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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

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  • 1.
        • Improving Access to Language In Mathematics
    • Emily Fagan & Amy Brodesky, EDC
    Welcome! Please complete the warm-up (HO 1)
  • 2. Our PD Projects
    • Addressing Accessibility in Mathematics
    • http: //edc . org/accessMath/
    • Mathematics Improvement Toolkit
    • (June or July 2009)
  • 3. 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
  • 4. 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
  • 5. 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.
  • 6. #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
  • 7. 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
  • 8. 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
  • 9. 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
  • 10. 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?
  • 11. 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
  • 12. #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
  • 13. PD Simulation: View and Discuss a Video
    • Goals:
    • Provide examples of strategies in action
    • Provide a shared experience to generate discussion
  • 14. 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
  • 15. 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
  • 16. 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
  • 17. 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?
  • 18. #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
  • 19. 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.
  • 20. 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
  • 21. 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
  • 22. 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
  • 23. 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
  • 24. Discuss Observations, Questions & Strategies Z
  • 25. Discuss Observations, Questions & Strategies X Y Z
  • 26. 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
  • 27. #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
  • 28. Vocabulary is Everywhere
    • Receptive
    • Reading
    • Listening
    • Requires:
    • Recognizing vocabulary
    • Understanding vocabulary
    • Expressive
    • Writing
    • Speaking
    • Requires:
    • Recalling vocabulary
    • Applying vocabulary
  • 29. 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
  • 30. 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
  • 31. 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
  • 32. Discuss with a Partner
    • What strategies did you observe the teachers use to help students understand vocabulary?
  • 33. 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.
  • 34. 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
  • 35. 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?
  • 36. “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.
  • 37. “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.
  • 38. 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?
  • 39. 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
  • 40. #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
  • 41. 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
  • 42. 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
  • 43. Share Your Experience
    • What are your suggestions for helping mathematics teachers with language and vocabulary strategies?
  • 44. Closing
    • Questions and Comments
    • [email_address] .org
    • [email_address]
  • 45. Optional Slides
  • 46. 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