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Improving Access to Language In Mathematics
Emily Fagan & Amy Brodesky, EDC
Welcome! Please complete the warm-up (HO 1)
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Our PD Projects Addressing Accessibility in Mathematicshttp://edc.org/accessMath/
Mathematics Improvement Toolkithttp://www.mgforum.org/(June or July 2009)
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Our PD Goals for Language in MathBuild teachers’ knowledge of…
the kinds of language demands in math lessons
common difficulties that students with learning disabilities
strategies for addressing these difficulties ways to plan accessible math lessons that
incorporate active language strategies
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Lessons Learned about PD on Language Strategies for Math
Tends to be a motivating and engaging topic for math teachers & special educators Helpful to unpack language demands & difficulties
Provides an opportunity for special educators to share expertise and to foster collaboration between special educators & math teachers
Needs to go beyond “activities” to integrating language strategies into math instruction
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Session Agenda
1. Language Demands in Mathematics2. Sample Lesson3. Writing in Math4. Math Vocabulary5. Planning for Language Accessibility
We hope you will leave with PD ideas to use with teachers in your schools/districts.
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#1: Examine the Language Demands in Mathematics Lessons
In this section, we will: Discuss the kinds of language demands in
mathematics lessons Learn about the complexities of reading in
mathematics Consider language challenges for students
with disabilities
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Communication Standard:Goals for Students Organize and consolidate their mathematical
thinking through communication;
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
Analyze and evaluate the mathematical thinking and strategies of others;
Use the language of mathematics to express mathematics ideas precisely.
Source: Principles and Standards for School Mathematics (NCTM), 2002
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Types of Language Demands
Receptive Reading Listening
Expressive Writing Speaking
Examples for students with disabilities:Reading: Decoding; ComprehensionListening: Auditory ProcessingWriting: Organizing ideas in writingSpeaking: Expressing ideas orally
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Student’s Perspective
Source: “Faking It” by C. Lee and R. Jackson
“When I am listening or reading a word problem, I sometimes leave out or reverse important information. When I am struggling through the words, I lose the meaning of the problem.”
Source: “Faking It” by C. Lee and R. Jackson
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Reading in Mathematics Class
Compare: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
MATHEMATICS TEXTThe sum of two numbers having the same sign can be found by adding their absolute values, the answer having the same sign as the numbers.
What differences do you notice?
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What’s different about reading mathematics texts?
Conceptually dense
Not just words – also symbols, tables, graphs and diagrams
Not just left to right-different directions
Different symbols are used to describe the same process Multiplication *, x, (), ●
Decoding symbols is different from decoding words. Symbols are like “sight words.”
Barton and Heidema, 2002, p. 1
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#2: Use a Sample Lesson for Professional Development
In this section, we will: watch and discuss a video of a lesson that
involves reading, discussing, and writing about abstract equations
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PD Simulation: View and Discuss a Video
Goals: Provide examples of strategies in action Provide a shared experience to
generate discussion
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Mathematics Lesson in Video Reviews vocabulary from their curriculum
Factored Form: (x+1)(x+4) Expanded Form: x2 + 4x + 1
Uses an area model for equations Uses Algebra Tiles (manipulatives)
x2 x
Algebra Tiles
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HO 2A: Lesson
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Video: BackgroundStudents Six 8th grade students, including students with disabilities
and English Language Learners Identified for additional support because they were having
difficulties in regular mathematics class As a group, these students tend to be reluctant to participate
Teacher Title I Mathematics Coach Co-teaches 8th grade mathematics class AND provides
additional mathematics support to these students
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As You Watch, Keep in Mind…
One teacher, one day An example to spark discussion
Focus Question What kinds of strategies does the teacher
use to make the language of the mathematics accessible?
HO 2: Video Notes
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Discuss: What kinds of difficulties did the
students have? What strategies did the teacher use to
make the language of mathematics more accessible?
What strategies do you find helpful for encouraging reluctant students to participate?
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#3: Focus on Writing Strategies for Mathematics Class
In this section, we will simulate a professional development experience in which teacher participants:
Write a response to a mathematics problem Examine student work samples Discuss writing strategies
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Why Write in Mathematics?
Writing can help students to: build understanding of mathematics organize and clarify ideas deepen their thinking communicate coherently and clearly remember mathematics content
Writing has many benefits. But, it also poses barriers for some students.
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PD Simulation:Looking at Student Work
What do teachers do? Write a response to a math problem. Discuss their experiences. Analyze the problem from accessibility
lens. Examine student work samples.
HO 3: Jumping Jacks
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Analyze Problem from an Accessibility Lens What are the math goals?
What are the demands on students?ConceptualLanguageVisual-Spatial
What potential difficulties would you anticipate for students?
HO 3 Jumping Jacks
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Looking at Student Work (LASW) Key Questions
1. What do you observe about the student’s math understanding?
2. What do you observe about the student’s writing?
HO 4 LASW Tool
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LASW Directions
1. Look at the samples from three 6th graders.
2. Then focus on Student Z. Write notes on your LASW Tool.
3. In small groups, discuss Student Z’s work. Strengths and Difficulties Questions and Strategies
HO 5 Students X, Y, Z
HO4 LASW Tool
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Discuss Observations, Questions & Strategies
Z
Discuss Observations, Questions & Strategies
X
Y
Z
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Teachers Discuss Writing Strategies for Math Look over the list of strategies. What strategies might be helpful to your
students, especially those with disabilities? Why?
What’s one strategy that you currently use? How do you use it?
HO6 Writing Strategies
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#4: Expand Teachers’ Repertoires of Vocabulary Strategies
In this section, we will examine pd activities designed to:
View video to spark reflection & discussion Explore vocabulary challenges Provide & practice strategies
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Vocabulary is Everywhere
Receptive Reading Listening
Requires: Recognizing vocabulary Understanding
vocabulary
Expressive Writing Speaking
Requires: Recalling vocabulary Applying vocabulary
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Complexities of Mathematics Vocabulary
Some terms… are shared with everyday English but have distinct
meanings in mathematics Right, volume, expression
sound like everyday English words Sum and Some
have more than one meaning in mathematics Square, round
are related and often confused Mean and median
Source: Rubenstein, R. 2007
HO 7: Math Vocabulary
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Vocabulary in the Geometry & Data Strands
2 Video Clips: 7th grade class: Data 6th grade class: Geometry
Video Reminder One teacher/one day An example to spark reflection and discussion
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As You Watch, Keep in Mind
Focus Question What strategies does each teacher use
to help students to understand the vocabulary in the lesson?
HO 8: Video Notes
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Discuss with a Partner What strategies did you observe the
teachers use to help students understand vocabulary?
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Sample Strategy: Visual Definitions
Polygons Not Polygons
Generate examples of shapes that are and are not the vocabulary word.
Ask students to come up with a definition for the word.
Vocabulary 4-Block Strategy
Median
The middle value in a set of ranked
data
1, 1, 4, 6, 7, 10,21
Median sounds like medium --the middle
Don’t forget to put the numbers from
smallest to largest!
This strategy helps students build understanding by organizing information about a term.
HO 9 Vocab. 4-block
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Discussion Questions for Teachers
Reflect on Your Experience In what ways did you find filling the 4-block to be
helpful to you? Were some blocks harder to fill in than others?
Discuss Ways for Using the 4-Block with Students Which words would you want your students to use? After students complete the cards, what are ways
they could continue to use them in active ways?
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“I Have, Who Has” Activity: Demo
Who has a five-sided polygon?
1. First player asks question
I have a pentagon.
Who has a 90◦ angle?
2. Player with matching word responds and then asks next question.
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“I have, Who has”DirectionsTo Get Started:1. Each person gets one or more cards.2. Talk with a partner about the meanings of the
vocabulary words on your cards.Play the Game:3. One person begins by reading the question only.4. The person who has the statement that matches,
reads the statement.5. That same person then reads the question on his/her
card.6. Play continues until all the cards have been used.
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Discussion Questions for Teachers
How do you or would you use the “I have, who has” vocabulary activity with students?
How would you make it more accessible to students with learning disabilities?
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Things to Keep in Mind: Vocabulary in Mathematics
Identify critical terms and phrases (5-7 is better than 20-25).
Students need many opportunities to speak, read, write and listen to mathematics vocabulary.
Sometimes the words that prevent students from solving a task are not mathematical terms.
Handout 10: Analyzing a Math Task
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#5: Provide Planning Processes and Tools
In this section, we will: Consider the challenges for teachers in addressing
language and vocabulary in instruction Share ideas for facing these challenges Examine sample planning processes and tools
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Common Challenges Vocabulary strategies, such as word walls
and index card dictionaries, are created but then are not used in active or ongoing ways
Math teachers may lack knowledge of language strategies and/or ways to incorporate strategies in lessons
Limited time in math lessons
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Suggestions for Math Supervisors Incorporate language and vocabulary
planning as a regular feature of lesson planning
Provide a structure for planning Encourage collaboration to share ideas
and resources Set and clarify expectations for
incorporating language strategies
Handout 11: Sample Planner
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Share Your Experience What are your suggestions for
helping mathematics teachers with language and vocabulary strategies?
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Optional Slides
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Suggestions: Using LASW in PD Caution: teachers may jump to strategies. Use an
organizer and provide ample time to discuss student’s strengths and difficulties first.
Consider questions to ask to gather more information before choosing strategies
Emphasize aligning strategies with math goals and student
Consider ways to build on student’s strengths to help address difficulties
Provide work from a range of learners