1. Welcome to Session 4: Making Math Language and Assessments More Accessible Please sign in. Fill out 3.1: Warm-Up in Section 3 of your binder. Coffee – in our room © 2010, EDC1

2. Topic #1: Introduction & Assignment Discussions In this section, we will: Follow-up on Session 3 Go over today’s agenda Share experiences using accessibility strategies Discuss articles 2

3. Goal Reminder: To make mathematics instruction more accessible to a to Improve Student Learning © 2010, EDC3

4. Ground Rules Reminder Contribute your ideas Respect others’ opinions Assume positive intentions Watch your own air time No side conversations Start and end on time Turn off cell phone ringers No texting or emailing “Parking Lot” © 2010, EDC4

5. Looking Back: Topics Collaborative Teaching Models Collaborative Planning Complexities of Collaboration Strengthening Communication 5 Your Feedback Positives Suggestions Your Assignments

6. © 2010, EDC Session 3: Agenda & Goals 1.Introduction & Assignment Discussions 2.Language in Mathematics 3.Word Problems 4.Math Vocabulary 5.Sample Lesson 6.Accessible Classroom Assessments 7.Adapting Tests and Quizzes 8.Planning Accessible Assessments Goals  Learn ways to make math language and assessments more accessible  Leave with ideas to try with students 6

7. © 2010, EDC Partner Discussions: Strategies Tried Please take out: Reflection Form, copy of strategy, & work sample from focal student Talk with a partner who you do not work with. On your turn: Describe the strategy and your reasons for using it How did you use the strategy? How helpful was the strategy for your focal student? What might you do differently if you used it again in the future? Time: 5 minutes each Strategy Reflection Form 7

8. © 2010, EDC Whole Group Share Out What’s one thing that you learned from your experience using the strategies? What’s one idea from your partner that you would like to try with your students? Why? 8

9. © 2010, EDC Discuss Article Take out the article, Building Students’ Understanding: The Equal Sign. Discuss: What are two points that stood out for you? Why? Choose a reporter who will share a few ideas with the whole group. Time: 10 minutes 9

10. © 2010, EDC Whole Group Share-Out What’s one idea from your article discussion that you want to share with the whole group? 10

11. © 2010, EDC Topic #2: Language in Mathematics In this section, we will: Learn about language demands and challenges for students Discuss focal students’ strengths and difficulties with math language 11

12. © 2010, EDC Math Communication Goals for Students Organize and consolidate their math thinking through communication Communicate their math thinking coherently and clearly Use the language of math to express math ideas precisely Analyze and evaluate the math thinking and strategies of others Source: Principles and Standards for School Mathematics (NCTM) 12

13. © 2010, EDC Types of Language Demands Receptive Reading Listening Expressive Writing Speaking Common Areas of Difficulty Reading: Decoding; Comprehension Listening: Auditory Processing Writing: Organizing ideas in writing Speaking: Expressing ideas orally 13

14. © 2010, EDC Focal Students & Math Language Take out Warm-Up 3.1 Discuss with a Partner What strengths and difficulties does your focal student have with math language? Reading Listening Writing Speaking Time: 5 min 3.1 14

15. © 2010, EDC Reading Math Texts vs. Fiction FICTION Dorothy lived in the midst of the great Kansas prairies, with Uncle Henry, who was a farmer, and Aunt Em, who was the farmer's wife. Their house was small, for the lumber to build it had to be carried by wagon many miles. Baum, L. F. p.1 MATH TEXT Based on the pattern, how could you figure out the number of small squares in any figure number? Write an equation to find the number of squares in Figure n. What differences do you notice? 15

16. © 2010, EDC Conceptual Density of Mathematics Text “One reason students struggle with reading mathematics is the sheer number of concepts packed into the text. According to Schell, math text presents more concepts per word, sentence, and paragraph than any other content-area text.” Source : Barton, M. and Heidema, C. (2002) p.14 16

17. © 2010, EDC What’s different about reading math texts? Not just left to right -- need to read in different directions Not just words – also tables, graphs diagrams, and symbols The process of decoding symbols is different from decoding words. Symbols are like “sight words.” One challenge is that different symbols are used to describe the same process. Multiplication *, x, (), ● 17

18. © 2010, EDC Topic #3: Word Problems In this section, we will: Solve and analyze a math problem Examine and discuss student work Learn about research on difficulties and strategies 18

19. © 2010, EDC Get to Know the Math Problem 1.Work on the problem. Write down the questions that you ask yourself to get started. 2.Discuss with a partner:  What questions did you ask yourself to get started?  How did you set up the table?  How did you come up with the algebraic expression? 3.2 Popcorn Problem 3.2A Answers 19

20. © 2010, EDC Share Approaches Two volunteers present different approaches to the whole group: What questions did you ask yourself to get started? How did you set up the table? How did you come up with the algebraic expression? 20

21. Apply the Framework: Consider the Math Key Math Goals Represent a situation with a table and symbolic expression What would you add to the goals? © 2010, EDC21

22. © 2010, EDC Analyze the Problem What are the task demands on students? Language Conceptual Organization What potential difficulties would you anticipate for your focal students? Next, we will look at actual work samples from two 7 th graders. 3.2 Popcorn Problem Ref. A on Yellow 22

23. © 2010, EDC Consider the Student: Examine Work Sample X 1. Work individually to: Look at the work sample for Student X Write notes on your LASW form in the first 2 columns. 2. In small groups, discuss Student X’s work: Strengths and Difficulties Diagnostic Questions Time: ~7 minutes 3.4 Student X 3.3 LASW Tool 23

24. Discuss Student X Evidence of strengths & difficulties? Questions to ask to find out more about the student’s math understanding? Strategies? A. B. C. © 2010, EDC24

25. © 2010, EDC Examine Work Sample from Student Y 1. Work individually to: Look at the work sample for Student Y Write notes on your LASW form in the first 2 columns. 2. In small groups, discuss Student Y’s work: Strengths and Difficulties Diagnostic Questions 3.5 Student Y3.3 LASW Tool 25

26. Discuss Student Y & Compare Evidence of strengths & difficulties? Diagnostic Questions & Strategies Similarities & Differences for X & Y? A. B. C. © 2010, EDC26

27. © 2010, EDC Sample Strategies for the Popcorn Problem Examine strategies individually Take a look at the sample strategies. Talk with a partner What’s one strategy that you would like to try with your students? Why? What is your experience using similar strategies? What works well? 3.6 Sample Strategies 27

28. © 2010, EDC Research on Word Problems Barriers for Students Irrelevant Information Extra Steps Length Research Findings Students with math learning disabilities do much worse than peers when the first two features are present. Similar findings for student with attention difficulties. Students who have both math and reading disabilities have the lowest performance on word problems Source: Berch & Mazzocco, 2007; Fuchs & Fuchs, 2002 28

29. © 2010, EDC Metacognitive Strategies What? A “plan of action” for problem solving that uses self- questioning and self-checking techniques. How? Use after students have understanding of the math concept or skill Teach strategies explicitly through teacher modeling, and guided & independent practice Why? Build student independence Help students solve problems Overcome memory difficulties 29

30. © 2010, EDC Sample Metacognitive Strategies A. RAFT for getting started on solving word problems Read the problem Ask yourself: What is the problem asking? Find the key information Think ahead: What will the answers look like? B. Problem Solving Checklists 3.7: RAFT 3.8: Problem Solving 30

31. © 2010, EDC Think Aloud Strategy What is a Think Aloud? As you solve a problem, talk about your thought processes and the questions you are asking yourself. Sample Prompts 1. What does the problem say? 2. What question(s) am I trying to answer? 3. What information do I have? Which information is important? 4. How will I solve the problem? 3.9 31

32. © 2010, EDC How is a Think-Aloud Different from Questions Teachers Ask Every Day? The the think-aloud strategy places explicit focus on: the process of self-questioning modeling helpful questions for students to ask themselves In everyday routines students may not notice the kinds of questions their teachers are asking Process for Using Think Aloud: Teacher models “thinking aloud.” Students practice strategy and learn to use it independently. 32

33. Discuss Meta-cognitive Strategies 1. Look at strategies 3.7-3.9. 2. Discuss: Share your experiences: How have you used the Think Aloud strategy or other meta-cognitive strategies with students? What works well? If you want to try a strategy: What strategy do you want to try? How might you use it with your students? © 2010, EDC33

34. © 2010, EDC Topic #4: Math Vocabulary In this section, we will: Learn about math vocabulary challenges Try sample strategies 34

35. Complexities of Math Vocabulary. Some terms: are shared with everyday English but have distinct math meanings Right, volume, expression, figure, is, sound like everyday English words Sum and Some have more than one math meaning Square, round Directions: 1. Read Handout 3.10 2. What’s one math word that your students find confusing? Source: Thompson & Rubenstein 2000 3.10 Vocabulary © 2010, EDC35

36. © 2010, EDC Small Words are also Important! Examples: A Any All Each It Is Of Off And Or Strategies: When reading aloud, clearly enunciate small words Build students’ awareness of the importance of paying attention to small words Source: Kenney, J. et al., 2005 36

37. Examples Hints to Help Me Remember Visual RepresentationDefinition in my own words Sample Strategy: Vocabulary 4-Block Term This strategy helps students build understanding by organizing information about a term. © 2010, EDC37

38. Sample 4-block for Median The middle value in a set of ranked data Median sounds like medium --the middle Don’t forget to put the numbers from smallest to largest! 1, 1, 4, 6, 7, 10,21 3.11 © 2010, EDC38 Median

39. © 2010, EDC Vocabulary Activity: “I have, Who has?” Goals: Experience an activity that you can use with students to review math vocabulary and build fluency Consider ways to make the activity more accessible to students with disabilities 39

40. Lunch © 2010, EDC40

41. © 2010, EDC “I Have, Who Has” Activity: Demo Who has a five-sided polygon? 1. Everyone gets a card. 2. First player reads question on card: I have a pentagon. Who has a 90 ◦ angle? 3. Player with matching word responds and then asks next question. 41

42. © 2010, EDC “I have, Who has”Directions Before Playing 1. Divide into groups. Stand in a circle. 2. Each person gets one or two cards. 3. Talk with a partner about the meanings of the vocabulary words on your cards. Play the Game 4. One person begins by reading his/her question only. 5. The person who has the statement that matches, reads the statement. 6. That same person then reads the question on his/her card. 7. Play continues until all the cards have been completed. 42

43. © 2010, EDC Discuss How do you or would you use the “I have, who has” vocabulary activity with your students? How do you or would you make it more accessible to your students with learning disabilities? 43

44. © 2010, EDC Closing Thoughts on Math Vocabulary Suggestions Identify critical terms Introduce vocabulary in the context of doing mathematics, not in isolation Provide multiple opportunities for students to hear, read & use terms Common Pitfall Vocab. strategies are created but then not actively used Word Wall turns into wall-paper Students don’t use the dictionaries that they worked hard to make What are your suggestions for avoiding this pitfall? 44

45. © 2010, EDC Topic #5: Sample Lesson In this section, we will: Watch and discuss a video of a lesson that involves reading, discussing, and writing about abstract equations Discuss the ways the teacher informally assesses the students’ understanding 45

46. © 2010, EDC Math Lesson in Video Reviews vocabulary from their math curriculum Factored Form: (x+1)(x+2) Expanded Form: x 2 + 3x + 2 Uses an area model for equations Uses Algebra Tiles (manipulatives) x2x2 x Algebra Tiles 1 3.12 Video Background, Top 46

47. © 2010, EDC Algebra Tiles Demo Use Algebra Tiles to multiply (x+1)(x+2) 47

48. © 2010, EDC Algebra Tiles Demo 1. First, use the tiles to build x + 1 x + 1 48

49. © 2010, EDC Algebra Tiles Demo 2. Then, build x + 2 x + 2 x + 1 49

50. © 2010, EDC Algebra Tiles Demo 3. Show the multiplication by filling in the rectangle. x times x = x 2 x + 2 x + 1 x2x2 50

51. © 2010, EDC Algebra Tiles Demo 4. Multiply: 1 times x = 1x 2 times x = 2x x + 2 x + 1 x2x2 51

52. © 2010, EDC Algebra Tiles Demo 5. Multiply the yellow tiles: 1 times 2 = 2 x + 2 x + 1 x2x2 The rectangle is completed. 52

53. © 2010, EDC Algebra Tiles Demo Dimensions: (x + 1) and (x + 2) Area: x 2 + 3x + 2 x + 2 x + 1 x2x2 ( x + 1)( x + 2) = x 2 + 3x + 2 53

54. © 2010, EDC Get to Know the Math Problem in the Video Read the problem on the bottom of 3.12. Write what the problem is asking in your own words. Talk with a partner: What did you write? What is your approach to solving the problem? 3.12 Bottom of Page 54

55. © 2010, EDC Video: Background Title I Math Coach who co-teaches 8 th grade math class and provides math support Uses alternative teaching model with six 8 th grade students, including students with disabilities and ELLs, who were having difficulties in the regular math class As a group, these students tend to be very quiet, and teachers could not tell what the students understood What do these students understand? 55

56. © 2010, EDC As You Watch, Keep in Mind… Video Reminder An example to spark discussion, not meant to be ideal Observe the teacher’s practices without judging Focus Questions What strategies does the teacher use to make the language of the mathematics accessible? How does the teacher find out about the students’ math understanding? 3.13 Video Notes 56

57. © 2010, EDC Sequence for Viewing “Math Support Class” Vocabulary Warm-Up Introduction to Main Problem Discussion Student Explanations Discussion Teacher’s Interview 3.13 Video Notes 57

58. © 2010, EDC After the Video: Discuss What strategies do you use to encourage quiet students, including ones with disabilities and English Learners, to talk about their math ideas? What questioning strategies do you use with your students? 58

59. Ideas to Take Away Write down 1-2 ideas from the morning that you would like to try with your students. Write down your ideas on Reference Sheet E. Share with a partner from another table. Time: 5-7 minutes © 2010, EDC Ref. E on green 59

60. © 2010, EDC Topic #6: Accessible Classroom Assessments In this section, we will: Discuss the need for making accommodations to math assessments Identify strategies to help students before, during, and after assessments Note: The focus is on classroom assessments and not on state tests. 60

61. © 2010, EDC Accessible Assessment Activity Goal Discuss different reasons for assessing students and for making accommodations to tests and quizzes Directions 1. Read the handout. 2. Highlight 2 quotes that stand out for you. 3. Discuss in small groups. Which quotes did you pick? Why? 3.14: Assessment Quotes 61

62. © 2010, EDC Before & During Assessments Activity Goal Discuss ways to support students before and during assessments Directions 1. Divide into groups of 3 or 4. 2. Choose one sample student for the group. 3. Discuss the questions and fill out Handout. 4. Be prepared to share two ideas with the whole group. 3.15: Sample Students 3.16: Chart 62

63. © 2010, EDC Whole Group Share-Out A reporter from each group shares: What are two ideas for providing support to your sample student before and during assessments? Why do you think that these suggestions would be helpful to this student? 63

64. © 2010, EDC Ways to support students after assessments Suggestions Have students analyze errors Conceptual, careless, computational What would you add to this list? 3.17 Suggestions 64

65. © 2010, EDC Topic #7: Adapting Tests and Quizzes In this section, we will: Consider a variety of ways to make tests more accessible Examine sample adaptations to assessments 65

66. © 2010, EDC Examine Sample Adaptations Directions Work in pairs. Compare the original quiz to the adapted version. Tear out the original quiz to make it easier to compare. Discuss: What kinds of adaptations were made? Note: Adaptations were made for a few problems not the whole quiz 3.18 Original Quiz - 3.19 Adapted Quiz - 3.20 Sample Adaptations 66

67. © 2010, EDC Discuss What adaptations were made to the quiz? How might these changes help students with learning disabilities? What kinds of adaptations do you make to classroom math tests? Note: Handout 3.20 has a list of suggestions. 3.19 & 3.20 67

68. © 2010, EDC Topic #8: Planning Accessible Assessments In this section, we will: collaborate with colleagues to plan accommodations for a test or quiz from our curriculum 68

69. © 2010, EDC Goals and Cautions for Adapting Assessments Goals Enable students to show their abilities and not be impeded by their disabilities Align accommodations with students’ strengths and difficulties and with the math assessment goals Cautions Lose integrity of math – Refer to the Standards (Handout) Set expectations too low 69

70. © 2010, EDC Planning Reminder: Alignment is Key! 70

71. © 2010, EDC Planning Time: Checklist 1. Get Organized Work with your teaching partner or in grade-level groups. Take out math test that you brought 2. Discuss and fill out the Planner. 3. Make adaptations to at least 2 test questions to make them more accessible to your focal students. 4. Action Plan Form: determine who, when, where, how you will gather examples of student work, lesson or assessment accommodations for your focal student. share ideas with colleagues from other groups. 3.21 Accessible Assessment Planner 71

72. © 2010, EDC Share Ideas Get organized into groups of 3 to talk with people from other planning groups. Discuss What are 2 strategies that you used to make the test/quiz more accessible to your students? Why did you choose these strategies? Time: 7 minutes 72

73. © 2010, EDC Topic #9: Day 4 Wrap-Up In this section, we will: Do a wrap-up activity Assignment for next time (Wednesday, March 11th, 2015) 73

74. Day 4 Wrap-Up: Math Standards Expressions & Equations Apply and extend previous understandings of arithmetic to algebraic expressions. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Analyze and solve linear equations Practice Standards 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Source: Common Core State Standards 74

75. © 2010, EDC Last Step Complete Feedback Form Thanks very much for participating in the course!! 75

76. © 2010, EDC Course Wrap-Up Activity Goals Reflect on your own learning Plan follow-up actions & share ideas Directions Write down 2 things that you learned. Look over the list of accessibility principles and identify 2 that you would like to strengthen. Write down 2 actions that you will take in the next month. Be specific! Then, well discuss the ideas in small groups. Note: The Wrap-up handout. It’s for you to keep. 3.22

77. © 2010, EDC Discuss in Small Groups Take turns sharing: What’s one idea that you learned in the course? Which accessibility principles do you want to strengthen? What follow-up actions are you planning to take? Discuss as a group: What are ways that we can support each other in taking these follow-up actions? Time: 5-10 minutes 77

78. Credits The course, Enhancing Instructional Practices in Mathematics was developed at Education Development Center, Inc (EDC). Website: http://edc.org/accessmathhttp://edc.org/accessmath The project was funded by the National Science Foundation, grant # ESI-0455765. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. This course is distributed through Michigan’s Integrated Mathematics Initiative (Mi) 2 a Mandated Activities Project (MAP) funded under the Individuals with Disabilities Education Act (IDEA) through the Michigan Department of Education, Office of Special Education. (MI) 2 assists the state in creating a cohesive and collaborative system of support and professional development among existing mathematics resources. The initiative identifies and promotes factors that facilitate improved outcomes for all students in mathematics. © 2010, EDC78