Teaching Math to English Language Learners in Grades 6-12

1. NJ Abbott Secondary Initiative Grades 6-12Academic RigorTeaching Mathematics to English Language LearnersHigh Schools That WorkMaking Middle Grades WorkNovember 14, 2005 SouthernRegionalEducationBoard

2. 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.

3. 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.

4. 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.

5. SIOP A research based Sheltered Instruction Observation Protocol

6. What Students Need to Learn: Language and Content • ESL Standards • What to Teach • How to Teach What Students Need • SIOP • Content Area Standards • What to Teach

7. What Students Need to Learn: Language and Content ESL Standards How to Teach Content Area What Students NeedStandards (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)

8. 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.

9. Comprehensible Input Section of the SIOP 4 3 2 1 0 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)

10. Speaking the Same Language • One of the keys to transferring information is to be able to develop a common language.

11. AXIS

12. CHORD

13. POWER

14. PRODUCT

15. RANGE

16. SOLUTION

17. YARD

18. Let’s Compare Our Definitions

19. AXIS

20. 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.

21. CHORD

22. 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.

23. POWER

24. 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.

25. 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.

26. PRODUCT

27. 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.

28. RANGE

29. 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.

30. 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.

31. SOLUTION

32. 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.

33. YARD

34. 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.

35. 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 0.9144 m (3 ft).

36. 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.

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

38. 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.

39. 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.

40. 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.

41. 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.

42. 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.

43. 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.

44. 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.

45. “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.

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

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

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

49. 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.

50. Let’s look at an alternate way to teach the geometry concepts of: • Point • Line • Plane