2. Slide 1 Welcome California Mathematics and Science Partnership (CaMSP) Year 2, Follow Up 3 January 22, 2011

3. Slide 2 Agenda: Making the Invisible Visible We will identify the language of explaining quadratic equations to teach this language effectively.

4. Slide 3 Essential Questions How can we identify the language that we need to teach our students so that they can discuss quadratic equations? What are effective instructional strategies that help students learn this language?

5. Slide 4 Step 1: Analyzing language use to identify the many features. Step 2: Limiting the features to a manageable number. Identifying Language to Teach

6. Slide 5 Identifying the language features to teach entails language analysis of texts—oral and written Written – written explanations, e.g., from the students’ textbooks and other resources Oral – transcribed language use – usually of teachers and students

7. Slide 6 Handout Let’s analyze how others describe quadratic equations. Student talk = output Our talk to students = input Language students read = input

8. Slide 7 We will be doing a task shortly that requires you to use a handout. Handout : The Language Needed to Explain Quadratic Equations

9. Slide 8 You need a handout that looks like this one:

10. Slide 9 Stand up! Hand up! Pair up!

11. Slide 10 Steps Read the handout on the language of quadratic equations. Take at least five minutes. Underline the language you might use to explain quadratic equations. Write down any additional language.

12. Slide 11 Steps Stand up when you are done and find a partner across the room. Put your hand up, smile and establish eye contact with someone else who has finished reading the handout. Do a high five. Partners interact for three minutes. They discuss the answers to several questions.

13. Slide 12 Task—Answer these questions: What language enables you to explain quadratic equations? Would you use any of the language in the handout? What additional language would you use?

14. Slide 13 Would you use any additional vocabulary?

15. Slide 14 What about prepositions?

16. Slide 15 Would anyone use the word functions? Would anyone say: Functions are rules that describe the relationship between two variables. They are commonly expressed as equations. Functions are often expressed as equations that include two variables, as in x+3=y.

17. Slide 16 What about function table? Did anyone say: Function tables represent pairs of numbers that follow a certain rule, or function.

18. Slide 17 Function Table (cont.) Did anyone say? A function table for x+3=y would include a column of corresponding numbers for "x" and a column for "y" to reveal a numerical pattern.

19. Slide 18 Would anyone give an example of a function table? Xy 18 210 312 414 y = 2x + 6

20. Slide 19 Column a line of numbers or words written under each other that goes down a page

21. Slide 20 Row a line of things or people next to each other

22. Slide 21 In a row One after another, consecutively

23. Slide 22 Would anyone use unknown numbers or the word let? Did anyone say: When you are looking for unknown numbers, let a variable represent that numbers?

24. Slide 23 What about the word represent?

25. 1.Partners find a place to sit down. They decide who is Partner 1 and who is Partner 2. 2.Teacher describes the task. Partners will take turns explaining what a quadratic equation is. 3.In pairs, Partner 1 explains a quadratic equation as Partner 2 listens and completes the graphic organizer. 4.Teacher calls “time”. 5.Partners switch roles. Partner 2 explains what a quadratic equation is as Partner 1 listens and completes the graphic organizer. Timed Pair Share

26. Slide 25 TASK: What language enables you to explain quadratic equation? First Partner: Explains quadratic equations. Second Partner: The partner completes the graphic organizer, writing down the language his/her partner has used. Both Partners: Discuss the language. Next, partners switch roles.

27. Slide 26 Take a minute to prepare.

28. Slide 27 What language did you or your partner use to explain quadratic equations? Reminder: Complete the graphic organizer.

29. Slide 28 Identifying Language Features to Teach STEP TWO: Narrowing the language features to a manageable number that you want students to learn.

30. Step 2: Narrowing the List of Features: Using the guiding questions below, determine what manageable list of features you would choose to teach. Guiding Questions Is the language feature unknown? Is the language feature unknown? Will it improve students’ ability to explain patterns? Will it improve students’ ability to explain patterns? Will it increase students’ understanding of math? Will it increase students’ understanding of math? Will students use the feature in other math assignments? Will students use the feature in other math assignments? Will knowledge of the feature help to improve students’ Will knowledge of the feature help to improve students’ knowledge of academic language and/or the language of math?

31. Slide 30 Key Language Features Task: Write 6 key features of language you would want to teach students before asking them to discuss or explain quadratic equations in partner activities.

32. Slide 31

33. Slide 32 Perfect Practice in Conversation Each time a teacher gets a student to practice a language feature correctly, it helps the student learn the feature! That’s right! Adapted from David Howe 2006

34. Slide 33 How Much Practice is Needed? Number of correct repetitions in a row of a new word needed to “automatize” the word - NICHD (R. Lyon, 1997)

35. What techniques can we use to make sure students deliberately practice using specific language?

36. Does anyone suggest reading explanations aloud to students, explaining the language in it and discussing it? What about asking students to read it aloud afterwards?

37. Deliberate modeling and repetition – individual, group and choral Reading Aloud: Tables, equations, algebraic expressions Mathematically Speaking Discussions and Analyses – e.g., of student notes, textbook explanations, teacher summaries …especially with word banks and/or sentence stems! Here are just a few (see handout for other ideas):

38. Choral Repetition Algebraic Expression Word PhraseOperation w + 4A number plus 4.Addition w – 4A number minus 4. Subtraction 4 x w or 4w4 times a numberMultiplication w 4 or w/44 divided by a number Division

39. Choral Repetition

40. Repetition 2x 2 + 3x + 1 = 0 x 2 + x = 2x + 3 (x+2)(x+3) = 5 x 2 - 6x + 2 = 0

41. Slide 40 Tips for Preparing Choral Response Activities Make sure to elicit at least four-six sentences, phrases or words Try to make sure all sentences, phrases or words are parallel in form

42. Choral Repetition for Answering Questions Think--Think how you would respond. Listen -- Listen to the directions or prompt Wait--Keep from blurting out the answer. Give everyone time to think. Respond--When given the signal say or write your response. Why should we use choral repetition?

43. Why is language use important? Kathryn Morgan Woodward, research associate Williams, T., Kirst, M., Haertel, E., et al. (2010). Gaining Ground in the Middle Grades: Why Some Schools Do Better. Mountain View, CA: EdSource. http://www.edsource.org/middle-grades-summary.html

44. Slide 43 Let’s look at the language in the released word problems on the California Standards Test in Mathematics.

45. Slide 44 What makes these problems difficult for English learners? With your one or two partners, determine the answers to the released algebra items. List the language in the problem that could be difficult for English learners to understand. Decide how you could teach it to them.

54. Slide 53 Debrief Share solutions. Discuss language that could cause English learners difficulties.

55. Slide 54 What the Research Says

56. Slide 55 Summary How can we identify the language students need to know to discuss patterns? What are effective instructional strategies we can use to help students use this language?

57. Slide 56 Take a Break