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NJ Abbott Secondary Initiative Grades Academic Rigor Teaching Mathematics to English Language Learners High Schools That Work Making Middle Grades Work November 14, 2005 Southern Regional Education Board

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**The Abbott Secondary Education Initiative focuses on three key areas for grades 6-12.**

Smaller organizational structures Academic Rigor Personalization Our goal is to ensure that Abbott districts translate these higher standards into their expectations for all students.

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**The Abbott Secondary Education Initiative focuses on three key areas for grades 6-12.**

Smaller organizational structures Academic Rigor Personalization Our goal is to ensure that Abbott districts translate these higher standards into their expectations for all students.

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**The Abbott Secondary Education Initiative**

These challenges are more acute in urban and rural districts. In addition, students from non-English-speaking backgrounds face additional challenges as they attempt to adjust to American schools and excel academically.

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**Sheltered Instruction Observation Protocol**

SIOP A research based Sheltered Instruction Observation Protocol

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**What Students Need to Learn: Language and Content**

ESL Standards What to Teach How to Teach What Students Need SIOP Content Area Standards

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**What Students Need to Learn: Language and Content**

ESL Standards How to Teach Content Area What Students Need Standards (What to Teach) SIOP (What to Teach) Listening in English Preparation Standard Speaking in English Building Background Benchmark Reading in English Comprehensible Input Performance Task Writing in English Strategies Scoring guide Interaction Practice/Application Lesson Delivery Review/Assessment Adapted from Juli Kendall (1998)

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Comprehensible Input Is one of the main components that distinguishes effective sheltered instruction from high-quality nonsheltered instruction. Is important and should be measured throughout the lesson to ensure that students are taking in and understanding what is being communicated to them.

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**Comprehensible Input Section of the SIOP**

N/A 10. Speech appropriate Speech sometimes Speech inappropriate for students’ inappropriate for for students’ proficiency proficiency level students’ proficiency level (i.e. slower rate, level enunciation, and simple sentence structure for beginners 11. Explanation of Explanation of academic Explanation of academic academic tasks tasks somewhat clear tasks unclear clear 12. Uses a variety of Uses some techniques Uses few or no techniques techniques to make to make content concepts to make content concepts content concepts clear clear clear (i.e. modeling, visuals, hands-on activities, demonstrations, gestures, body language)

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**Speaking the Same Language**

One of the keys to transferring information is to be able to develop a common language.

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AXIS

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CHORD

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POWER

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PRODUCT

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RANGE

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SOLUTION

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YARD

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**Let’s Compare Our Definitions**

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AXIS

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AXIS Health: second vertebra in neck: the second vertebra in the neck, which acts as the pivot on which the head and first vertebra turn Agriculture: central part of plant: the main part of a plant, usually the stem and the root, from which all subsidiary parts develop Geometry: one of two or more lines on which coordinates are measured. Often on a graph two axis form its left and lower margins.

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CHORD

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CHORD Construction: horizontal connecting part: the horizontal part of a truss designed to absorb tension, for example, in a roof. Mathematics: A segment whose endpoints are points on a circle.

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POWER

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**POWER Transportation: electricity: electricity made available for use.**

Transportation: measure of rate of doing work: a measure of the rate of doing work or transferring energy, usually expressed in terms of wattage or horsepower. Transportation: energy to drive machinery: energy or force used to drive machinery or produce electricity.

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POWER Continued Mathematics: number of multiplications: the number of times a quantity is to be successively multiplied by itself, usually written as a small number to the right of and above the quantity.

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PRODUCT

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PRODUCT Business: company’s goods or services: the goods or services produced by a company. Mathematics: result of multiplying: the result of the multiplication of two or more quantities.

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RANGE

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RANGE Transportation: distance traveled without refueling: the farthest distance that a vehicle or aircraft can travel without refueling. Agriculture: open land for grazing farm animals: a large area of open land on which farm animals can graze. Construction: north-south strip of townships: a north-south strip of townships six miles square and numbered east and west from a meridian in a U.S. public land survey.

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RANGE Continued Mathematics: set of values: the set of values that can be taken by a function or a variable. Statistics: extent of frequency distribution: the difference between the smallest and the largest value in a frequency distribution.

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SOLUTION

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SOLUTION Health: fluid with substance dissolved in it: a substance consisting of two or more substances mixed together and uniformly dispersed, most commonly the result of dissolving a solid, fluid, or gas in a liquid. It is also, however, possible to form a solution by dissolving a gas or solid in a solid or one gas in another gas. Mathematics: value satisfying an equation: a value for a variable that satisfies an equation.

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YARD

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YARD Business: Slang for one billion dollars. Used particularly in currency trading, e.g. for Japanese yen since on billion yen only equals approximately US$10 million. It is clearer to say, " I'm a buyer of a yard of yen," than to say, "I'm a buyer of a billion yen," which could be misheard as, "I'm a buyer of a million yen.“ Agriculture: livestock enclosure: an enclosed area of land for livestock.

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YARD Continued Agriculture: land around a house: the area of land immediately surrounding a house, often covered with grass or landscaping. Agriculture: winter grazing area: an area of land where deer, moose, or other animals graze in winter. Mathematics: imperial unit of length: a unit of length equal to m (3 ft).

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**Identifying Levels of Second Language Acquisition**

It is very important that teachers determine the English language acquisition levels of their students. Once this is ascertained, teachers can make content comprehensible based on the language needs of each student. Teachers can also encourage students to increase their English proficiency by providing activities and opportunities for them to frequently use English.

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The following seven stages of language acquisition are fluid: that is, students do not move in concrete steps from one stage to another.

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**Beginning (Pre-Production)**

Students have little comprehension of oral and written English, and they are unable to produce much if any oral or written English at this point. Teachers should provide abundant listening opportunities, use many physical gestures and movement to convey meaning, and include a great deal of context for shared reading and writing.

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**Beginning (Early Production)**

Students have limited English comprehension but they can now give one or two word oral responses. For students learning to read English, teachers can use predictable and patterned books and encourage them to label and manipulate pictures or fill in contextualized sentences.

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**Beginning (Early Speech Emergence)**

Students speak in simple sentence and can comprehend highly contextualized oral and written information. Teachers can expect students to respond to simple open-ended questions. They should continue to provide sufficient language development opportunities and include many activities that require students to read, write, listen, and speak.

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Intermediate (Early) Students have some proficiency in communicating simple ideas. They have comprehension of contextualized information. Teachers can encourage these students to expand on simple responses while developing critical thinking skills.

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Intermediate Students have proficiency in communicating ideas and they can comprehend contextualized information in English. Teachers should provide explicit instruction in figurative language, making predictions, using text features to read a book, and English grammar. These students can participate in generative activities that promote higher levels of thinking.

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Early Advanced Students can communicate well and have adequate vocabulary to achieve academically. They have a good comprehension of information. Teachers should provide for a variety of realistic writing and speaking opportunities. These students can be exposed to activities to further practice critical thinking skills.

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Advanced Students have near native speech fluency and expanded vocabulary to achieve academically. They have good comprehension of information in English. These students can lead group discussions, and they should be given the opportunity to do presentations and have many opportunities to produce oral and written forms of communication.

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“Numerous studies reveal that a knowledge of mathematics vocabulary directly affects achievement in arithmetic particularly problem solving”. Barton, ML & Heidema, c (2002) Teaching Reading in Mathematics 2nd Ed.

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Common sense tells us that as more words can be used in a meaningful manner, the easier it becomes to communicate effectively.

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Today, we are going to look at some techniques we can use in our mathematics classrooms to make content concepts clear.

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Today, we are going to look at some techniques we can use in our mathematics classrooms to make content concepts clear. Comprehensible Input

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Alternate Materials Use many materials to make content comprehensible to students. The more variation you find, the better you will be able to connect with different students’ learning styles and backgrounds.

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**Let’s look at an alternate way to teach the geometry concepts of:**

Point Line Plane

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**Visualizing a 3-Dimensional Space page 8**

Materials: 3 Index Cards (per person) Hole Punch Scotch Tape Uncooked spaghetti (one per person)

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**Visualizing a 3-Dimensional Space page 8**

Materials: 3 Index Cards (per person) Hole Punch Scotch Tape Uncooked spaghetti (one per person)

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**Visualizing a 3-Dimensional Space**

Directions: 1. Punch a hole in each index card. Label the holes F, G, and H. 2. Tape the three index cards together to form a corner (i.e. two adjacent walls and a ceiling). 3. Draw a line through F. Label this line l. 4. Put a piece of spaghetti through holes F and G.

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**Visualizing a 3-Dimensional Space**

What do the holes represent? What does the spaghetti represent? What do the index cards represent? How many points do line l and the spaghetti have in common?

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**Visualizing a 3-Dimensional Space**

Draw a line on the same index card as l in such a way that it will not have any points in common with line l, even though both lines continue forever Label this line m. How many lines can you draw that will satisfy this condition?

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**Visualizing a 3-Dimensional Space**

Draw a line on an index card that does not contain line l in such a way that it will not have any points in common with the other lines, even though they continue forever Label this line x. How many lines can you draw that will satisfy this condition?

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**Visualizing a 3-Dimensional Space**

Draw a line that is completely contained in two index cards Label this line n. How many lines can you draw like this using the same two index cards?

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**Visualizing a 3-Dimensional Space**

Use your model to create each of the following situations, if possible. A line and a plane with exactly one point in common. A line and a plane with exactly two points in common. A line and a plane with exactly no points in common.

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**Vocabulary Activities**

As teachers we often think of vocabulary cards for review. However, they can also be used to introduce or frontload vocabulary at the beginning of a lesson. This process helps students build background knowledge and increases comprehension of the lesson or unit they will be studying.

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**Visual Boxing Word Parallel Personal Association Railroad Tracks**

Definition Two lines are parallel if they are in the same plane and never intersect Something NOT the Word Perpendicular Lines One street dead ends into another

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**Word Problems (Math Connection)**

The teacher gives students a list of vocabulary words from the chapter. Then the students, working either independently or in pairs, use two or three of the vocabulary words to create a word problem which can then be solved by other class members.

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**Word Problem Example Sum Plus First Total Add Next Altogether More**

Addition How Many First, I had three apples, then I found nine more apples. How many apples do I have altogether?

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Vocabulary Notebook Students will create and maintain a notebook specifically for mathematic vocabulary words. The notebook will include the word, the textbook or dictionary definition, the student’s own definition, and an example. This notebook can be used as reference throughout the course.

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**Vocabulary Notebook Example**

Net: A two-dimensional pattern you can form into a three-dimensional figure. A pattern for making a box, can, pyramid or other object. You cut it out and fold it. Textbook definition Student definition Example Box Cube Can Cylinder

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Vocabulary Cards One side of the card is reserved for the term/concept word and illustration. The drawing is a visual clue that is significant for the student making the card, and will help trigger the meaning of the word. The definition of the word is written on the reverse side of the card. A sentence that uses the word in a rich context may also be included.

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**Vocabulary Cards Example**

Front Parallel Back Two lines are parallel if they are in the same plane and never intersect.

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Vocabulary Cards Incorporate the use of the vocabulary cards in your lessons. Use the cards as a reference for class discussions, spelling and/or meanings. Develop review or word games that require the use of the cards. If you have a word wall, include words from the vocabulary cards.

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Connect Two Students need to be able to see connections between the various concepts they are learning about in mathematics. This is extremely important for vertical alignment as well as for horizontal alignment. Once students have their vocabulary for the unit, ask them to choose two words from their list. Students will then make connections with the two mathematical words they have chosen. This may be done as a written paper or a page with words and graphics as illustrations.

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**Connect Two Example Data Set Data Value Mode Mean**

Median Outlier Measure of Central Tendency A data set is a table of information and each piece of information is a data value. In the example below, the prices form a data set. Each price is a data value. Store Price Wal-Mart $19.95 Target $21.00

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**Graphic Organizer: Concept Mapping**

Graphic organizers are a way for students to make connections between concepts and vocabulary words. There are 5 basic steps to follow

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**Graphic Organizer: Concept Mapping**

Step 1: Students write down as many different words as they can that relate to a word the teacher gives them. Step 2: Students work in small groups. Each group must sort the cards they just created into at least 4 different categories. Step 3: Students check to see if they put their cards into appropriate categories. Step 4: The teacher leads the class in a discussion of the categories the students decided on and create a class concept map on the board. Step 5: The teacher then recreates the class map on a worksheet and gives each student a copy of the map. The students then adjust and refine their maps as they learn more about the concept.

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**Graphic Organizer: Concept Mapping**

Volume Length Gallon Deciliter Kiloliter Quart Pint Liter Kilometer Centimeter Millimeter Yard Inch Foot Measurement Numbers Weight Tools 9 12 3 Pound Kilogram Milligram Ounce Decigram Yardstick Meterstick Ruler Caliper Tape Measure

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**Every Student Gets a Chance**

The teacher writes a new concept or idea on the board and reads it aloud. He or she then asks for a volunteer to read aloud what was written. Then, instead of moving on to another concept or example, the teacher asks for a second volunteer to read aloud the same information. This continues so that each student who feels comfortable can choose to read the information aloud.

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**Every Student Gets a Chance**

Students who are at beginning levels of English proficiency will feel more comfortable repeating information after they have heard it spoken by each of their classmates. In this activity, students are hearing the same input over and over from other students, rather then from the teacher. Thus they hear other pronunciations, inflections, and intonations.

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**Every Student Gets a Chance**

This activity is very effective for teaching, practicing, and reinforcing a concept such as place value and reading large numbers, and for helping students remember important definitions and vocabulary.

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**Every Student Gets a Chance**

For example, English learners need to learn the words million, thousand, hundred, and tens and ones in order to read the number 196,325,704 Teach students to identify the numbers in their sets of three: 196 (one hundred ninety six) million 325 (three hundred twenty five) thousand 704 (seven hundred four)

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**“Recognition of a working mathematics vocabulary is very important**

“Recognition of a working mathematics vocabulary is very important. Students must be able to translate words into their appropriate mathematical symbols”. (Rothman and Cohen, 1989)

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It is important that you specifically teach mathematics word lists and vocabulary. The student who can recognize a mathematical operation when described through multiple words or phrases can translate these words into a meaningful number sentence and perform the requisite computation.

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Because mathematics has its own unique vocabulary, you, the math teacher, must teach vocabulary explicitly. Use slower speech, clear enunciation, controlled vocabulary, syntax, and sentence length. Pose questions and design tasks that engage students in higher-level thinking. Ask students to justify ideas orally and in writing.

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Tips for Teachers Insist that students use correct mathematical vocabulary in their explanations (when developmentally appropriate). Make sure students are familiar with the terms used in the New Jersey Core Content Standards. Make a conscious effort to focus on Comprehensible Input. Implement at least one of the strategies we discussed today in your classroom this year.

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Remember that students at lower levels of English proficiency are not necessarily functioning at lower levels of cognitive ability. Frequently, these students are able to use higher level thinking skills in their primary language but have a more difficult time understanding the academic content and expressing their knowledge in English.

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Thank you for coming! If you have any questions, please feel free to contact me. Betsy Urschel

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**Word Wall Display of vocabulary/concept words.**

Always place the words on a specific wall area, so students will know to refer to this site for the current vocabulary. When new terms are introduced, move the “old” words to a different location where they are still accessible. Have students, periodically, “read the wall” for review.

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**Word Wall Example Angles**

Obtuse Angle: An angle whose measure is between 900 and 1800. Right Angle: An angle whose measure is 900. Acute Angle: An angle whose measure is between 00 and 900.

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