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Mathematics Instruction

Mathematics Instruction . EDCI 5474. In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000. Guiding Questions. What factors impair performance? How do standards impact students?

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Mathematics Instruction

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  1. Mathematics Instruction EDCI 5474

  2. In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

  3. Guiding Questions • What factors impair performance? • How do standards impact students? • What math skills are essential? • What teaching strategies can be applied? • What methods are effective for teaching basic math facts? • What methods are effective for problem solving?

  4. Knowing and Doing Math • Knowing • Comprehend basic principles • More than one way to explain • More than one acceptable answer • “Difference between 2 numbers” • Doing • Apply strategies to complete item • “take away”

  5. Factors • 60% of students with LD • Reading, writing, attending, memory, language, motivation • (Montague, Bos, & Doucette, 1991) • Procedural & representational • (Geary, 1993) • Failure to understand concepts, lack pre-requisite skills, maintain facts • (Cox, 1975; Miller & Milam, 1987; et. al) • Need direction instruction, strategic

  6. Problem solving Communication ideas Reasoning Everyday applications Reasonableness Estimation Computational skills Algebraic thinking Measurement Geometry Statistics Probablity NCTM

  7. Effective Instruction • Appropriate math content • Problem solving, communicating ideas, everyday applications, computation • Establish goals & expectations • Assessment • Systematic & explicit instruction • Demonstrate-prompt -practice sequence • Highly organized, step by step presentation what, when and why use target skill • Insure understanding and task demands • Use learning principles • Attention, reinforcement, varied practice motivation

  8. Efficient Teaching • Demonstrate • Guided practice with prompts/feedback • Independent practice with feedback • Advanced organizers • Mastery of skill as generalization level

  9. Teach to understand concepts • Concrete-representational-abstract sequence • Learning concepts and rules • e.g. communative property of addition, inverse relationship, place value, # time 0 = 0 • Monitor progress • Check for understanding, interact, demonstrate • Provide feedback • Essential promote learning, mastery, independent learning, plan activities, motivation, confidence abilities • Immediate, basic & elaborate

  10. Teach to mastery • Automaticity • Benefits – retention, higher level skills, completion, positive feelings • Independent practice • Games, peers, computers, self monitor • Teach problem solving skills • Math knowledge, application, engage thinking • Strategy instruction parallel

  11. Teach generalization • Perform different situations • Motivation to apply, discuss why and how used, varied examples, mastery to use rather than remember • Positive attitude • Goal setting, success on prior skills, progress chart, high expectations, enthusiasm, reinforcing

  12. Math Curricula • Distar Arithmetic – SRA • Connecting Math Concepts • Edmark • Project MATH • Real Life Math • Strategic Math • Touch Math • Rapid, sequenced, scripted, direct instruction • 1 2 3 4 5 6 7 8 9

  13. Strategic Math • Pretest lesson • Teach concrete application • Teach representational application • DRAW (Discover, Read problem, Answer with drawing, Write answer) • Teach abstract application • Posttest • Provide practice to fluency • Strategic Math Series, Mercer & Miller, 1991

  14. Math Methods for SWD • Curriculum-based Assessment & Error Analysis • Spiral curriculum • Fast paced, insufficient practice, developmental sequence gaps, order of concepts, number of concepts • Performance: frustration < 70 to success 90% • Construct probes for error patterns • “Slice back” to re-teach lower skill

  15. Concrete to Seimconcrete • Manipulatives rather than pictures or numerals and symbols • Repeated opportunities • Relate manipulatives to numbers immediately • Build understanding of concepts • Questions and verbalize thinking • Check answers with manipulatives

  16. Direct Instruction • Focused, explicit, interactive • Tasks analyzed, clear examples (models), questions & feedback • Hi success • Models, demonstration, time delay • Systematic practice in real world contexts • Provide calculators as postsecondary level

  17. Sequence & Rule Based • Resequence texts • e.g. teach “zero” facts earlier • Sameness to reduce memorization • E.g. 0 times any number = 0

  18. Build Strategies • Self instruction & mnemonics • Good with direct instruction • Associate pictures, visual imagery • Should not substitute for practice for mastery • Good for rote memory deficits

  19. Motivation for Practice • Games • Bingo, blackjack, jeopardy, math basketball • Real Life • Newspapers, internet, technical courses, solve real life problems • Self-Monitoring, Goal Setting • Record, graph, choice of goals, conference, self-talk

  20. Cooperative Learning • Interactive practice, group rewards • Computer Instruction • Tutorial, drill & practice, software • With teacher directed instruction

  21. Teacher Student Dialogues • Math reasoning & problem solving • Explicit modeling centered on concepts • Verbal rehearsal, feedback, guided practice, check for understanding • Think alouds, scaffolded practice

  22. Instructional Tips • Number Sense – numbers to objects • One to one correspondence • Readiness skill • Numeration • Number values • Seriation • Ordinal, less/more • Place value • Ones, tens, hundreds

  23. Basic Facts & Operations • Addition • Sticks, counters, dots on cards, Touch Math, sums of ten, number lines, 1-5 w/9-5 below • Subtraction • Counters, sticks, number line, tally marks, Touch Math, • Multiplication • Groups in rows, Geoboards-cubes, teach rules, fingers • Division • Counters, number line to 25

  24. Complex Operations • Understand place value, regrouping, state the operation, graph paper • Addition with regrouping • Concrete manipulatives, mnemonic or visual reminders

  25. Other Essential Skills • Fractions • Need systematic practice, examples • Explicitly define whole, fractions equal parts • Fair sharing • Formal symbols, ½ or ¼ • Concrete aids before teaching rules • Mastering Fractions – interactive videodisc • Need more time

  26. Decimals • Concrete manipulatives • Represent fractions with denominators 10 or 100 • Visual representation less that whole • Algebra • Direct instruction, think alouds, concrete to abstract, strategy (FOIL)

  27. Arithmetic Word Problems • Group problems around familiar themes • Pictures & manipulatives of the problem • Attack word problems • Emphasize understanding with visuals, question for important information, model strategies for solving, give feedback during process - SOLVE

  28. Enhance Instruction • Increase instructional time, reduced independent practice • Review, directed instruction, guided practice, independent practice with feedback • Use concrete objectives • Teach key math terms, “sum” • Small group instruction • Real life examples • Varied reinforcement styles, process rather product • Lock, R.H. (1996). Adapting Mathematics Instruction in General Education for Students with Mathematics Disabilities, CLD.

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