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.
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- ________________________
• 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
38
Student-Centered Discussion
(Image Source: http://www.icalweb.com/wiki/index.php?title=Classroom_Focus)
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?)
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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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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 [email protected]
360-903-0131
Erynn [email protected]
sites.google.com/site/erynntorrey503-201-7455
Thank you for your time. If you have any questions, please feel free to contact us: