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Language in the Math Classroom
 

Language in the Math Classroom

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Language in the Math Classroom; A Workshop for Mathematics and Special Educators focuses on ways in which middle- grades math and special education teachers can support students with the language ...

Language in the Math Classroom; A Workshop for Mathematics and Special Educators focuses on ways in which middle- grades math and special education teachers can support students with the language demands of the middle grades math classroom. This presentation is part of a broader workshop for educators. More information at http://middlegradesmath.org

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    Language in the Math Classroom Language in the Math Classroom Presentation Transcript

          • Improving Access to Language In Mathematics
      • Emily Fagan & Amy Brodesky, EDC
      Welcome! Please complete the warm-up (HO 1)
    • Our PD Projects
      • Addressing Accessibility in Mathematics
      • http: //edc . org/accessMath/
      • Mathematics Improvement Toolkit
      • http://www.mgforum.org/
      • (June or July 2009)
    • Our PD Goals for Language in Math Build 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
    • 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
    • Session Agenda
      • Language Demands in Mathematics
      • Sample Lesson
      • Writing in Math
      • Math Vocabulary
      • Planning for Language Accessibility
      • We hope you will leave with PD ideas to use with teachers in your schools/districts.
    • #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
    • 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
    • Types of Language Demands
      • Receptive
      • Reading
      • Listening
      • Expressive
      • Writing
      • Speaking
      • Examples for students with disabilities:
            • Reading : Decoding; Comprehension
            • Listening : Auditory Processing
            • Writing : Organizing ideas in writing
            • Speaking : Expressing ideas orally
    • 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
    • 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 TEXT The 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?
    • 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
    • #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
    • PD Simulation: View and Discuss a Video
      • Goals:
      • Provide examples of strategies in action
      • Provide a shared experience to generate discussion
    • Mathematics Lesson in Video
      • Reviews vocabulary from their curriculum
        • Factored Form: ( x +1)( x +4)
        • Expanded Form: x 2 + 4 x + 1
      • Uses an area model for equations
      • Uses Algebra Tiles (manipulatives)
      x 2 x Algebra Tiles 1 HO 2A: Lesson
    • Video: Background
      • Students
      • Six 8 th 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 8 th grade mathematics class AND provides additional mathematics support to these students
    • 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
    • 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?
    • #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
    • 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.
    • 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
    • Analyze Problem from an Accessibility Lens
      • What are the math goals ?
      • What are the demands on students?
        • Conceptual
        • Language
        • Visual-Spatial
      • What potential difficulties would you anticipate for students?
      HO 3 Jumping Jacks
    • 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
    • LASW Directions
      • 1. Look at the samples from three 6 th 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
    • Discuss Observations, Questions & Strategies Z
    • Discuss Observations, Questions & Strategies X Y Z
    • 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
    • #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
    • Vocabulary is Everywhere
      • Receptive
      • Reading
      • Listening
      • Requires:
      • Recognizing vocabulary
      • Understanding vocabulary
      • Expressive
      • Writing
      • Speaking
      • Requires:
      • Recalling vocabulary
      • Applying vocabulary
    • 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
    • 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
    • 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
    • Discuss with a Partner
      • What strategies did you observe the teachers use to help students understand vocabulary?
    • 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
      • The middle value in a set of ranked data
      Median 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
    • 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?
    • “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.
    • “I have, Who has” Directions
      • To 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.
    • 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?
    • 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
    • #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
    • 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
    • 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
    • Share Your Experience
      • What are your suggestions for helping mathematics teachers with language and vocabulary strategies?
    • Closing
      • Questions and Comments
      • [email_address] .org
      • [email_address]
    • Optional Slides
    • 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