The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 4th Edition © 2010 Pearson Education, Inc. All rights reserved. Mathematics Chapter 14

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 2 Focus Questions- How do math strategies differ from early number concepts to advanced computations? What strategies help students remember facts? How can strategies be used with students with special needs? What strategies are helpful when teaching money skills? How can manipulatives help students succeed in math?

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 3 Mathematics and Students with Disabilities Learning disabilities May have difficulty with memory and strategy use Processes and strategy use with math problems Mental Retardation Acquisition of math concepts Remembering and executing facts and procedures Math reasoning Emotional Impairment Often score below average on mathematics achievement Attention Problems Difficulties organizing information

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 4 Components of Effective Mathematics Instruction Focus on “big ideas”- generalizable concepts rather than individual details Teach “conspicuous” strategies for conducting math operations and solving problems Make efficient use of time on prioritized objectives Communicate strategies in a clear, explicit manner Provide practice and review to promote retention

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 5 Tips for Teachers Select appropriate, comprehensive math content Select goals that establish high expectations Provide systematic and explicit instruction Monitor progress frequently and systematically Teach to mastery Promote a positive attitude Teach students to generalize

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 6 Development of mathematical understanding Progress from concrete representations (beads and blocks) to Semiconcrete representations (pictorial) to Abstract representations (graphic) Functioning also improves with direct instruction, reinforcement, mnemonics, & strategies training

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 7 Levels of Understanding Concrete Manipulation of objects to understand computational processes Learner concentrates on both the manipulated objects and the symbolic processes that describe the manipulations Finger counting

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 8 Levels of Understanding cont’d. Semiconcrete Working with illustrations of items in performing math tasks Dots, lines, pictures, etc. The emphasis is on developing associations between visual models and numerical equations

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 9 Levels of Understanding cont’d. Abstract The use of numerals to solve math problems Students who experience problems in math usually need experiences at the concrete and semiconcrete levels before they can use numerals meaningfully

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 10 Strategies for Beginning Math Teach number concepts More, less, any, none, each Teaching Counting Best acquired with practice Components of counting Acoustic Point counting Resultative counting Counting on Skip counting  What activities can you use to teach this concept?

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 11 Teaching Addition & Subtraction Manipulatives beads, buttons, base 10 blocks Number lines to promote operations Promote number writing Questioning to promote understanding of symbols TOUCH MATH to promote computation Materials represent quantity by dots on each of the numbers 1-9 Practice with facts

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 12 Strategies for Addition & Subtraction Specific strategies for facts Teach adding with zero, doubles, “count-ons,” doubles plus one, pattern 9 facts, “other 10 sums,” that leaves 8 facts to learn Subtraction facts Teach subtraction as inverse of addition Use tutoring pairs, computer software Strategies for place value and regrouping Base-10 blocks  What activities can you use to teach these skills?

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 13 Response to Intervention Use small group tutoring as a Tier 2 intervention First-grade students who score poorly during the third through fifth weeks of the year may need additional remedial assistance including: Concrete materials Computer software Practice with facts

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 14 Error Analysis for Reteaching Problem Inadequate fact mastery Failure to apply learned strategies Reversal (2 = 6) Regrouping error Reversed subtraction Place value error Algorithmic error Possible Intervention Reteach facts Reteach strategies Teach writing orientation Reteach regrouping Reteach procedures Reteach place value Reteach algorithm using models, demonstrations, and graph paper

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 15 Teaching Multiplication Facts Manipulatives “Count-bys” Count by 2, 3, 5, 10 Use strategies for facts Drill and practice, flashcards, computers Target essential facts Bent Finger Strategy for x9 Pegword Strategy Mnemonic strategies Pegwords Times Tables the Fun Way program

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 16 Teaching Multiplication & Division Algorithms Teach sequence of arithmetic operations Mnemonics like My Dear Aunt Sally Demonstration Plus Permanent Model Demonstrate how to complete problem AND place model on 3 x 5 card so student can use when example needed Teach modified long division Use error analysis to inform instruction  What activities can you use to teach these skills?

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 17 Cognitive Strategies for Problem Solving Use of steps can help students remember how to solve word problems 1. Read the problem 2. Think about the problem 3. Decide the operation 4. Write the math sentence 5. Do the problem 6. Label the answer 7. Check every step

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 18 Strategies for Problem Solving FAST DRAW Find what you are solving for Ask yourself, “what are the parts of the problem?” Set up the numbers Tie down the sign Discover the sign Re-read the problem Answer the problem with pictures Write the answer

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 19 Math Problem Solving and Self-Monitoring When solving the problem, did I: Read about the problem? Think about the problem? Decide the operation? Write the math sentence? Do the problem? Label the answer? Check every step?

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 20 Strategies for Money & Time Practice coin recognition and counting money with appropriate materials Use appropriate methods and materials for teaching about time Some students may benefit from digital clocks and watches Use authentic experiences for teaching time and money How long is it between these two shows on TV?  Identify an authentic activity can you use to teach these concepts.

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 21 Teaching Algebra Many students with disabilities have difficulties because of basic skills deficits, self-efficacy, and abstract nature of content Good instruction includes: Organized, explicit teaching of concepts Direct teaching of cognitive routines Systematic teaching to prioritized, general objectives

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 22 Strategies for Algebra Use manipulatives for negative numbers Teach algebraic representations early Teach strategies for computation Mnemonics like FOIL- First terms, Outer + Inner and Last Teach strategies for solving quadratic equations Teach problem-solving strategies Self-questioning Concrete, semiconcrete, or abstract presentations

The Inclusive Classroom, 4 th Edition Mastropieri/Scruggs © 2010 Pearson Education, Inc. All Rights Reserved. 23 Teaching Functional Math Functional math includes aspects of mathematics that serve people in their daily lives Calendars Checks Cooking Bill paying  What other functional math skills can you incorporate into your teaching? How can you make more math instruction functional?