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

3. Slide 2 www.wordle.net

4. Slide 3 Agenda: Making the Invisible Visible We will identify the language of patterns and ways to teach this language effectively. We will reflect on recent research related to the language of patterns and teaching this language effectively.

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

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

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

8. Slide 7 Handout Let’s analyze how we talk about patterns. Student talk = output Our talk to students = input

9. Slide 8 We will be doing a task shortly that requires you to use two handouts. Handout 1: Patterns Handout 2: The Language Needed to Explain Patterns

10. Slide 9 You need a handout that looks like this one: Grade 6

11. You also need this handout.

12. Slide 11 Stand up! Hand up! Pair up!

13. Slide 12 Steps Read the handout on the language of patterns. Circle the language you might use to explain Pattern A. Stand up when you are done. Put your hand up, smile and establish eye contact with someone else who has finished reading the handout.

14. Slide 13 Steps Find a partner. Do a high five. Partners interact for three minutes. They discuss the answers to several questions.

15. Slide 14 Task—Answer these questions: What language enables you to explain patterns? Would you use any of the language in the handout? What additional language would you use?

16. Slide 15 Would you use any additional vocabulary?

17. Slide 16 Vocabulary TO GO UP to increase by a number Add: a number plus 2 a number added to 2 TO GO DOWN to decrease by a number Subtract: a number minus 2 a number less 2

18. Slide 17 Vocabulary Downward Upward Sideways

19. Slide 18 Vocabulary Pattern: A design or an arrangement of numbers that models a general rule. Term: Each design or number in the pattern

20. What additional expressions would you use? Equivalent to Different from Similar to

21. Slide 20 What about prepositions? On the top of the square The figure in the middle On the right

22. Slide 21 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.

23. Slide 22 What about function table? Did anyone say: Function tables represent pairs of numbers that follow a certain rule, or function.

24. Slide 23 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.

25. Slide 24 Would anyone give an example of a function table? Xy 18 210 312 414 y = 2x + 6

26. Slide 25 Column a line of numbers or words written under each other that goes down a page

27. Slide 26 Row a line of things or people next to each other

28. Slide 27 In a row One after another, consecutively

29. Slide 28 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?

30. 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 the patterns (B and C). 3.In pairs, Partner 1 explains Pattern B as Partner 2 listens and completes the graphic organizer. 4.Teacher calls “time”. 5.Partners switch roles. Partner 2 explains Pattern C as Partner 1 listens and completes the graphic organizer. Timed Pair Share

31. Slide 30 TASK: What language enables you to explain patterns? First Partner: Draws a table to explain the pattern to his/her partner. Second Partner: The partner completes the graphic organizer, writing down the language his/her partner has used. Both Partners: Discuss the language.

32. Slide 31 Take a minute to prepare a table.

33. Slide 32 Partners should draw a table and explain it.

34. Example Figure Number of Squares 1 2 3 4?

35. Slide 34 Pattern B

36. Slide 35 Pattern C

37. Slide 36 What language did you or your partner use to explain patterns? Reminder: Complete the graphic organizer.

38. Slide 37 Identifying Language Features to Teach STEP TWO: Narrowing the language features to those that students need to learn.

39. 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?

40. Slide 39 Key Language Features Task: Write 6 key features of language you would want to teach students before asking them to explain patterns in partner activities.

41. Slide 40

42. Slide 41 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

43. Slide 42 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)

44. What techniques can we use to teach students specific language features?

45. 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):

46. 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

47. Choral Repetition Algebraic Expression Word PhraseOperation w + 4 w – 4 4 x w or 4w w 4 or w/4

48. Slide 47 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

49. 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.

50. Slide 49 Question Why do we need to use choral repetition in our classes?

51. Slide 50 What the Research Says

52. Slide 51 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?

53. Slide 52 Take a Break