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PPt-Math-Interventions (Ramirez, C., Templa R.).ppt

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PPt-Math-Interventions (Ramirez, C., Templa R.).ppt

  1. 1. DEVELOPMENTALLY APPROPRIATE PRACTICES IN EARLY LANGUAGE, LITERACY AND NUMERACY MATH INTERVENTION
  2. 2. Move one stick to make the number sentence correct.
  3. 3. Move one stick to make the sentence correct.
  4. 4. Move three sticks to make the fish face the opposite way.
  5. 5. Session I: COMMON ERRORS and ERROR ANALYSIS
  6. 6. Preview • What causes difficulties in learning Math? • What are the potential areas of difficulties in learning Math? • What information can we obtain from a student’s work?
  7. 7. What causes difficulties in learning Math?
  8. 8. Mathematics is a symbolic language used to: • express relationships – spatial, numeric, geometric, algebraic, and trigonometric, in both real and imaginary dimensions ; • communicate concepts through symbols; • reinforce and practise sequential and logical thinking. (Clayton, 2003)
  9. 9. A. Nature of Math (Chinn & Ashcroft, 1998) • Interrelated Parts are learned that later on build into wholes. What are needed to learn: • place values? • adding dissimilar fractions? • long division?
  10. 10. A. Nature of Math (Chinn & Ashcroft, 1998) • Interrelated Parts are learned that later on build into wholes. What will happen when a student does not learn some of these parts?
  11. 11. A. Nature of Math (Chinn & Ashcroft, 1998) • Sequential The learning of higher skills depends on the learning of basic skills.
  12. 12. A. Nature of Math (Chinn & Ashcroft, 1998) • Sequential
  13. 13. A. Nature of Math (Chinn & Ashcroft, 1998) • Sequential The learning of higher skills depends on the learning of basic skills. What will happen when the basic skills are not learned?
  14. 14. A. Nature of Math (Chinn & Ashcroft, 1998) • Reflective The meaning of concepts expand as lessons progress.
  15. 15. Polynomials Fractions Decimals A. Nature of Math (Chinn & Ashcroft, 1998) • Reflective Wholes What will happen when the meaning of concepts do not expand?
  16. 16. B. Structure (Chinn & Ashcroft, 1998) Math is learned from concrete to abstract Levels of difficulty build up as the lessons progress.
  17. 17. B. Structure (Chinn & Ashcroft, 1998) Implications: 1. If the basic levels are skipped or not well-taught, the foundations of learning become shaky. 2. When foundations are shaky, learning becomes segmented, thus the student has to resort to memorization. 3. When lessons are simply memorized, more effort is needed to learn higher-level lessons.
  18. 18. C. Skills and Processes (DepEd Math Curriculum 2013) • Knowing and understanding • Estimating, computing, and solving • Visualizing and modelling • Representing and communicating • Conjecturing, reasoning, proving, and decision-making • Applying and connecting
  19. 19. D. Characteristics of School Math • There are rules but they do not apply all the time • Answers are either right or wrong • Tasks require concentration
  20. 20. E. Math Language • Symbols + – x  =       A = r2 • Vocabulary Algebra, perimeter, sine even, pound, table • Syntax and Semantics seven more than one, quarter of a half, a difference of two
  21. 21. What are the potential areas of difficulties in learning Math? (Chinn & Ashcroft, 1998)
  22. 22. Preview 1. Direction and sequence 2. Perception 3. Retrieval 4. Speed of working 5. Math language 6. Cognitive Style 7. Conceptual Ability 8. Anxiety, stress, self- image
  23. 23. A. Direction and Sequence 1. Directional confusion
  24. 24. A. Direction and Sequence 2. Sequencing Problems counting on vs. counting backwards, place values
  25. 25. B. Perception 3. Visual Difficulties
  26. 26. B. Perception 4. Spatial Awareness
  27. 27. C. Retrieval 5. Working Memory and Short-term Memory 6. Long-term Memory
  28. 28. 7. Speed of Working
  29. 29. 8. Math Language • Vocabulary knowledge • a symbol with different names vs. a name for different symbols
  30. 30. Solve 70 1540 The answer is 22
  31. 31. 9. Cognitive Style (Chinn & Ashcroft,1998) Analyzing and Identifying the Problem 1. Tends to overview, holistic, puts together. 2. Looks at the numbers and facts to estimate an answer or restrict range of answers. Controlled exploration. 1. Focuses on the parts and details. Separates. 2. Looks at the numbers and facts to select a relevant formula or procedure. Grasshopper Inchworm
  32. 32. Solving the Problem Grasshopper Inchworm 3. Answer orientated. 4. Flexible focusing. Methods change. 5. Often works back from a trial answer. Multi-method. 6. Adjusts, breaks down/ builds up numbers to make an easier calculation. 3. Formula, procedure orientated. 4. Constrained focus, Uses a single method. 5. Works in serially ordered steps, usually forward. 6. Uses numbers exactly as given. Cognitive Style (Chinn & Ashcroft, 1998)
  33. 33. Solving the Problem Grasshopper Inchworm 7. Rarely documents method. Performs calculation mentally. 8. Likely to appraise and evaluate answer against original estimate. Checks by alternate method. 9. Good understanding of the numbers, methods and relationships. 7. More comfortable with paper and pen. Documents method. 8. Unlikely to check or evaluate answer. If check is done, uses same procedure or method. 9. Often does not understand procedure or values of numbers. Works mechanically. Cognitive Style (Chinn & Ashcroft, 1998)
  34. 34. 10. Conceptual Ability • IQ Score • Abilities in the Multiple Intelligences
  35. 35. 10. Conceptual Ability • Impact of Brain-based Condition(s) • Social or behavioral skills-related • Autism • Asperger’s Syndrome • Attention-Deficit/Hyperactivity Syndrome • Communication skills-related • Language Acquisition • Receptive / Expressive Language Difficulties
  36. 36. 10. Conceptual Ability • Impact of Brain-based Condition(s) • Cognitive/learning skills-related • MR/ Intellectual Disability • Learning Disabilities • Long and Short-term Memory Deficits • Physical or sensory skills-based • Visual Impairment • Hearing Impairment
  37. 37. 10. Conceptual Ability • Dyscalculia • Dyscalculia is usually perceived of as a specific learning difficulty for mathematics, or, more appropriately, arithmetic. (http://www.bdadyslexia.org.uk/) • Dyscalculia is a brain-based condition that makes it hard to make sense of numbers and math concepts. (https://www.understood.org/)
  38. 38. 11. Anxiety, Stress, and Self-image • Effect of experiences and environment • Attitude towards Math
  39. 39. Exercise: ERROR ANALYSIS
  40. 40. ERROR ANALYSIS
  41. 41. ERROR ANALYSIS
  42. 42. ERROR ANALYSIS
  43. 43. ERROR ANALYSIS (Refer to Worksheet)
  44. 44. Session II: MATH REMEDIATION
  45. 45. Preview 1. Introduction to Remediation 2. Some Remedial Teaching Strategies 3. Principles of Remediation 4. The Remedial Plan
  46. 46. The commonly accepted idea of remediation as a careful effort to reteach successfully what was not well taught or not well learned during the initial teaching. (Glennon & Wilson, 1972) What is remediation?
  47. 47. Students who show lags in math performance that are unlike his or her potential or performance in other academic areas Who needs math remediation?
  48. 48. Do not allow children who may have special needs to go from one grade to another without a professional team assessing the student for eligibility for services and supports. "Waiting" is NOT an effective, educational practice. Although the process of referral can be cumbersome, it is well worth it when it identifies needs that can be met during the educational life of the child. – Barbara T. Doyle, Johns Hopkins School of Education
  49. 49. The Remediation Process 1) Identify the concepts, skills, procedures to be retaught. 2) Collect supporting information, such as anecdotes, work portfolio, and assessment reports. 3) Select appropriate re-teaching methods and strategies. 4) Provide remediation. 5) Evaluate and determine next steps.
  50. 50. 1) Structure of Mathematics 2) The student’s strengths and difficulties • Error analysis • Formal Testing • Diagnostic Testing 3) Remedial instruction strategies What a Remedial Math Teacher Needs to Know
  51. 51. SOME TEACHING STRATEGIES
  52. 52. a. Rounding 1. Use landmark numbers 5 0 10
  53. 53. b. Solving 1. Use landmark numbers
  54. 54. a. Grids 2. Use graphic organizers
  55. 55. b. Tables (rows and columns) 2. Use graphic organizers
  56. 56. c. Grids and spaces for long division 2. Use graphic organizers
  57. 57. d. Guide questions and spaces 2. Use graphic organizers
  58. 58. a. Order of operations 3. Use mnemonics
  59. 59. b. Parts of a subtraction sentence 3. Use mnemonics
  60. 60. c. Long division 3. Use mnemonics
  61. 61. a. Properties of addition and multiplication 4. Show patterns and properties
  62. 62. b. Breaking numbers down / decomposing 4. Show patterns and properties
  63. 63. c. The hundreds chart 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
  64. 64. a. Unlock new terms 5. Teach math vocabulary
  65. 65. b. Teach word analysis 5. Teach math vocabulary
  66. 66. c. Tell the background story 5. Teach math vocabulary
  67. 67. 6. Visualize and verbalize
  68. 68. PRINCIPLES OF INTERVENTION
  69. 69. 1. Build on what the child knows  Show interconnectedness of lessons  Promote reasoning Principles of Intervention (Chinn & Ashcroft, 2007)
  70. 70. 2. Acknowledge the student’s learning style  T’s best method might not work  Let student discover the strategies that work for him Principles of Intervention (Chinn & Ashcroft, 2007)
  71. 71. 3. Make math developmental  Use the concrete-representational- abstract progression  Employ gradual transfer Principles of Intervention (Chinn & Ashcroft, 2007)
  72. 72. 4. Use the language that communicates the idea  Use the child’s language  Use visuals, real objects, experiences Principles of Intervention (Chinn & Ashcroft, 2007)
  73. 73. 5. Use the same basic numbers to build an understanding of each process or concept  Make instruction success-oriented Principles of Intervention (Chinn & Ashcroft, 2007)
  74. 74. 5. Teach ‘why’ as well as ‘how’ Principles of Intervention (Chinn & Ashcroft, 2007)
  75. 75. 7. Keep a responsive balance in all of teaching Principles of Intervention (Chinn & Ashcroft, 2007) If the child does not learn the way you teach, then you must teach the way he learns. - Harry Chasty
  76. 76. REMEDIAL PLANNING (Refer to Worksheet)
  77. 77. Remedial Planning
  78. 78. Basic Information
  79. 79. Why does the student need to undergo remediation? Who made the referral?
  80. 80. What do we know about the child, in relation to math learning?
  81. 81. What do we know about the student, in relation to math learning?
  82. 82. What behaviors did the student show – during and outside math sessions? What do we want to do about these behaviors?
  83. 83. What behaviors did the student show – during and outside math sessions?
  84. 84. What is the student’s most recent Math performance?
  85. 85. What is the student’s most recent Math performance?
  86. 86. What do we do now? / What’s the plan? An overview
  87. 87. What do we do now? / What’s the plan?
  88. 88. Session III: PLANNING FOR INTERVENTIONS (Workshop)
  89. 89. REMEDIAL PLANNING (Refer to Worksheet)
  90. 90. REFERENCES: Bley, N.S. and Thornton, C.A. (2001). Teaching mathematics to students with learning disabilities, 4th ed. USA: Pro-Ed. Chinn, S. and Ashcroft, J. (1998). Mathematics for dyslexics: A teaching handbook, 2nd ed. UK: Whurr. Chinn, S. and Ashcroft, J. (2007). Mathematics for dyslexics: Including Dyscalculia, 3rd ed. England: John Wiley and Sons. Doabler, C.T., et.al. (2012). Evaluating Three Elementary Mathematics Programs for Presence of Eight Research-Based Instructional Design Principles. Learning Disability Quarterly, 35(4), 200-211. Lalley, J.P. and Miller, R.H. (2002).Computational Skills, Working Memory, and Conceptual Knowledge in Older Children with Mathematics Learning Disabilities. Education, 126(4), 747-755. Mabbott, D.J. and Bisanz, J. (2008). Computational Skills, Working Memory, and Conceptual Knowledge in Older Children With Mathematics Learning Disabilities. Journal of Learning Disabilities, 41(1), 15-28. Miles, T.R. and Miles, E, Eds. (1992). Dyslexia and mathematics. USA: Routledge.

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