expediting comprehension for

Expediting Comprehension forEnglish Language Learners

Dr. María N. Trejo

MATHEMATICS & LITERACYELEMENTARY LEVEL

Margarita Calderón & Associates, Inc.

OBJECTIVES

• How vocabulary impacts reading and math knowledge.

• How to select vocabulary in mathematics.

• How to teach vocabulary for mathematics.

• How to use research-based and evidence-based strategies with ELs, struggling readers, and students with special needs in mathematics.



Mathematics, Reading & Writing

The relationship among reading, writing, and mathematics did not become a subject of discussion until the appearance of standards-based mathematics curricula of the 1990s.


New and Expanded Goals

NCTM proposed a distinction between theteaching of arithmetic and mathematics. To master and demonstrate mastery of mathematics, instruction would have to expand to:

1)Teaching for understanding2) Student-center learning3) Concept-building vs. memorization of facts4) Ability to communicate mathematical understanding to others

National State Core Standards – MATHEMATICS K-6

These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up.

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

National State Core Standards – MATHEMATICS K-6

The Standards for Mathematical Content are a balanced combination of procedure and understanding-- connecting the practices to the content.

Students who lack understanding of a topic may rely on procedures too heavily: they may be less likely to consider analogous problems, to represent problems coherently, to justify conclusions, to apply the mathematics to practical situations, to use technology mindfully to work with the mathematics,to explain the mathematics accurately to other students, to step back for an overview, orto deviate from a known procedure to find a shortcut.

In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices


ELS --LITERACY & MATHEMATICS

THE GREATEST DIFFICULTY IN LEARNING THE LANGUAGEOF MATHEMATICS IS THAT A DOUBLE DECODING MUST GO ON DURING THE ENTIRE PROCESS. STUDENTS MAY NEED TO:

- Decode unspoken (daily or social) words- Translate these into different context of mathematics usage- Decode written mathematics words or symbols or signs- Connect to concepts that may or may not be present in prior knowledge

For Els, you may also have to consider:

- Lack of English - social or daily language- Lack of English - academic mathematics language- Lack of familiarity with mathematics

[Barton and Heidema (202)]


VOCABULARY AND SYMBOLS

--words mean different things in mathematics and nonmathematics contexts (divide by; divide into; highway divide)

--two different words sound the same (sine – sign; sum– some)

More than one word is used to describe the same concept (plus – sum – add- ; mean, medium, range, mode)

--there are similarities in root meanings ( number, numeral; computer, compute)

Math is expressed in multiple ways; with words and / or symbols (multiply six times 2; 6 plus 6; 6 X 2; six times two; etc)


Math texts challenge all students, but more so ELs because they include words, symbols, and procedures.

✔Vocabulary may be confusing because words mean different things in mathematics and non-mathematics contexts (relationship); because two different words sound the same (sine and sign); or because more than one words is used to describe the same concept (sum, total, aggregate, addition).

✔Symbols may be confusing either because they look alike ( division or square root √ ) or because different representations may be used to describe the same process (multiplication ×, ⁄, ( ), * )

✔Graphic representations may be confusing because of formatting variations such as bar graphs versus line graphs; or graphics are not read in the same direction.


Explicit instruction of “Small Words”

ELs need to learn specific vocabulary and symbols much like they learn “sight” words – via explicit instruction and memorization.

Teach them the variation of words due to usage, such as; The, a, are, at, can one, ones, ten, tens, and, or, number, numeral, how, many, how many, what, write, it, each, which, do, all, same, exercises, here, there, has, and have.


Please write or express the following examples in words.Time: 12:15 P.M.Measurement: 1 lb and 4 oz.Height: 5’ 7”

Please express or write the following in symbols:

Time: Six forty-five in the morning.Measurement: Twelve and a half miles.Height: Six yards, two feet, and nine inches.

Illustrate five ways to express 64 divided by 4. Explain in your own words the difference among ADD, ADDITION, and ADDITIVE.

EXAMPLES: Activities


ACTIVITY: Text Features

In your mathematics textbooks, please do the following:

Scan the Text – look for graphs, footnotes, instructions, headings, tables, bold headings or words,

read and review these text features. Discuss with a partner what you learn and predict what the lessons will be about.

Ask provoking questions, identify excess information in the page or in the sentences.

Discuss where you have seen the use of mathematics information, why mathematics is important.

ACTIVITY – SCAN AND DISCUSS FEATURES IN DAILY NEWSPAPERS

1.0 Connect the importance of mathematics to daily lives.

2.0 Point to the variety of mathematics and geometry uses in your daily life and in careers.

3.0 Create enthusiasm and interest in mathematics.


MATHEMATICS TEXTS’ FEATURES

≥ more concepts per sentence and paragraph

≥ very compact style; with little redundancy

≥ words, numeric and non-numeric symbols to decode

≥ pages laid out in various ways, VS. left-to-right ≥ graphics, sidebars, or excess information to interpret,

distract or add to the comprehension.

≥ written above the grade level for which they are intended.


READING MATHEMATICS

NOTE

In a traditional paragraph, the topic sentence and main idea often comeat the beginning, with details following.

In a mathematics problem, the key idea or question comes at the end of the paragraph (How many apples are left? Find the Volume of the cylinder.)

SENTENCE CONSTRUCTION

LITERATURE:Reclassified Els are those who are no longer receiving specialized English instructional services because they can participate in an English-only classroom. However, they usually continue to struggle in reading, writing, and math, and they often struggle with standardized tests.

MATHEMATICS:Lucy is looking for the perfect outfit for the first day of school. She needs to decide what to put together to make an outfit. If she has two pairs of shoes, three shirts, and two pairs of pants that all coordinate, how many outfits can she make? Justify your answer.

Semantic Awareness

It is a mindset.

$ Teachers motivate and show students how important it is to be learning words to solve problems.

¢ Students are aware of the power of words they read, hear, write and speak.

£ Semantic awareness helps students become more skillful and precise in word usage at many levels of complexity and sophistication.


EXAMPLE


A.The numbers below follow a pattern. 70 700 7,000 70,000

Which expression shows one way to find the next number in this patterns?

a) 7 × 10b) 7 × 100c) 70,000 × 10d) 70,000 × 100

Why is Vocabulary Instruction Important in Math?

• Vocabulary knowledge correlates with reading comprehension.

• Reading comprehension correlates with procedural and content knowledge.

• Content knowledge correlates with academic success.

• Comprehension depends on knowing between 90% and 95% of the words in text.

• Knowing words means explicit instruction not just exposure. Students need 12 production opportunities to own a word.


Academic Language in Mathematics:

What is academic language? (TTYP)What is academic vocabulary in

mathematics?How do we select and teach

vocabulary in mathematics? Mathematics have words, symbols,

and multiple applications.


Math & Literacy Instruction

– General Rules for ELs-• Integrate concepts of vocabulary, symbols, proper

academic grammatical structures, and text features. • Use strategies that include concrete objects,

graphics, manipulatives, and activities that clarify and reinforce concepts.

• Have students work together to solve problems, require active involvement, encourage the use of new vocabulary and new math concepts.

Adapt Math Story Problems

Sample Strategies-Provide explicit instructions and practice with reading and

writing word problems. Teach students to identify key words for solving word problems and identifying mathematical operations.

-Model the problem solving process by talking aloud while solving problems on the overhead, chalkboard, or interactive white board to demonstrate thinking processes. (Think Aloud)

-Give students a computation problem to solve and then have them write the steps used to solve it. Require complete English sentences.

http://homeschooling.suite101.com/article.cfm/12_tips_for_solving_word_problems

Explicit Instruction in Vocabulary

STEP 1

SELECT VOCABULARY TO PRE-TEACH BEFORE PRESENTING CONTENT, TEACHER READ ALOUD, OR STUDENT READING OF ANY TEXT.

STEP 2

TEACH VOCABULARY USING 7 STEPS WITH AMPLE STUDENT INTERACTION.

STEP 3

STUDENTS READ, DISCUSS, AND WRITE USING NEW VOCABULARY


Summary of Vocabulary Tiers 1, 2, 3 For ELLs

TIER 1 -- Basic words ELLs need to communicate, read, and write. Those that should be taught.

TIER 2 -- Information processing words that nest Tier 3 words in long sentences, polysemous words, transition words, connectors; more sophisticated words for rich discussions and specificity in descriptions.

TIER 3 -- Subject-specific words that label content discipline concepts, subjects, and topics. Infrequently used academic words.


Criteria Preselecting for Selecting Words to Teach

It is critically important to the discipline.

It is critically important to this unit.

It is important to the understanding of the concept.

It is not critical but useful for ELLs.

It is not useful at this time.


Your Turn!In the following example, = Select words, phrases, and symbols

in the definition to pre teach, --in the Instructions, --and sample problem = Select two or three words to for each Tier

that you would want to pre teach.



A farmer picked a bunch of grapes that had between twenty and thirty grapes in the bunch. Which of the followig could be the number of grapes in the bunch?

A.☐ 31B.☐ 23C.☐ 19D.☐ 12

This is a word problem for second grade standardized state exam. Consider that Els at various levels of English proficiency, and reading proficiency will be asked to solve thi problem.

Math Problem – Second Grade

Identify & Classify Words

Type of Words Tier 3 Tier 2 Tier 1Polysemous

Phrases (bundled up words, idioms)

Cognates

Connectors & transition wordsHomophones

Other: Symbols, equations, formulas


Vocabulary Tiers for ELLs

Tier 1Simple WordsCognates

Tier 2Process, Idioms,Sophisticated, polysemous,

Tier 3Content Words,Key vocabulary

BunchBunchPickednumber

BetweenCould behad

TwentyThirty



READING MATHEMATICS & ELs

PROCEDURES TO SOLVING MATH PROBLEMS --All students need to …

(1) read the entire problem to find the key question being asked,

(2) re read to find the key details needed to solve the problem,

(3) re read several times to visualize the pieces or steps to solving the problem.

AND REMEMBER!!!!!!

(4) ELs always need (a) explicit review and instruction of vocabulary, and (b) to re read to understand key English vocabulary as well as concepts.

Sample: Word Problem

AVERAGES –upper elementary gradesDEFINITION: An average, or mean, simplifies a set of numbers

into a single number that approximates the value of the set.

THE PROBLEM: Find the average of the following set of numbers: 5, 4, 7, and 8.

Activity: TYP – (1) Identify and discuss the words or phrases that may cause

difficulties for ELs,

Your Turn!

ACTIVITY

TTYP and discuss what has been presented so far. Think of issues or concerns that you want to more information about.


Strategy: Partner Reading Word Problems

• Step 1 – Partner Reading Option 11. The teacher reads and models strategies.2. Partner A reads the first sentence. Partner B helps.3. Partner B reads the next sentence. Partner A helps.4. After each paragraph, partners “put their heads

together” and summarize what they read.5. Partners continue reading the whole problem.


Strategy for Solving Word ProblemsProportions….

Step 2 - Solving the Problem – Pairs or Triads

℗write down the question.℗underline confusing or unknown words or phrases to ask

your team, teacher or other students for clarification.℗eliminate unnecessary information and wrong answers.℗discuss and “guess” selected answers with other groups or

the entire class.



INSTRUCTIONS= Read and re read the entire problem,

underline the key question discuss details needed to solve the problem

identify the vocabulary words you need to show your answers

= express the problem in numerical figures,

= Write down the steps to solving the problem.

= solve the problem.

Outlining Word Problems


Number Sense: 6th Grade

STANDARDS: Solving addition, subtraction, multiplication, and division problems, including those that use positive and negative integers and combinatinations of operations.EXAMPLE---Simplify to make the calculations as simple as possible and identify the properties you used at each step:

1. 95 + 276 +

2. −19 + 37 + 19

3. −16 (−8 + 9 )

4. (−7)(17) ( 8)(17)

5. (−8)(−4)(19)(6+(−6))

Selecting Key Words & Phrases

The Tennessee Academic Vocabulary Project.- Selected key words and phrases that they deemed important for

understanding mathematics and other key subject areas.Words and phrases were selected by groups of volunteer subject matter and grade level specialists.

- Approximately 30 were identified for each subject area for K-6. Other terms and phrases were to be added by individual teachers.

- Research indicates that about 400 per year are typically addressed in programs that emphasize vocabulary instruction.

- In mathematics 244 terms and phrases are listed for grades K-8.(Marzano, 2004)

However, these are mostly Tier 3 – content specific. What is missing are Tier 2 and Tier 1 needed by ELs.

Corners

• Why is math vocabulary important?• Name key steps for teaching math word

problems.• Explain four ways to show numbers.• Mystery question …

Expediting Comprehension forEnglish Language Learners

THANK YOUDr. María Trejo, [email protected]

MATHEMATICS & LITERACYELEMENTARY LEVEL


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