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 –

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, EDC 1

© 2010, EDC

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

Goal Reminder: To make mathematics instruction

more accessible to a

to Improve Student Learning

IEP

IEP

504

IEP

Range of Learners

© 2010, EDC 3

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, EDC 4

© 2010, EDC

Looking Back:

Topics Collaborative Teaching

Models Collaborative Planning Complexities of

Collaboration Strengthening

Communication

5

Your FeedbackPositives

Suggestions

Your Assignments

© 2010, EDC

Session 3:Agenda & Goals

1. Introduction & Assignment Discussions2. Language in Mathematics3. Word Problems4. Math Vocabulary5. Sample Lesson6. Accessible Classroom Assessments7. Adapting Tests and Quizzes8. Planning Accessible Assessments

Goals Learn ways to make math language and

assessments more accessible Leave with ideas to try with students

6

© 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 Form7

© 2010, EDC

Whole GroupShare 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

© 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

© 2010, EDC

Whole Group Share-Out

What’s one idea from your article discussion that you want to share with the whole group?

10

© 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

© 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

© 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

© 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 SpeakingTime: 5 min

3.1

14

© 2010, EDC

Reading Math Texts vs. Fiction

FICTIONDorothy 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 TEXTBased 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

© 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

© 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

© 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

© 2010, EDC

Get to Know the Math Problem1. 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 Problem3.2A Answers

19

© 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

Apply the Framework:Consider the MathKey Math Goals Represent a situation with a table and

symbolic expression What would you add to the goals?

© 2010, EDC 21

© 2010, EDC

Analyze the Problem

What are the task demands on students?LanguageConceptualOrganization

What potential difficulties would you anticipate for your focal students?

Next, we will look at actual work samples from two 7th graders.

3.2 Popcorn ProblemRef. A on Yellow

22

© 2010, EDC

Consider the Student: Examine Work Sample X1. 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 X3.3 LASW Tool

23

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, EDC 24

© 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 Y 3.3 LASW Tool25

Discuss Student Y & Compare Evidence of strengths & difficulties? Diagnostic Questions & Strategies Similarities & Differences for X & Y?

A.

B.

C.

© 2010, EDC 26

© 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 Strategies27

© 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

© 2010, EDC

Metacognitive StrategiesWhat?

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 practiceWhy?

Build student independence Help students solve problems Overcome memory difficulties

29

© 2010, EDC

Sample Metacognitive Strategies

A. RAFT for getting started on solving word problems

Read the problemAsk yourself: What is the problem asking?Find the key informationThink ahead: What will the answers look

like?

B. Problem Solving Checklists3.7: RAFT

3.8: Problem Solving30

© 2010, EDC

Think Aloud StrategyWhat is a Think Aloud? As you solve a

problem, talk about your thought processes and the questions you are asking yourself.

Sample Prompts1. 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?

3.931

© 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

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, EDC 33

© 2010, EDC

Topic #4: Math Vocabulary

In this section, we will: Learn about math vocabulary

challenges Try sample strategies

34

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 3.102. What’s one math word that your students find

confusing?

Source: Thompson & Rubenstein 20003.10 Vocabulary

© 2010, EDC 35

© 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., 200536

ExamplesHints to Help Me

Remember

Visual Representation

Definition inmy own words

Sample Strategy:Vocabulary 4-Block

Term

This strategy helps students build understanding by organizing information about a term.

© 2010, EDC 37

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, EDC 38

Median

© 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

Lunch

© 2010, EDC 40

© 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

© 2010, EDC

“I have, Who has”DirectionsBefore Playing1. 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 Game4. 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

© 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

© 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 termsCommon 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 makeWhat are your suggestions for avoiding this

pitfall?44

© 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

© 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)

x2x

Algebra Tiles

1

3.12 Video Background, Top46

© 2010, EDC

Algebra Tiles DemoUse Algebra Tiles to multiply (x+1)(x+2)

47

© 2010, EDC

Algebra Tiles Demo1. First, use the tiles to build x + 1

x +

1

48

© 2010, EDC

Algebra Tiles Demo2. Then, build x + 2

x + 2

x +

1

49

© 2010, EDC

Algebra Tiles Demo3. Show the multiplication by filling in the rectangle. x times x = x2

x + 2

x +

1 x2

50

© 2010, EDC

Algebra Tiles Demo4. Multiply: 1 times x = 1x 2 times x = 2x

x + 2

x +

1 x2

51

© 2010, EDC

Algebra Tiles Demo5. Multiply the yellow tiles: 1 times 2 = 2

x + 2

x +

1 x2

The rectangle is completed.

52

© 2010, EDC

Algebra Tiles Demo Dimensions: (x + 1) and (x + 2)

Area: x2 + 3x + 2

x + 2

x +

1

x2

(x + 1)(x + 2) = x2 + 3x + 2

53

© 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 Page54

© 2010, EDC

Video: Background Title I Math Coach who co-teaches 8th grade math

class and provides math support

Uses alternative teaching model with six 8th 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

© 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 Notes56

© 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 Notes57

© 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

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

© 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

© 2010, EDC

Accessible Assessment ActivityGoal Discuss different reasons for assessing students

and for making accommodations to tests and quizzes

Directions1. 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 Quotes61

© 2010, EDC

Before & During Assessments ActivityGoal Discuss ways to support students before and

during assessmentsDirections1. 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 Students3.16: Chart

62

© 2010, EDC

Whole GroupShare-OutA 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

© 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

© 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

© 2010, EDC

Examine Sample AdaptationsDirections 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 quiz3.18 Original Quiz - 3.19 Adapted Quiz

- 3.20 Sample Adaptations 66

© 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

© 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

© 2010, EDC

Goals and Cautions for Adapting AssessmentsGoals 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

© 2010, EDC

Planning Reminder:Alignment is Key!

7070

© 2010, EDC

Planning Time: Checklist1. 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 Planner71

© 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

© 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

Day 4 Wrap-Up:Math StandardsExpressions & 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 Standards1. 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

© 2010, EDC

Last Step

Complete Feedback Form

Thanks very much for participating in the course!!

75