Building math vocabulary skills

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  • PATTY:
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  • LOGAN: What does each word imply about content that is being addressed? Is there a different skill set or body of information required with each? Do students really know the difference?
  • LOGAN: What does each word imply about the task at hand? Is there a different skill set required with each? Do students really know the difference?
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  • LOGAN: Also known as concept maps
  • LOGAN: Example
  • LOGAN: Have them try one for “Vertical Angle Pairs”
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  • LOGAN: Tell story about UCTM presentation and my misconception about the meaning of the term “variable”
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  • LOGAN: A variable “varies” A constant does not vary (it is a fixed number). Constants can be known or unknown.
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  • LOGAN: Answer: a variable.
  • LOGAN: Answer: an unknown constant. If we consider x as a variable, then the left-hand side of the equation can vary. This is problematic because the right-hand side of the equation is fixed.
  • LOGAN: Answer: a variable. Y is a variable too. It varies with respect to x based on the relationship described by the equation, but it still varies.
  • LOGAN: Answer: a variable.
  • LOGAN: Answer: a constant. It is not a single number, it is rather a set of numbers (if we solve it, we find that x is the set of all numbers less than 5), but the set doesn’t vary. More particularly, we could say that x represents an unknown set of constants.
  • LOGAN: Answer: a variable. Although the domain is limited (x can’t be 5), x still varies. Variable doesn’t mean it can be any real number, it just means “varies”
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  • Building math vocabulary skills

    1. 1. Building Math Vocabulary Skills Patty Norman Logan Toone Davis School District
    2. 2. Why Build Vocab. Skills?
    3. 3. Why Build Vocab. Skills?
    4. 4. Why Build Vocab. Skills?
    5. 5. Mathematics as a Second Language <ul><li>The degree to which a student knows a word may vary, and that level of word knowledge has implications for vocabulary instruction. Dale and O‘Rourke (1986) identified four levels of word knowledge: </li></ul><ul><li>1. I never saw it before </li></ul><ul><li>2. I’ve heard of it, but I don’t know what it means </li></ul><ul><li>3. I recognize it in context - it has something to do with… </li></ul><ul><li>4. I know it </li></ul>
    6. 6. Mathematics as a Second Language <ul><li>A particular solution to a differential equation is a function y=f(x) that satisfies the differential equation. A general solution is an expression with arbitrary constants that represents the family of all particular solutions. </li></ul><ul><li>What vocabulary has to be known in order to translate the definition? </li></ul><ul><li>Defining or translating does not in itself create an understanding of the language . </li></ul>
    7. 7. ELL Strategies <ul><li>Students do not learn mathematical vocabulary by memorizing definitions. Rather, they construct meaning for mathematical vocabulary by actually doing authentic and meaningful mathematics. </li></ul><ul><li>The teacher must be purposeful in constructing learning experiences that direct the student’s attention to specific vocabulary. </li></ul>
    8. 8. <ul><li>Definitions alone are not sufficient to know a word and it is not necessary to be able to define a word in order to know it. Definitions provide information about the word; however, students also need to know how the word functions in different contexts. For students to learn the word, they benefit from a meaningful explanation of the word, rather than simply a definition. Stahl & Fairbanks (1986) found that providing students with both definitional and contextual information significantly improves comprehension. </li></ul>
    9. 10. ELL Strategies <ul><li>Language Objectives </li></ul><ul><ul><li>Focus on developing students’ vocabulary </li></ul></ul><ul><ul><ul><li>Brainstorm </li></ul></ul></ul><ul><ul><ul><li>Outline </li></ul></ul></ul><ul><ul><ul><li>Draft </li></ul></ul></ul><ul><ul><ul><li>Revise </li></ul></ul></ul><ul><ul><ul><li>Edit </li></ul></ul></ul><ul><ul><ul><li>Justify opinions </li></ul></ul></ul><ul><ul><ul><li>Negotiate meaning </li></ul></ul></ul><ul><ul><ul><li>Provide detailed explanations </li></ul></ul></ul><ul><ul><ul><li>Stating conclusions </li></ul></ul></ul><ul><ul><ul><li>Summarizing information </li></ul></ul></ul><ul><ul><ul><li>Making comparisons </li></ul></ul></ul>
    10. 12. Strategies: Semantic Maps New Concept Characteristics Characteristics Characteristics Characteristics Category Example Example Example What it’s Not
    11. 13. Strategies: Semantic Maps Polynomial Function A function consisting of a monomial or a sum of monomials Terms have coefficients and a variable raised to a power (degree) In standard form if terms are written in descending order of exponents (L-R) Functions f ( x ) = 3 x 2 + 2 x + 1 <ul><li>Variables don’t have negative exponents. </li></ul><ul><li>Variables are not in the exponent position. </li></ul><ul><li>Variables can’t have rational exponents (roots, etc.) </li></ul>f ( x ) = a n x n + a n -1 x n -1 + … + a 1 x + a 0
    12. 14. Try One … Vertical Angle Pairs Characteristics Characteristics Characteristics Characteristics Category Example Example Example What it’s Not
    13. 15. Angle Aerobics <ul><li>Line </li></ul><ul><li>Ray </li></ul><ul><li>Line segment </li></ul><ul><li>Midpoint </li></ul><ul><li>Acute </li></ul><ul><li>Obtuse </li></ul><ul><li>Right </li></ul><ul><li>Slide/Translation </li></ul><ul><li>Flip Reflection </li></ul><ul><li>Turn/Rotation </li></ul><ul><li>Congruent </li></ul><ul><li>Similar </li></ul>
    14. 16. Writing <ul><li>Students use targeted vocabulary to reflect on and organize their thoughts around related mathematical ideas—e.g. journals, justification of solution strategies, etc. </li></ul>
    15. 18. Quick Pic Book <ul><li>Vocabulary Self-Selection Strategy: </li></ul><ul><li>Personal Dictionaries </li></ul><ul><li>“ When students are shown how to identify key content vocabulary, they become adept at selecting and learning words they need to know, and given opportunities to practice, comprehension improves.” </li></ul><ul><li>(Shearer, Ruddell, & Vogt, 2001) </li></ul>
    16. 19. Journal
    17. 21. <ul><li>Students learn mathematics best by using it, and understanding the language of math gives students the skills they need to think about, talk about, and assimilate new math concepts as they are introduced. </li></ul>
    18. 22. <ul><li>Much instruction focuses students on “doing” mathematics, yet this deprives them of the words they need to communicate what they are learning in relevant ways. </li></ul><ul><li>Mathematical language is used and understood around the world, and conventional mathematics vocabulary gives learners the means of communicating those concepts universally. </li></ul>
    19. 23. Using Correct Vocabulary <ul><li>An example …. </li></ul>
    20. 24. Definitions of “variable” <ul><li>--Nichols & Schwartz, Mathematics Dictionary and Handbook </li></ul>
    21. 25. Definitions of “variable” <ul><li>--Kaplan, McMullin, Algebra to Go: A Mathematics Handbook </li></ul>
    22. 26. Definitions of “variable” <ul><li>--Holt, Pre-Algebra , 2008 </li></ul>
    23. 27. Are we using the proper terms?
    24. 28. When we use “letters” <ul><li>All letters are not variables! A letter can represent a quantity that varies (variable), but it can also represent an unknown constant. </li></ul>
    25. 29. What is x ? <ul><li>A “variable” or an “unknown constant”? </li></ul>
    26. 30. What is x ? <ul><li>A “variable” or an “unknown constant”? </li></ul>
    27. 31. What is x ? <ul><li>A “variable” or an “unknown constant”? </li></ul>
    28. 32. What is x ? <ul><li>A “variable” or an “unknown constant”? </li></ul>
    29. 33. What is x ? <ul><li>A “variable” or an “unknown constant”? </li></ul>
    30. 34. What is x ? <ul><li>A “variable” or an “unknown constant”? </li></ul>
    31. 35. So … <ul><li>Should we really be saying </li></ul><ul><ul><li>“ solve for the variable” </li></ul></ul><ul><ul><li>“ isolate the variable” </li></ul></ul><ul><ul><li>“ get the variable all by itself” </li></ul></ul>
    32. 36. Textbooks Even do it Sometimes <ul><li>-- Houghton Mifflin, 6 th Grade Math , 2007 </li></ul>
    33. 37. Textbooks Even do it Sometimes <ul><li>-- McDougall Littell, Algebra 2 , 2007 </li></ul>
    34. 38. Textbooks Even do it Sometimes <ul><li>-- McDougall Littell, Algebra 2 , 2007 </li></ul>
    35. 39. Who Cares? <ul><li>Discuss why it might be important to distinguish between constants and variables with your students. </li></ul>

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