Supporting ELLs in Mathematics: Ideas for Math Coaches

1. Supporting ELLs in Mathematics: Ideas for Math Coaches Jennifer M. Bay-Williams University of Louisville June 9, 2011 Language Coaching Culture

2. Welcome! • With 2-3 people sitting near you, share: • Your Name • A recent experience that has had an impact on your professional life. • A ‘mathematically-distinct’ word [means something distinct in math as compared to other settings, for example, similar]

3. Skill Efficiency • Fast-paced setting • Teacher modeling • Teacher-directed questions that require specific correct answers • Substantial time for students to practice (Hiebert & Grouws, 2007)

4. Conceptual Understanding • Making mathematical relationships explicit • Allowing students to struggle with important mathematical ideas (Hiebert & Grouws, 2007)

5. Three Key Features Feature 1: It must begin where the students are. Feature 2: The problematic or engaging aspect of the problem must be due to the mathematicsthat the students are to learn. Feature 3: It must require justification andexplanation for answers and methods. (Van de Walle, Karp, Bay-Williams, 2010)

6. Language Coaching Culture

7. What you can do • Focus on important mathematics • Make content relevant • Incorporate students’ identities • Ensure shared power (Van de Walle, Karp, Bay-Williams, 8E)

8. Culturally Responsive Teaching in Mathematics Reflective Questions • Focus on important mathematics • Make content relevant • Incorporate students’ identities • Ensure shared power

9. What you can do • Focus on important mathematics • Make content relevant • Incorporate students’ identities • Ensure shared power (Van de Walle, Karp, Bay-Williams, in press)

10. What you can do Incorporate student identities

11. Compare the following procedures: 495 495 3) 1485 3) 1485 - 12 28 28 15 – 27 0 15 – 15 0 (Midobuche, 2001)

12. What do you notice? 495 495 3) 1485 3) 1485 - 12 28 28 15 – 27 0 15 – 15 0 (Midobuche, 2001)

13. How will you respond? 495 495 3) 1485 3) 1485 - 12 28 28 15 – 27 0 15 – 15 0 (Midobuche, 2001)

14. Hundred Penny Box (Mathis, 1986) The story describes a 100-year-old woman who remembers an important event that happened to her for every one of her hundred pennies (one for each year). Each penny is more than a piece of money; it is a “memory trigger” for her life. Activity Collect one penny from each year of your life starting from the year of your birth and not missing a year. Ask family members to help you identify one special memory from each year. Create a penny time line of important events. (examples: first steps, accidents, vacations, pets, and births of siblings)

15. Hundred Penny Box (Mathis, 1986) How can you use the timeline to meet content in the Common Core State Standards? “I was an only child until I was 3 ½” 0 1 2 3 4 5 6 … “I learned how to ride a bike when I was 6” 0 2 4 6 8 10

16. Six areas of mathematics are found universally • counting • measuring • locating • designing and building • playing (e.g., “Mancala”) and • explaining (e.g., telling stories) (Bishop, 2001). THINK-PAIR & SHARE Think - of something in your curriculum that connects to one of these areas. Pair & Share– What is your topic? How can you connect it to individuals, culture and families?

17. What you can do Ensure shared power

18. How does power play out in a classroom?

19. What you can do: • Facilitate student interactions • Accountability • Cooperative Grouping • Explicitly developed classroom norms • Multiple solution strategies • Effective questioning strategies

20. Culture What can you do to nurture culturally-responsive classrooms? Language Coaching Culture

21. Language Coaching Culture

22. What you can do • Know about Math Vocabulary Issues • Provide Vocabulary Support • Analyze tasks/lessons from language lens

23. Pick a Word • Square • Horizontal • Obtuse • Vertical • Ten • Irrational • Absolute • Power • Integral • Zero • Equality • Percentage • Divided • Average • Mean • Constant • Odd • Even

24. 1. Math Vocabulary Issues • Many everyday words have ‘mathematically-distinct’ meanings • Some vocabulary is only encountered in math class • Many words may be used to signal the same concept/topic • Meaning is often related to the context • Logical connectors can pose problems

25. 1. Math Vocabulary Issues Definitions • Definitions are more precise than in other domains, and unique in that: • They are based on the least amount of information needed • There is “nesting” within definitions (relationships are implied, but not stated) • Square Trade: Left-definition • Right – tell all

26. Definitions “Perhaps the biggest misconception is that teaching vocabulary means teaching formal dictionary definitions. There are a number of traditional teaching practices related to vocabulary that deserve to be left in the ‘instructional dust bin’. The key weakness in all of these practices involves the cognitively limited or rote interaction students have with the new word/concept.” —Marzano, Pickering, & Pollock, 2005

27. 2. Provide Vocabulary Support: When?

28. 2. Provide Vocabulary Support: When? Before? • Can equip students with tools that will increase participation • Takes away time that students have to explore the problem, and may, inadvertently, lower the cognitive demand of the problem

29. 2. Provide Vocabulary Support: When? During? • Can make it more meaningful • Could bog down the activity, using more time

30. 2. Provide Vocabulary Support: When? After? • Good to review, apply in other contexts • If vocabulary was relevant, might have lost kids along the way

31. It depends . . . context or concept? What Should You Do?

32. 2. Provide Vocabulary Support: When? Adapted from Bay-Williams, & Livers, 2009

33. Vocabulary: Context

34. Vocabulary: Concept

35. 2. Provide Vocabulary Support: Ideas

36. $10,000 Pyramid Example Quadrilateral Perpendicular Parallel Four Angle Congruent

37. 2. Connect language to concept. Link Sheet

38. Social Networking

39. Description Visual Representation Symbols Related Operation or Concept Example Link Sheet The mean is the average of the numbers: adding up all the numbers and dividing by how many numbers there are. Mean 8 + 12 + 3 + 5 + 7 + 1 6 Mean is the process of “evening out” like finding out what the price would be if all items cost the same.

40. 3. Analyze Tasks: Comprehensible Input The mean of a set of four numbers is 5. Three of the numbers are 4.3, 8.15, and 1.65. What is the fourth number of the data set? How did you find it?

41. 3. Analyze Tasks: Comprehensible Input What might pose a challenge to ELLs? Fernandez, Anhalt, & Civil, 2009

42. 3. Analyze Tasks: Guarding Language Original Text (see handout): Raphael wants to make posters for his sale by enlarging his 8 1.2” by 11” ad. Raphael thinks big posters will get more attention, so he wants to enlarge his ad as much as possible. The copy machines at the copy shop have cartridges for three paper sizes: 8 1/2” by 11”, 11” by 14”, 11” by 17”. The machines allow users to enlarge or reduce documents by specifying a percent between 50% and 200%. For example, to enlarge a document by a scale factor of 1.5, a user would enter 150%. This tells the machine to enlarge the document to 150% of its current size. A. Can Raphael make a poster that is similar to his original ad on any of the three paper sizes - without having to trim off part of the paper? Why or why not?(Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004)

43. Guarded & Supported Language ‘Guarded’ (modified) Text (one example): Raphael is having a sale. He made an advertisement on paper that is 8 1/2” by 11”, but he wants to make it as big as possible. There are three sizes of paper: 8 1/2” by 11”, 11” by 14”, or 11” by 17”. He can make the copy machine change the size of the paper by choosing a percent between 50% and 200%. For example, to make the advertisement bigger by a scale factor of 1.5, Raphael would choose 150%. This will make the advertisement 150% bigger than it is now.

44. Language What can you do to nurture language support in standards-based mathematics? Language Coaching Culture

45. Language Coaching Culture

46. Three-Phase Coaching Cycle How can you support teachers in developing the dual lens on content and language?

47. Successfully teaching students from culturally and linguistically diverse backgrounds-especially students from historically marginalized groups-involves more than just applying specialized teaching techniques. It demands a new way of looking at teaching that is grounded in an understanding of the role of culture and language in learning. -Ana Maria Villegas & Tamara Lucas

48. Questions? THANK YOU! Contact Information: j.baywilliams@louisville.edu

49. Bibliography Bay-Williams, J. M., & Livers, S. (2009). Supporting math vocabulary acquisition. Teaching Children Mathematics, 16(4), 238-245. Bishop, A. J. (2001).What values do you teach when you teach mathematics? Teaching Children Mathematics, 7(6), 346-349. Fernandez, M. L., Anhalt, C., & Civil, M. (2009). Mathematical interviews to assess Latino students. Teaching Children Mathematics, 16(3), 162–169. Lappan, G., Fey, J., Fitzgerald, W., Friel, S., & Phillips, E. (2004). Moving straight ahead: Linear relationships. Boston, MA: Pearson/Prentice Hall. Marzano, R. J., Pickering, D., & Pollock, J. E. (2005). Classroom instruction that works: Research-based strategies for increasing student achievement. Upper Saddle River, NJ: Pearson/Merrill Prentice Hall. Mathis, S. B., Dillon, L., & Dillon, D. (1986). The hundred penny box. New York, NY: Puffin Books. Midobuche, E. (2001). Building cultural bridges between home and the mathematics classroom. Teaching Children Mathematics, 7(9), 500-502. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (In press.). Elementary and middle school mathematics teaching developmentally (8th Edition). Boston, MA: Allyn and Bacon. Villegas, A. M., & Lucas, T. (2007). The culturally responsive teacher. Educational Leadership, 64(6), 28-33. Virginia Department of Education. (2004). Mathematics: Strategies for teaching limited English proficient (LEP) students: A supplemental resource to the K-12 mathematics standards of learning enhanced scope and sequence. Richmond, VA: Virginia Department of Education.