Blanche Jackson Glimps, Contributor The Inclusive Classroom: Strategies for Effective Differentiated Instruction By Margo A. Mastropieri Thomas E. Scruggs Blanche Jackson Glimps, Contributor The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Mathematics Chapter 15 The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Objectives Describe, evaluate, and implement various strategies for teaching mathematics. Provide instructional strategies for such concepts as counting, one-to-one correspondence, numeration, geometry, number lines, writing numbers, and understanding symbols. Describe and implement strategies for remembering addition and subtraction facts. List early addition and subtraction problem-solving strategies and multiplication and division concepts. Identify teaching strategies for incorporating calculators and introducing new vocabulary for multiplication and division facts, and describe when these strategies are appropriate. The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Objectives (cont.) Understand and implement multiplication and division algorithms strategies. Describe and implement strategies for mathematics for operations on money, time, and fractions. Explain the use of manipulative materials and strategies for computation, solving quadratic equations, and problem-solving in algebra. Describe and evaluate strategies for mathematical reasoning. The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Mathematics and Students with Disabilities Learning disabilities May have difficulty with memory and strategy use Processes and strategy use with math problems Low motivation and affect Intellectual disabilities Acquisition of math concepts Remembering and executing facts and procedures Mathematical reasoning Emotional or Behavioral disorders Often score below average on mathematics achievement Attention Problems Difficulties organizing information The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Mathematics and Students with Disabilities Hearing impairments, communication disorders, ELLs May have difficulty with the English language and communication aspects of mathematics Visual impairments Perform well on mathematics tasks with appropriate adaptations Physical impairments May need specific assistance if concrete manipulatives materials are used The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Teaching Math in Inclusive Settings Research-based principles for effective remediation in mathematics Explicit instruction Instructional design A strong conceptual basis Drill and practice Cumulative review Motivators Progress monitoring The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

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, and strategies training The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Strategies for Beginning Math Teach early 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 Subitizing The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Strategies for Beginning Math Teach one-to-one correspondence Before later concepts can be mastered, students must understand the concept of numerical equivalence Introduce geometry in early years The concept of shapes Present non-instances The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Addition and Subtraction Manipulatives beads, buttons, dried beans, 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 and specific strategies for facts The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Teaching Addition and Subtraction Practice and specific strategies for facts Drill with flashcards Practice with a partner Subtraction facts More difficult to learn than addition facts Use of tutoring pairs, computer software, and homework can help promote mastery Place value and regrouping Use of base-10 blocks Use of a self-monitoring checklist The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Teaching Addition and Subtraction Teaching early problem solving with addition and subtraction Graduated word problem sequence strategy RTI for early prevention and identification Tier 1-high quality instructional procedures for the general education class Small group tutoring as Tier 2 intervention Students who failed to respond profitably from the Tier 2 instruction could be considered for special education The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

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 The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Teaching Division Facts Calculators when appropriate Reinforce arithmetic vocabulary Addend, sum, minuend, subtrahend, difference, product, divisor Demonstration Plus Permanent Model Demonstrate how to complete a particular type of problem with steps on someplace accessible Modified long division Construct the problem as usual but draw a line straight down vertically from the end of the problem Use error analysis to inform instruction Determine the type of error students make The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Teaching Problem Solving Promote use of word meaning Reinforce arithmetic vocabulary “Ask for one, tell for one” strategy for determining implied operations Teach cognitive strategies Solve It! (seven step strategy to solve word problems) SAY, ASK, and Check “(self-instruction training) Use Tier 2 problem-solving interventions “Hot Math” The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Cognitive Strategies for Problem Solving Use of steps can help students remember how to solve word problems Read 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: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Money and Time Practice coin recognition and counting money with appropriate materials Use appropriate methods and materials for teaching about time Use student clocks that can be set to specific times Model times or specific features of a clock and ask students to repeat on their own clock model Assign peer partners who are fluent in telling time Some students may benefit from digital clocks and watches The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Fractions and Decimals Use appropriate methods and materials for teaching fractions Involve students’ experiences as much as possible Use appropriate methods and materials for teaching decimals Decimals should not be an overwhelming challenge, if students have exhibited proficiency in aspects of arithmetic The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Area and Volume Concepts Provide visual and three-dimensional representations Teach “big ideas” Provide students with a more general idea of themes, rather than a large number of unrelated formulas and problem solutions The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Strategies for Algebra Use manipulatives for negative numbers Teach problem-solving strategies Number lines, financial debt example, algebra tiles Teach algebraic representations early Teach strategies for computation Mnemonics like FOIL- First terms, Outer + Inner and Last Teach strategies for solving quadratic equations Self-questioning Concrete, semiconcrete, or abstract presentations The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.

Teaching Functional Math Functional math includes aspects of mathematics that serve people in their daily lives Calendars Checks Calculating household expenses Filling out income tax forms Bill paying The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN 0132659859 © 2014, 2010, 2007, 2004, 2000 Pearson Education, Inc. All rights reserved.