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**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

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**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

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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.

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**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 Numbers MIGHT be universal, but story problems are not Cultural differences (how math is taught, units used for measurement, temperature, etc.) Academic lang/vocab-ELL students are not equipped for Many non-ELL students also struggle with these types of problems for many of the same reasons CALP: (Cognitive Academic Language Proficiency)

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**Math & Linguistics Multi-meaning (Polysemous) words Synonyms**

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. There are several linguistic issues that can get in the way of understanding math word problems Polysemous words 2 words w/ same spelling & pronunciation but different meanings

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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! When student “pick out” the numbers from the text and guess an operation to use, they are not understanding the problem’s context or the vocabulary in the problem, which will lead to bigger deficits later on -The reading and comprehending of math texts is a complex and frustrating process for students

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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

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**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

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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) -we just need to adjust the strategies for math -we must have elements in our lessons that hit each of the 5 domains

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**How do the ELP Standards support math?**

Through the Practices and the K-12 Practices Matrix Go to the Practices Matrix, page 34

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**Standards 1-7: Content-Area Practice Focus Standards 8-10: Language Specific Focus**

construct meaning from oral presentations and literary and informational text through grade-appropriate listening, reading, and viewing 2 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 Function Page 6. Here are the 10 ELP Standards. Point out – for people who are familiar with CCSS they will recognize the concept of “anchor standards” – that there are 10 ELP Standards common to all grade levels (on page 6). The ELP Standards address areas that are central to more rigorous college-and-career-ready standards: Standards 1 through 7 involve the language necessary for ELLs to engage in the content-specific practices associated with ELA & Literacy, mathematics, and science. In other words, FUNCTION. They begin with a focus on extraction of meaning and then progress (CLICK HERE TO REVEAL ARROW) to engagement in these standards. In other words, they build on each other so the depth at which a student can “do” these standards increases. Standards 8 through 10 home in on some of the more micro-level linguistic features that are undoubtedly important to focus on but especially in the service of the other seven standards. In other words, FORM. Note: 8-10 are more reminiscent of the previous WA ELD Standards. Form

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**Standards for Mathematical Practice**

Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Refer participants to the handout with the description of the CCSS Standards for Mathematical Practices.

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**Structuring the Practices**

This organization of the Standards for Mathematical Proficiency was developed by one of the principal authors of the Common Core State Standards for Mathematics, Dr. William McCallum, University of Arizona. His rationale for this organization is as follows: In the progressions project, we’ve been discussing how best to represent the standards for mathematical practice. The practices are signposted throughout the documents, but we’ve also been thinking about how to provide some structure for the practice standards that will help people avoid fruitless tagging exercises in their efforts to integrate the practice standards into the content standards. If you think about it long enough you can associate just about any practice standard with any content standard, but this sort of matrix thinking can lead to a dilution of the force of the practice standards—if you try to do everything all the time, you end up doing nothing. This diagram is an attempt to provide some higher order structure to the practice standards, just as the clusters and domains provide higher order structure to the content standards.

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**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. 1st hour. 30 min to get here , 30 mins to do task

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**4 BIG Ideas for Teaching Math Story Problems:**

Explicit instruction of vocabulary/keywords Regular use of visuals Provide opportunities for oral processing Teach strategies for story comprehension

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**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 but be careful students aren’t pulling the words out and deciding meaning in isolation

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**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) TRY FOR 3 DOMAINS IN EACH LESSON

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**Math Vocabulary Classroom Practices: Vocabulary and Keywords:**

Should not be introduced in isolation Should be supported by graphic organizers/visuals Should be introduced, practiced, & reviewed with student talk time & write time Connect words to one another (categories, examples/non- examples, etc.) Venn diagrams, part/whole charts, t-charts, etc. Think/Pair/Share with set partners & roles to increase student talk and engagement (sentence frames/starters to guide discussions)

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**Grab some words Big idea words that are also concepts**

Related to your next (or recent) unit Keep them ready for later

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**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

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**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 Dual-coding theory of how the brain stores information Most instruction is linguistic in nature Creating an image to connect to the linguistic form will enhance what students can recall

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**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

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Time to Draw! Going back to what we just discussed, draw a quick nonlinguistic representation to help you remember/explain each of the 4 BIG IDEAS: Vocabulary/Keyword Instruction Meaningful Visuals Oral Processing Time (Structured Partner Talk) Comprehension Strategies Be ready to share with a partner!

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**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! 2nd hour

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**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 (ie the range between the 2 students should not be too drastic) -strengthens skills of the higher student in the pair (build confidence, practice) -the lower student in the pair will be pushed because they will see higher math and reading skills modeled for them -This strategy reaches the language domains of SPEAKING and LISTENING in the math classroom

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**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) Ed(middle) 2. Jeff Ben 3. Bill Rob 4. Maria Tom 5. Bob Jose 6. Katie Brock 7. Alex James 8. Steve Sarah 9. Tina Nikita 10. Ted (middle) Joe (lowest)

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Let’s Partner-up! 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. 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 -Partner 1 will be the person with higher abilities, partner 2 will be the person with lower abilities -In a classroom setting, I would structure discussion time so students with higher abilities get to share their ideas first during partner work to allow students of lower math and language abilities to have the oral language and math ideas modeled for them beforehand -Can use creative names for partners: milk and cookies, chips and salsa, products and quotients, area and perimeter, etc.

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**Partner Talk: Think-Pair-Share**

STEPS: 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 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 -This strategy reaches the language domains of SPEAKING and LISTENING in the math classroom -Can tell partners who will speak first (usually the higher level student) and sentence frames/sentence starters could also be provided to guide the students

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**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.)

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**BIG IDEA #4: Comprehension**

The Problem: The Solution: 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 Use summarizing & retelling strategies to aid in comprehension Graphic organizers (story elements) Oral language: Math Talk Moves Drawings of the story situation Begins the Math Talk Moves section

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**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)

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**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- ________________________

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Math Story Map Use this organizer to help students understand what the story is about

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Talk Moves in Math While teachers of both younger and older children work hard to provide their students with the best literacy experiences, oral language is often neglected in the classroom The variety of language used at home and school has a direct bearing on children's literacy. Because of the complexity of the language development processes, caregivers in the home and school need to be aware of ways to enhance opportunities for children to learn effective communication. 35

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**Excess Teacher Talk Swamps Children**

4/20/2017 Beware!! 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 One assumption is that the teacher's role is to teach--is usually interpreted to mean that to teach means to talk. Accordingly, teachers spend hours and hours teaching by talking while the children sit listening passively. Such conventional teaching-learning is one of the obstacles preventing the real development of oral language. Children leaving these classrooms tend to carry this passivity over to their learning attitudes, and tend to be "disabled" in their learning abilities, as well. Hong, Z., Kortner, A,N, (1995). Oral Language Development across the Curriculum, K-12. ERIC Digest. ERIC Clearinghouse on Reading English and Communication Bloomington IN. ED389029 Too much teacher talk Teachers talk too quickly Teachers do not adjust their instructional language to meet the needs of their students Teaching moves into small groups but the language stays the same! Research in 1912 found that teachers talk 64% of the time in classroom discussions. This is relatively consistent in classrooms today Carmel Crevola Carmel Crevola - Module 1 36

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**Teacher-Centered Discussion**

(Image Source:

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**Student-Centered Discussion**

(Image Source:

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**Partner-Centered Discussion**

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**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?” paces.com/talk+moves

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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.

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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. Always press for reasoning? Where does it say that in the text. Talk us through your reasoning. You have some thinking and reasoning. Open it up. Externalize their thinking.

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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

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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.

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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.

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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. In order to have students agree to disagree you have to have listened.

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**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

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**1st Grade 4th Grade 5th Grade 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

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**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. 3rd hour: discuss talk moves, videos, etc. Lunchtime

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**4 BIG Ideas for Teaching Math Story Problems:**

Explicit instruction of vocabulary/keywords Regular use of visuals Provide opportunities for oral processing Teach strategies for story comprehension

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**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 Take into account the cultures in your classroom and how they can be thoughtfully incorporated into the stories

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**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

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**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)

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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: 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)

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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.

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**Resources & References**

Handouts and power point for this presentation can be found at: sites.google.com/site/erynntorrey or Archer, Anita (2003). Vocabulary Development, Hart, Janis M. (1996). “The Effect of Personalized Word Problems.” Teaching Children Mathematics, Vol. 2, No. 8, 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: /RRQ Kinsella, K. (2012). Evidence-based principles to guide English language development in the Common Core Standards era. Retrieved from learners/pdf/Kinsella_ELD_CCSS_ Handout.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 Zwiers, J. (2008). Building academic language: Essential practices for content classrooms, Grades 5– 12. San Francisco, CA: Jossey-Bass Teacher Education.

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**If you have any questions, please feel free to contact us:**

Thank you for your time. If you have any questions, please feel free to contact us: David Irwin Erynn Torrey sites.google.com/site/erynntorrey

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