ch12lectPP420

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ch12lectPP420

  1. 1. CHAPTER TWELVE TEACHING MATH
  2. 3. <ul><li>It is estimated that between 5 and 10 percent of school age children have some form of math learning disabilities. </li></ul><ul><li>(Fuchs, Fuchs, & Hollenbeck 2007; Geary, 2004) </li></ul>
  3. 4. 2009 National Assessment of Educational Progress in Mathematics <ul><li>In 2009, approximately 28% of fourth-grade students performed below a basic level of achievement; only 39% attained a proficient mathematics achievement level. </li></ul><ul><li>About 27% of eighth-grade students were below a basic level of mathematics achievement; only 34% achieved proficient mathematics standards. </li></ul>
  4. 5. Basic Terms and Processes <ul><li>Addition </li></ul><ul><ul><li>addend, sum </li></ul></ul><ul><li>Subtraction </li></ul><ul><ul><li>minuend, subtrahend, difference, sum, know addend </li></ul></ul><ul><li>Multiplication </li></ul><ul><ul><li>multiplicand or factor; multiplier or factor, product </li></ul></ul><ul><li>Division </li></ul><ul><ul><li>quotient or factor; dividend or product, divisor or factor </li></ul></ul>
  5. 6. Basic Facts <ul><li>There are 390 basic facts: </li></ul><ul><ul><li>100 addition </li></ul></ul><ul><ul><li>100 subtraction </li></ul></ul><ul><ul><li>100 multiplication </li></ul></ul><ul><ul><li>90 division </li></ul></ul>
  6. 7. Research on Effective Math Instruction <ul><li>Curriculum design, teacher behavior, and student engagement directly influence the mathematics achievement of students with learning problems. </li></ul><ul><li>Educators need to examine existing research and literature to determine what should be taught in a math curriculum and the best practices for how to teach it. </li></ul>
  7. 8. Prevention of Math Difficulties <ul><li>4 principles: </li></ul><ul><ul><li>Instruct at a quick pace with varied instructional activities and high levels of engagement </li></ul></ul><ul><ul><li>Set challenging standards for achievement </li></ul></ul><ul><ul><li>Incorporate self-verbalization methods </li></ul></ul><ul><ul><li>Present physical and visual representation of number concepts or problem-solving situations </li></ul></ul>
  8. 9. Components of Effective Math Instruction <ul><li>Selecting appropriate mathematics content </li></ul><ul><li>Teaching the acquisition of math </li></ul><ul><li>Teaching mastery </li></ul><ul><li>Teaching problem solving </li></ul><ul><li>Teaching generalization </li></ul><ul><li>Using explicit-implicit math instruction </li></ul><ul><li>Promoting a positive attitude toward math </li></ul>
  9. 10. <ul><li>Twelve Components of Essential Mathematics </li></ul><ul><li>1. Problem solving. </li></ul><ul><li>2. Communication of mathematical ideas. </li></ul><ul><li>3. Mathematical reasoning. </li></ul><ul><li>4. Application of mathematics to everyday situations. </li></ul><ul><li>5. Alertness to the reasonableness of results. </li></ul><ul><li>6. Estimation. </li></ul><ul><li>7. Appropriate computational skills. </li></ul><ul><li>8. Algebraic thinking. </li></ul><ul><li>9. Measurement. </li></ul><ul><li>10. Geometry. </li></ul><ul><li>11. Statistics. </li></ul><ul><li>12. Probability. </li></ul>
  10. 11. <ul><li>Mathematics proficiency includes </li></ul><ul><li>conceptual understanding, </li></ul><ul><li>procedural fluency, </li></ul><ul><li>strategic competence, </li></ul><ul><li>adaptive reasoning, </li></ul><ul><li>and productive disposition. </li></ul>
  11. 12. Instructional Practices for Computation and Problem Solving <ul><li>Two math facts programs </li></ul><ul><li>Concrete-Semiconcrete-Abstract (CSA) activities </li></ul><ul><li>Basic rules and algorithms </li></ul><ul><li>Problem-solving interventions </li></ul><ul><li>Life Skills math </li></ul><ul><li>Estimation </li></ul><ul><li>Calculators </li></ul>
  12. 13. Instructional Practices for Computation and Problem Solving (cont’d) <ul><li>Because many students with learning problems fail to master basic facts, two programs are discussed in the text for teaching math facts: </li></ul><ul><ul><li>Thornton and Toohey Math Facts Program </li></ul></ul><ul><ul><li>Mercer and Miller Math Facts Program </li></ul></ul>
  13. 14. Instructional Practices for Computation and Problem Solving (cont’d) <ul><li>Concrete-Semiconcrete-Abstract Activities: </li></ul><ul><ul><li>Place value </li></ul></ul><ul><ul><li>Addition: sums-to-9 </li></ul></ul><ul><ul><li>Addition: sums-to-18 </li></ul></ul><ul><ul><li>Addition with regrouping </li></ul></ul><ul><ul><li>Subtraction facts (1-9) </li></ul></ul><ul><ul><li>Subtraction facts (10-18) </li></ul></ul><ul><ul><li>Subtraction with regrouping </li></ul></ul>
  14. 15. Concrete-Semiconcrete-Abstract Activities (cont’d) <ul><ul><li>Multiplication </li></ul></ul><ul><ul><li>Division </li></ul></ul><ul><ul><li>Division with remainder </li></ul></ul><ul><ul><li>Recognition of unit fractions </li></ul></ul><ul><ul><li>Addition of fractions with the same denominators </li></ul></ul><ul><ul><li>Addition and subtraction of mixed fractions </li></ul></ul>
  15. 16. Instructional Practices for Computation and Problem Solving (cont’d) <ul><li>Basic Rules and Algorithms: </li></ul><ul><ul><li>Addition rules </li></ul></ul><ul><ul><li>Additional algorithms </li></ul></ul><ul><ul><li>Subtraction rules </li></ul></ul><ul><ul><li>Subtraction algorithms </li></ul></ul><ul><ul><li>Multiplication rules </li></ul></ul><ul><ul><li>Multiplication algorithms </li></ul></ul><ul><ul><li>Division rules </li></ul></ul><ul><ul><li>Division algorithms </li></ul></ul><ul><ul><li>Fraction algorithm </li></ul></ul>
  16. 17. Instructional Practices for Computation and Problem Solving (cont’d) <ul><li>Problem-Solving Interventions: </li></ul><ul><ul><li>Interventions that use sequential steps </li></ul></ul><ul><ul><li>Interventions that use the CSA (concrete-semiconcrete-abstract) sequence </li></ul></ul><ul><ul><li>Interventions that use graphic representation </li></ul></ul>
  17. 18. Instructional Practices for Computation and Problem Solving (cont’d) <ul><li>Life Skills Math </li></ul><ul><li>Estimation </li></ul><ul><li>Calculators </li></ul>
  18. 19. Math Activities <ul><li>Readiness </li></ul><ul><ul><li>Classification </li></ul></ul><ul><ul><li>Ordering </li></ul></ul><ul><ul><li>One-to-One Correspondence </li></ul></ul><ul><ul><li>Counting </li></ul></ul><ul><ul><li>Greater Than, Less Than </li></ul></ul>
  19. 20. Math Activities (cont’d) <ul><li>Place Value: </li></ul><ul><ul><li>Chip Trading Games </li></ul></ul><ul><ul><li>Bank Game </li></ul></ul><ul><ul><li>Making Columns </li></ul></ul><ul><ul><li>Pegboard </li></ul></ul><ul><ul><li>Place Value Cards </li></ul></ul><ul><ul><li>Place Value Table </li></ul></ul>
  20. 21. Math Activities (cont’d) <ul><li>General Computation: </li></ul><ul><ul><li>Small Work Samples </li></ul></ul><ul><ul><li>Mystery Math </li></ul></ul><ul><ul><li>Learning Ladders </li></ul></ul>
  21. 22. Math Activities (cont’d) <ul><li>Addition: </li></ul><ul><ul><li>Nail Abacus </li></ul></ul><ul><ul><li>Number Line </li></ul></ul><ul><ul><li>Dot Addition </li></ul></ul><ul><ul><li>Computational Cues </li></ul></ul><ul><ul><li>Addition Facts Family </li></ul></ul>
  22. 23. Math Activities (cont’d) <ul><li>Subtraction: </li></ul><ul><ul><li>Nail Abacus </li></ul></ul><ul><ul><li>Number Line </li></ul></ul><ul><ul><li>Addition-Subtraction Pattern </li></ul></ul><ul><ul><li>Self-Monitoring Subtraction Strategy </li></ul></ul>
  23. 24. Math Activities (cont’d) <ul><li>Multiplication: </li></ul><ul><ul><li>Array Multiplication </li></ul></ul><ul><ul><li>Napier’s Rods </li></ul></ul><ul><ul><li>Multiplication Chart </li></ul></ul><ul><ul><li>Addition-Multiplication Pattern </li></ul></ul><ul><ul><li>Dot Cards </li></ul></ul>
  24. 25. Math Activities (cont’d) <ul><li>Division: </li></ul><ul><ul><li>Number Line </li></ul></ul><ul><ul><li>Dividing Numbers Into Parts </li></ul></ul><ul><ul><li>Dot Division </li></ul></ul><ul><ul><li>Long Division Steps </li></ul></ul>
  25. 26. Math Activities (cont’d) <ul><li>Fractions: </li></ul><ul><ul><li>Number Line </li></ul></ul><ul><ul><li>Fraction Chart </li></ul></ul><ul><ul><li>Fraction Bars </li></ul></ul><ul><ul><li>Multiplying Fractions with Grids </li></ul></ul>
  26. 27. Math Activities (cont’d) <ul><li>Time: </li></ul><ul><ul><li>Number Line </li></ul></ul><ul><ul><li>Record Schedule </li></ul></ul><ul><ul><li>Examining Schedules </li></ul></ul><ul><ul><li>Calendar Quiz </li></ul></ul>
  27. 28. Math Activities (cont’d) <ul><li>Decimals/Money: </li></ul><ul><ul><li>Number Line </li></ul></ul><ul><ul><li>Completion of Missing Parts </li></ul></ul><ul><ul><li>Expanded Place Value Chart </li></ul></ul><ul><ul><li>Money Cards </li></ul></ul><ul><ul><li>Real Money </li></ul></ul><ul><ul><li>Coupon Shopping </li></ul></ul><ul><ul><li>Taking Orders </li></ul></ul><ul><ul><li>Check the Charge </li></ul></ul>
  28. 29. Math Activities (cont’d) <ul><li>Measurement: </li></ul><ul><ul><li>Measure Box </li></ul></ul><ul><ul><li>Measurement and You </li></ul></ul>
  29. 30. Math Activities (cont’d) <ul><li>Word Problems: </li></ul><ul><ul><li>Story Problems </li></ul></ul><ul><ul><li>Table Problems </li></ul></ul>
  30. 31. Instructional Games in Math <ul><li>Math War </li></ul><ul><li>Pig Game </li></ul><ul><li>Make the Numbers Count </li></ul><ul><li>Rook Math </li></ul><ul><li>Math Concentration </li></ul><ul><li>Fraction Game </li></ul><ul><li>Toss a Bean Bag </li></ul><ul><li>Multiplication and Division Facts Rummy </li></ul><ul><li>Travel Game </li></ul><ul><li>Basketball Math </li></ul><ul><li>Counting Coins </li></ul><ul><li>Rate Game </li></ul><ul><li>Fraction Blackjack </li></ul><ul><li>Fraction Removal </li></ul><ul><li>Decimal Shapes </li></ul>
  31. 32. Self-Correcting Math Materials <ul><li>Flip-Sider Math Cards </li></ul><ul><li>Clipping Answers </li></ul><ul><li>Math Squares </li></ul><ul><li>Color Code Folders </li></ul><ul><li>Fast Facts </li></ul><ul><li>Snoopy Math </li></ul><ul><li>Equivalent Fractions, Decimals, Percents </li></ul>
  32. 33. Commercial Math Programs <ul><li>Connecting Math Concepts </li></ul><ul><li>Corrective Mathematics </li></ul><ul><li>Great Leaps Math </li></ul><ul><li>Key Math 3 – Essential Resources </li></ul><ul><li>Strategic Math Series </li></ul><ul><li>TransMath </li></ul>
  33. 34. Computer Software Programs in Math <ul><li>Fraction Attraction </li></ul><ul><li>Math Blaster </li></ul><ul><li>Math FACTMASTER </li></ul><ul><li>Math Munchers for the 21 st Century </li></ul>

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