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 demands of the middle grades math classroom. This presentation is part of a broader workshop for educators. More information at

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Language in the Math Classroom

  1. 1. <ul><ul><ul><li>Improving Access to Language In Mathematics </li></ul></ul></ul><ul><li>Emily Fagan & Amy Brodesky, EDC </li></ul>Welcome! Please complete the warm-up (HO 1)
  2. 2. Our PD Projects <ul><li>Addressing Accessibility in Mathematics </li></ul><ul><li> http: //edc . org/accessMath/ </li></ul><ul><li>Mathematics Improvement Toolkit </li></ul><ul><li> </li></ul><ul><li>(June or July 2009) </li></ul>
  3. 3. Our PD Goals for Language in Math Build teachers’ knowledge of… <ul><li>the kinds of language demands in math lessons </li></ul><ul><li>common difficulties that students with learning disabilities </li></ul><ul><li>strategies for addressing these difficulties </li></ul><ul><li>ways to plan accessible math lessons that incorporate active language strategies </li></ul>
  4. 4. Lessons Learned about PD on Language Strategies for Math <ul><li>Tends to be a motivating and engaging topic for math teachers & special educators </li></ul><ul><ul><li>Helpful to unpack language demands & difficulties </li></ul></ul><ul><li>Provides an opportunity for special educators to share expertise and to foster collaboration between special educators & math teachers </li></ul><ul><li>Needs to go beyond “activities” to integrating language strategies into math instruction </li></ul>
  5. 5. Session Agenda <ul><li>Language Demands in Mathematics </li></ul><ul><li>Sample Lesson </li></ul><ul><li>Writing in Math </li></ul><ul><li>Math Vocabulary </li></ul><ul><li>Planning for Language Accessibility </li></ul><ul><li>We hope you will leave with PD ideas to use with teachers in your schools/districts. </li></ul>
  6. 6. #1: Examine the Language Demands in Mathematics Lessons <ul><li>In this section, we will: </li></ul><ul><li>Discuss the kinds of language demands in mathematics lessons </li></ul><ul><li>Learn about the complexities of reading in mathematics </li></ul><ul><li>Consider language challenges for students with disabilities </li></ul>
  7. 7. Communication Standard: Goals for Students <ul><li>Organize and consolidate their mathematical thinking through communication; </li></ul><ul><li>Communicate their mathematical thinking coherently and clearly to peers, teachers, and others; </li></ul><ul><li>Analyze and evaluate the mathematical thinking and strategies of others; </li></ul><ul><li>Use the language of mathematics to express mathematics ideas precisely. </li></ul><ul><li>Source: Principles and Standards for School Mathematics (NCTM), 2002 </li></ul>
  8. 8. Types of Language Demands <ul><li>Receptive </li></ul><ul><li>Reading </li></ul><ul><li>Listening </li></ul><ul><li>Expressive </li></ul><ul><li>Writing </li></ul><ul><li>Speaking </li></ul><ul><li>Examples for students with disabilities: </li></ul><ul><ul><ul><ul><li>Reading : Decoding; Comprehension </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Listening : Auditory Processing </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Writing : Organizing ideas in writing </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Speaking : Expressing ideas orally </li></ul></ul></ul></ul>
  9. 9. Student’s Perspective <ul><li>Source: “Faking It” by C. Lee and R. Jackson </li></ul>“ 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. 10. Reading in Mathematics Class <ul><li>Compare: </li></ul><ul><li>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. </li></ul><ul><li>Baum, L. F. p.1 </li></ul><ul><li>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. </li></ul><ul><li>What differences do you notice? </li></ul>
  11. 11. What’s different about reading mathematics texts? <ul><li>Conceptually dense </li></ul><ul><li>Not just words – also symbols, tables, graphs and diagrams </li></ul><ul><li>Not just left to right-different directions </li></ul><ul><li>Different symbols are used to describe the same process </li></ul><ul><ul><li>Multiplication *, x, (), ● </li></ul></ul><ul><li>Decoding symbols is different from decoding words. Symbols are like “sight words.” </li></ul><ul><li>Barton and Heidema, 2002, p. 1 </li></ul>
  12. 12. #2: Use a Sample Lesson for Professional Development <ul><li>In this section, we will: </li></ul><ul><li>watch and discuss a video of a lesson that involves reading, discussing, and writing about abstract equations </li></ul>
  13. 13. PD Simulation: View and Discuss a Video <ul><li>Goals: </li></ul><ul><li>Provide examples of strategies in action </li></ul><ul><li>Provide a shared experience to generate discussion </li></ul>
  14. 14. Mathematics Lesson in Video <ul><li>Reviews vocabulary from their curriculum </li></ul><ul><ul><li>Factored Form: ( x +1)( x +4) </li></ul></ul><ul><ul><li>Expanded Form: x 2 + 4 x + 1 </li></ul></ul><ul><li>Uses an area model for equations </li></ul><ul><li>Uses Algebra Tiles (manipulatives) </li></ul>x 2 x Algebra Tiles 1 HO 2A: Lesson
  15. 15. Video: Background <ul><li>Students </li></ul><ul><li>Six 8 th grade students, including students with disabilities and English Language Learners </li></ul><ul><li>Identified for additional support because they were having difficulties in regular mathematics class </li></ul><ul><li>As a group, these students tend to be reluctant to participate </li></ul><ul><li>Teacher </li></ul><ul><li>Title I Mathematics Coach </li></ul><ul><li>Co-teaches 8 th grade mathematics class AND provides additional mathematics support to these students </li></ul>
  16. 16. As You Watch, Keep in Mind… <ul><li>One teacher, one day </li></ul><ul><li>An example to spark discussion </li></ul><ul><li>Focus Question </li></ul><ul><li>What kinds of strategies does the teacher use to make the language of the mathematics accessible? </li></ul>HO 2: Video Notes
  17. 17. Discuss: <ul><li>What kinds of difficulties did the students have? </li></ul><ul><li>What strategies did the teacher use to make the language of mathematics more accessible? </li></ul><ul><li>What strategies do you find helpful for encouraging reluctant students to participate? </li></ul>
  18. 18. #3: Focus on Writing Strategies for Mathematics Class <ul><li>In this section, we will simulate a professional development experience in which teacher participants: </li></ul><ul><li>Write a response to a mathematics problem </li></ul><ul><li>Examine student work samples </li></ul><ul><li>Discuss writing strategies </li></ul>
  19. 19. Why Write in Mathematics? <ul><li>Writing can help students to: </li></ul><ul><li>build understanding of mathematics </li></ul><ul><li>organize and clarify ideas </li></ul><ul><li>deepen their thinking </li></ul><ul><li>communicate coherently and clearly </li></ul><ul><li>remember mathematics content </li></ul><ul><li>Writing has many benefits. But, it also poses </li></ul><ul><li>barriers for some students. </li></ul>
  20. 20. PD Simulation: Looking at Student Work <ul><ul><li>What do teachers do? </li></ul></ul><ul><ul><li>Write a response to a math problem. </li></ul></ul><ul><ul><li>Discuss their experiences. </li></ul></ul><ul><ul><li>Analyze the problem from accessibility lens. </li></ul></ul><ul><ul><li>Examine student work samples. </li></ul></ul>HO 3: Jumping Jacks
  21. 21. Analyze Problem from an Accessibility Lens <ul><li>What are the math goals ? </li></ul><ul><li>What are the demands on students? </li></ul><ul><ul><li>Conceptual </li></ul></ul><ul><ul><li>Language </li></ul></ul><ul><ul><li>Visual-Spatial </li></ul></ul><ul><ul><li> </li></ul></ul><ul><li>What potential difficulties would you anticipate for students? </li></ul>HO 3 Jumping Jacks
  22. 22. Looking at Student Work (LASW) Key Questions <ul><li>1. What do you observe about the student’s math understanding ? </li></ul><ul><li>2. What do you observe about the student’s writing ? </li></ul>HO 4 LASW Tool
  23. 23. LASW Directions <ul><li>1. Look at the samples from three 6 th graders. </li></ul><ul><li>2. Then focus on Student Z. Write notes on your LASW Tool. </li></ul><ul><li>3. In small groups, discuss Student Z’s work. </li></ul><ul><ul><li>Strengths and Difficulties </li></ul></ul><ul><ul><li>Questions and Strategies </li></ul></ul>HO 5 Students X, Y, Z HO4 LASW Tool
  24. 24. Discuss Observations, Questions & Strategies Z
  25. 25. Discuss Observations, Questions & Strategies X Y Z
  26. 26. Teachers Discuss Writing Strategies for Math <ul><li>Look over the list of strategies. </li></ul><ul><li>What strategies might be helpful to your students, especially those with disabilities? Why? </li></ul><ul><li>What’s one strategy that you currently use? How do you use it? </li></ul>HO6 Writing Strategies
  27. 27. #4: Expand Teachers’ Repertoires of Vocabulary Strategies <ul><li>In this section, we will examine pd activities designed to: </li></ul><ul><li>View video to spark reflection & discussion </li></ul><ul><li>Explore vocabulary challenges </li></ul><ul><li>Provide & practice strategies </li></ul>
  28. 28. Vocabulary is Everywhere <ul><li>Receptive </li></ul><ul><li>Reading </li></ul><ul><li>Listening </li></ul><ul><li>Requires: </li></ul><ul><li>Recognizing vocabulary </li></ul><ul><li>Understanding vocabulary </li></ul><ul><li>Expressive </li></ul><ul><li>Writing </li></ul><ul><li>Speaking </li></ul><ul><li>Requires: </li></ul><ul><li>Recalling vocabulary </li></ul><ul><li>Applying vocabulary </li></ul>
  29. 29. Complexities of Mathematics Vocabulary <ul><li>Some terms… </li></ul><ul><li>are shared with everyday English but have distinct meanings in mathematics </li></ul><ul><ul><li>Right, volume, expression </li></ul></ul><ul><li>sound like everyday English words </li></ul><ul><ul><li>Sum and Some </li></ul></ul><ul><li>have more than one meaning in mathematics </li></ul><ul><ul><li>Square, round </li></ul></ul><ul><li>are related and often confused </li></ul><ul><ul><li>Mean and median </li></ul></ul><ul><ul><li>Source: Rubenstein, R. 2007 </li></ul></ul>HO 7: Math Vocabulary
  30. 30. Vocabulary in the Geometry & Data Strands <ul><li>2 Video Clips: </li></ul><ul><li>7th grade class: Data </li></ul><ul><li>6th grade class: Geometry </li></ul><ul><li>Video Reminder </li></ul><ul><li>One teacher/one day </li></ul><ul><li>An example to spark reflection and discussion </li></ul>
  31. 31. As You Watch, Keep in Mind <ul><li>Focus Question </li></ul><ul><li>What strategies does each teacher use to help students to understand the vocabulary in the lesson? </li></ul>HO 8: Video Notes
  32. 32. Discuss with a Partner <ul><li>What strategies did you observe the teachers use to help students understand vocabulary? </li></ul>
  33. 33. Sample Strategy: Visual Definitions <ul><li>Polygons Not Polygons </li></ul><ul><li>Generate examples of shapes that are and are not the vocabulary word. </li></ul><ul><li>Ask students to come up with a definition for the word. </li></ul>
  34. 34. Vocabulary 4-Block Strategy <ul><li>The middle value in a set of ranked data </li></ul>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. 35. Discussion Questions for Teachers <ul><li>Reflect on Your Experience </li></ul><ul><li>In what ways did you find filling the 4-block to be helpful to you? </li></ul><ul><li>Were some blocks harder to fill in than others? </li></ul><ul><li>Discuss Ways for Using the 4-Block with Students </li></ul><ul><li>Which words would you want your students to use? </li></ul><ul><li>After students complete the cards, what are ways they could continue to use them in active ways? </li></ul>
  36. 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. 37. “I have, Who has” Directions <ul><li>To Get Started: </li></ul><ul><li>1. Each person gets one or more cards. </li></ul><ul><li>2. Talk with a partner about the meanings of the vocabulary words on your cards. </li></ul><ul><li>Play the Game: </li></ul><ul><li>3. One person begins by reading the question only . </li></ul><ul><li>4. The person who has the statement that matches, reads the statement. </li></ul><ul><li>5. That same person then reads the question on his/her card. </li></ul><ul><li>6. Play continues until all the cards have been used. </li></ul>
  38. 38. Discussion Questions for Teachers <ul><li>How do you or would you use the “I have, who has” vocabulary activity with students? </li></ul><ul><li>How would you make it more accessible to students with learning disabilities? </li></ul>
  39. 39. Things to Keep in Mind: Vocabulary in Mathematics <ul><li>Identify critical terms and phrases (5-7 is better than 20-25). </li></ul><ul><li>Students need many opportunities to speak, read, write and listen to mathematics vocabulary. </li></ul><ul><li>Sometimes the words that prevent students from solving a task are not mathematical terms. </li></ul>Handout 10: Analyzing a Math Task
  40. 40. #5: Provide Planning Processes and Tools <ul><li>In this section, we will: </li></ul><ul><li>Consider the challenges for teachers in addressing language and vocabulary in instruction </li></ul><ul><li>Share ideas for facing these challenges </li></ul><ul><li>Examine sample planning processes and tools </li></ul>
  41. 41. Common Challenges <ul><li>Vocabulary strategies, such as word walls and index card dictionaries, are created but then are not used in active or ongoing ways </li></ul><ul><li>Math teachers may lack knowledge of language strategies and/or ways to incorporate strategies in lessons </li></ul><ul><li>Limited time in math lessons </li></ul>
  42. 42. Suggestions for Math Supervisors <ul><li>Incorporate language and vocabulary planning as a regular feature of lesson planning </li></ul><ul><li>Provide a structure for planning </li></ul><ul><li>Encourage collaboration to share ideas and resources </li></ul><ul><li>Set and clarify expectations for incorporating language strategies </li></ul>Handout 11: Sample Planner
  43. 43. Share Your Experience <ul><li>What are your suggestions for helping mathematics teachers with language and vocabulary strategies? </li></ul>
  44. 44. Closing <ul><li>Questions and Comments </li></ul><ul><li>[email_address] .org </li></ul><ul><li>[email_address] </li></ul>
  45. 45. Optional Slides
  46. 46. Suggestions: Using LASW in PD <ul><li>Caution : teachers may jump to strategies. Use an organizer and provide ample time to discuss student’s strengths and difficulties first. </li></ul><ul><li>Consider questions to ask to gather more information before choosing strategies </li></ul><ul><li>Emphasize aligning strategies with math goals and student </li></ul><ul><li>Consider ways to build on student’s strengths to help address difficulties </li></ul><ul><li>Provide work from a range of learners </li></ul>