Helping ELLs Speak Math…What’s the Problem and How Can

We Solve It?

A Presentation by David IrwinLanguage 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 Number Harvest Technical Language

Abstract Ideas Lack of Context CALP Linguistics

Content-Specific Vocabulary Comprehension 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 FocusStandards 8-10: Language Specific Focus

1construct meaning from oral presentations and literary and informational text through grade-appropriate listening, reading, and viewing

2participate in grade-appropriate oral and written exchanges of information, ideas, and analyses, responding to peer, audience, or reader comments and questions

3speak and write about grade-appropriate complex literary and informational texts and topics

4construct grade-appropriate oral and written claims and support them with reasoning and evidence

5conduct 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

8determine the meaning of words and phrases in oral presentations and literary and informational text

9 create clear and coherent grade-appropriate speech and text

10make accurate use of standard English to communicate in grade-appropriate speech and writing

Func

tion

Form

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

• Partner a higher

ability student with a

middle ability student and a middle ability student with a lower ability student

• This is called “Precision

Partnering” (Anita Archer)

*Lower students in each pair

will have a model with higher

math and language skills

*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) 11.Ed(middle)2. Jeff 12. Ben3. Bill 13. Rob4. Maria 14. Tom 5. Bob 15. Jose6. Katie 16. Brock7. Alex 17. James8. Steve 18. Sarah9. Tina 19. Nikita10. Ted (middle) 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

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Talk Moves in Math

• 2/3 of the talk in classrooms is done by teachers

• 2/3 of the talk is about controlling or directing

Excess Teacher Talk Swamps Children

Cross & Nagel 1969

Carmel Crevola

37(Image Source: http://www.icalweb.com/wiki/index.php?title=Classroom_Focus)

Teacher-Centered Discussion

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Student-Centered Discussion

(Image Source: http://www.icalweb.com/wiki/index.php?title=Classroom_Focus)

Partner-Centered Discussion

S

SS

SS S

S

S 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?”• Wait time

• “Take your time…we’ll wait…”

• 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?”

https://melrosemathgradek.wikispaces.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.

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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 Grade4th Grade5th 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.

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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 back- ground 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. Explicit instruction of vocabulary/keywords2. Regular use of visuals (Non-Linguistic Representations)3. Opportunities for oral processing (Precision Partners)4. 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-language-learners/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.

David Irwindave@langdevopps.comwww.langdevopps.com

360-903-0131

Erynn Torreyteachertorrey@gmail.com

sites.google.com/site/erynntorrey503-201-7455

Thank you for your time. If you have any questions, please feel free to contact us: