunity to break into
“precision partners,” who you
will work on and off with for
the remainder of our session
• To simulate an actual set of precision
partners, play rock paper scissors to
decide who will be the higher/lower
student.
• Partner 1 will be the higher student.
• Higher student usually goes first to model
In a classroom, students would never
know whether they are the higher or
lower person in their pair.
Partner Talk:
Think-Pair-Share
STEPS:
• Think Time
• extend wait time
• Math Talk Moves: Pair Share Time
• structured or not, depending on
question that was asked
• Whole Group Share Time
• Can call on individuals, use GLAD
numbers, sticks, online name picker,
volunteers
• Have students do some writing
about what they discussed
OUTCOMES:
• Gives ELL students time to process
• Students can check their answer
with a peer first, non-threatening
environment to try out the
language
• A form of accountability for
students & the teacher can
informally assess student
understanding and language
• Students are using another layer of
language
Partner Practice
Think about these questions in your head (or write):
• How could you encourage partner talk in your classroom?
• I will encourage partner talk in my classroom by ___________.
• How could you be intentional about giving students (especially
ELLs) structured time to talk and process their ideas during
math?
• I will be intentional about giving my ELLs structured
processing/talking time by ___________.
• Be prepared to share with your partner. (Partner 1 shares first.)
BIG IDEA #4: Comprehension
The Problem:
• ELL students do not
understand the context
surrounding the math
within story problems
• They are not fully
comprehending the story
situation
• They pull out numbers &
choose an operation they
think might work
The Solution:
• Use summarizing & retelling
strategies to aid in
comprehension
• Graphic organizers (story
elements)
• Oral language: Math Talk
Moves
• Drawings of the story
situation
Summarize the Math Story
• Treat the math story like a story in literacy:
• Pull out character(s), setting, & events (Janis Heigl)
• Have students discuss what the story is about and
share the story elements with a partner
(SPEAKING and LISTENING)
• Complete a graphic organizer or draw a picture to
show understanding
(WRITING and VISUAL LITERACY)
Let’s Summarize!
• Read the story 2 times to
yourself.
• Partner 1 reads the story
aloud to Partner 2
• Partner 2 starts by telling
one story element, then
Partner 1 takes a turn
STORY: Juanita and Ben were eating
a pizza. Ben ate 1/3 of the pizza.
Juanita ate 1/4 of the pizza. How
much of the pizza did they eat in all?
Story Elements:
Who- ________________________
Where- _______________________
What- ________________________
Math Story Map
Use this organizer to help students understand what the story is about
Talk Moves in Math
35
Excess Teacher Talk
Swamps Children
Cross & Nagel 1969
• 2/3 of the talk in classrooms is
done by teachers
• 2/3 of the talk is about
controlling or directing
Carmel Crevola
Teacher-Centered Discussion
(Image Source: http://www.icalweb.com/wiki/index.php?title=Classroom_Focus)
37
Student-Centered Discussion
(Image Source: http://www.icalweb.com/wiki/index.php?title=Classroom_Focus)
38
Partner-Centered Discussion
S
S
S
S
T
Math Talk Moves
• 8 Talk Moves
• Repeating
• “Can you repeat what ________ just
said in your own words?”
• Revoicing/Restating
• “So you’re saying that …”
• Reasoning
• “What was your thinking?”
• Adding On
• “Would someone like to add on?”
• “Who thinks they can explain why
this is a good move?”
• Say More
• “Tell us more about your thinking?”
• “Can you expand on that?”
• Agree/Disagree & Why
• “Do you agree or disagree with that
idea? Why?”
• Example/Non-example
• “Can you give us an example of
that?”
• Wait time
• “Take your time…we’ll wait…”
https://melrosemathgradek.wikis
paces.com/talk+moves
Repeating
• Students restate a contribution of a classmate either verbatim
or paraphrased.
• Useful when an idea is out on the floor and teacher wants
more engagement.
• Repeating, even when reformulated in your own words,
requires another layer of thinking.
• It is somewhat challenging to repeat classmates'
contributions.
• The expectation that students be able to repeat
contributions is useful. Students are "on call" and must
attend to conversation.
• Even teachers find the task challenging in meetings, etc.
• This move changes the level at which people listen.
41
Revoicing/Restating
• The teacher repeats part or all of a student's utterance and asks the
student to verify whether the interpretation is correct.
• Especially helpful to teachers when they do not understand what was said.
• Revoicing is not simply repeating, The third part (verification) is necessary. (I
infer…. Is that right? Is that correct?)
42
Reasoning
Teacher asks students to explain how or why they came to their
position.
• Move can also referred to as "press for reasoning.“
• Pressing can include asking why, requiring evidence, citing text, questioning
methods, etc.
• Ultimate goal is to open a student's reasoning process to the rest of the class
so that others can learn and respond.
43
Adding on
• A student adds more information or interpretation to what another
student has said
• Students are listening and processing on what classmates are saying and
thinking
44
Waiting
• Teacher allows quiet thinking time for students to develop responses.
• While not technically a "talk" move, wait time is equally important.
• It is important to provide students time to think.
• Waiting for a student response may feel uncomfortable to some, but
with practice is becomes natural.
• Moving on rapidly is not always to most beneficial choice for students.
• Students who are normally quiet can provide especially insightful
responses if teacher uses wait time. The idea that this puts undue
pressure on students is false.
• This move allows more students to participate and builds confidence in
those less accustomed to speaking out.
45
Say More…
• Ask a student to elaborate on what she said, or ask another student
to "add on" or "say more" about a classmate's contribution.
• This move is helpful whether or not the teacher understands the initial
contribution.
• Sometimes this move is overlooked because it is so straightforward.
• Students enjoy having a platform from which to start their comment.
46
Agree or Disagree
• Teacher asks student whether they agree or disagree with a
comment, then also asks why.
• It is important to add the "why" when using this move.
• The yes or no question of "Do you agree or disagree?" is a good start point to
engage students in the deeper thinking of "why?“
• Effective move to control and encourage close attention to classmates'
contributions.
47
Example or Counterexample?
• Student asked to provide an example or counter-example of his or a
classmate's contribution.
• This move is particularly useful in math, but also in other subject areas.
• Calling upon other students to provide examples serves as an effective check
for understanding.
• Counterexamples are productive in math when disproving a claim, etc.
48
Hand Moves
Repeat
Add on
Agree
Disagree
New thought
Math Talk Moves videos
• Note when you see each Talk Move being used in each video
• Use the half sheet
1st Grade
4th Grade
5th Grade
But, Where do I Start?
• Start with one move.
• The revoicing move can be introduced into teaching
without fanfare.
• Students can learn revoicing techniques with
explicit coaching.
• Revoicing is highly effective yet simple.
51
4 BIG Ideas for Teaching Math Story
Problems:
1. Explicit instruction of vocabulary/keywords
2. Regular use of visuals
3. Provide opportunities for
oral processing
4. Teach strategies for story comprehension
Other Ideas to Consider…
• Use students’ names and real family members in
your story problems to create personal connections
with the math. Add them if possible.
• Use real-life situations to
give students proper background knowledge and make
stories applicable
Activity
• With a partner, complete the Story Problem
Practice packet
• Identify the who/where/what for each problem
• Practice the Talk Move for each problem
Online Resources
• 1XL
• MelroseMathGradeK (not just for Grade K)
• MelroseMath Talk Moves
• Eureka Math
• Dad’s Word Problem Worksheets
• Random Name Picker (there are lots more)
• Investigations
• Math Learning Disabilities
• Math Learning Center (Bridges)
Planning Time
• It is important to have a plan in place for your math instruction so you
can be intentional .
• Using your differentiated lesson plan format, find a way to put
at least 2 of these strategies into an example math lesson to
make it more appropriate for ELL students.
• Your plan should include 2 strategies from the 4 BIG IDEAS:
1.
2.
3.
4.
Explicit instruction of vocabulary/keywords
Regular use of visuals (Non-Linguistic Representations)
Opportunities for oral processing (Precision Partners)
Strategies for story comprehension: Treat math problems like a story (Math Talk
Moves)
Learning Targets:
I can explain why math and math problem
solving are such difficult tasks for students,
especially English Language Learners.
I can identify at least 2 explicit language
strategies I can implement during math
instruction to strengthen ELL students’
problem solving skills and math vocabulary.
Resources & References
• Handouts and power point for this presentation can be found at:
sites.google.com/site/erynntorrey or www.langdevopps.com
• Archer, Anita (2003). Vocabulary Development,
http://ela.fcoe.org/sites/ela.fcoe.org/files/Anita%20Archer031.pdf
• Hart, Janis M. (1996). “The Effect of Personalized Word Problems.” Teaching Children Mathematics,
Vol. 2, No. 8, 504-505.
• Marzano, Robert Classroom instruction that works (Marzano)
• Carlo, M. S., August, D., McLaughlin, B., Snow, C. E., Dressler, C., Lippman, D. N.,…White, C. E. (2004).
Closing the gap: Addressing the vocabulary needs for English language learners in bilingual and
mainstream classrooms. Reading Research Quarterly, 39(2), 188–215. doi:10.1598/RRQ.39.2.3
• Kinsella, K. (2012). Evidence-based principles to guide English language development in the Common
Core Standards era. Retrieved from http://teacher.scholastic.com/products/teach-english-languagelearners/pdf/Kinsella_ELD_CCSS_4-19-12Handout.pdf
• Moschkovich, J. (2014). Supporting ELLs in mathematics: Mathematics tasks with annotations and
other resources for implementing the Common Core State Standards. Developed for the
Understanding Language Initiative. Stanford, CA: Stanford University Graduate School of Education.
Retrieved from http://ell.stanford.edu/teaching_resources/math
• Zwiers, J. (2008). Building academic language: Essential practices for content classrooms, Grades 5–
12. San Francisco, CA: Jossey-Bass Teacher Education.
Thank you for your time.
If you have any questions, please feel
free to contact us:
David Irwin
dave@langdevopps.com
www.langdevopps.com
360-903-0131
Erynn Torrey
teachertorrey@gmail.com
sites.google.com/site/erynntorrey
503-201-7455