Inclusionary MathematicsChapter 15“The Inclusive Classroom”Margo A. Mastropieri &Thomas E. Scruggs4th Edition Abigail Kaylor*Adele Mestas*Lorie Rainey*Catherine Russell*Linda Weatherford
Mathematics Today National Council of Teachers of Mathematics (NCTM) established Principles and Standards for School Mathematics with 6 overarching principles:
Implications for Students with disabilities NCTM suggested these students may need: Many students with disabilities exhibit difficulties in:
Oral rather than written
Memory and general strategy use
Literacy and Communication
Specific processes and strategies associated with math problems
Low motivation and affect
Designing effective mathematics instruction Focus on “Big Ideas”- generalizable concepts rather than individual details Teach “conspicuous” strategies, not to broad or specific, for conducting math operations Efficient use of time on prioritized objectives Clear, explicit communication of strategies Practice and review to promote retention Progress from concrete, to semi-concrete, to abstract
Teaching Beginning Math Early Number Concepts: More, less, any, none, none left, together, how many, each. Counting Strategies: Acoustic counting, Point Counting, Resultative counting(order irrelevant), Counting on(starting from specified number), Skip counting, Subitizing (counting w/o actually counting) 1 to 1 Correspondence: Different sets of objects can be matched according to quantity Introduce Geometry: various shapes in various sizes to examine and explore
Teaching Addition and subtraction Use Manipulatives: beads, buttons, dried beans, base-10 blocks Use Number Lines: transitioning from counting to number operations, addition, subtraction, negative numbers Strategies for Number Writing: models, stencils, copying dashed numbers, additional practice Use Questions to Understand Symbols: What does the +,=,*, / mean?
Use Touch Math for addition: materials that have numbers with corresponding amount of dots on them to provide visual representation. Practice and Specific Strategies: songs, peer quizzing, flashcards, rhymes, review Strategies for Place-value and Regrouping: use base blocks to make constructs to represent larger numbers as groups of smaller numbers Early Problem Solving: use of manipulatives alongside fun math word problems, math games with counting Response to Intervention: Tier 2 support through small group tutoring using concrete, pictorial, graphic materials, practice software.
Teaching Multiplication & Division Manipulatives to Model Concepts: Create a set of 3 blocks, and ask the student to make three more sets of 3. Then explain that they have a set of 3, four times. Division can be done by pulling from a total into smaller groups. “Count-Bys”: learning to count by 2’s and 5’s helps strengthen multiplication concepts. Specific Strategies: Use drill and practice to establish verbal math facts such as times table. Identify key facts. Teach multiplication techniques using hands, teach through mnemonics.
Use Calculators: sometimes calculators can eliminate the need for memorization of facts, or to scaffold the practice of multiplication and checking work. Reinforce Arithmetic Vocab: Learn and apply math terms and practice using them. Specific Strategies for Algorithms: Students must learn the order of operations (Please Excuse My Dear Aunt Sally) and how to track steps and follow-through on processes. Teach modified long division) Inform Students Through Error Analysis: Determine with the students the types of errors they make. Use them to guide further practice
Teaching Problem Solving Word Meanings: Explicitly teach how to read word problems and identify the symbols within the language. In-depth analysis of what word concepts mean. Practice creating math sentences. Cognitive Strategies: Promote 7 step strategy: Read the problem Think About/Paraphrase the problem Decide the operation Write the math sentence Do the math problem Label the answer Check every step
Teaching Money & Time Coin Recognition and Money Counting: Use appropriate materials and examples, teach value of coins after names are learned. Use relevant problems. Appropriate Methods and Materials for Time: use clock manipulatives with movable hands, use peer-models, possibly use digital clocks to scaffold concept of time.
Teaching Fractions & Decimals Materials and Models for Fractions: relate concept to students’ lives (i.e. sharing, pizza, cutting in half) and use models that can be generalized into community. Materials and Models for Decimals: Graph paper to help alignment, Decimal squares allow for parts of a whole to be shaded in to represent decimals of 100 or 1000.
Teaching Area & Volume Visual and 3-D representations: movable transparency overlays, blocks, magnets all will help students develop this concept. Teach Big Ideas: Establish the root of all volume formulas and what they represent. This way students can still solve a problem based on concept instead of formula recall.
Teaching Algebra Manipulatives to Teach Negative Numbers: different colored blocks can be assigned to mean positive or negative and model the problem Early Algebra Concepts: early algebra concpets can be leanred by using blank spaces or fun symbols like smiley faces (4+2=____; 3+q=6) Computation Strategies: ways to remember steps and procedures; FOIL First, Outer, Inner, Last Quadratic Equations: teach all three methods: factoring, completing the square, quadratic equation. Algebra tiles can be used to model process
Problem-Solving Strategies: Employ STAR strategy: Search the word problem(read carefully, find facts, ask questions) Translate the problem into a pictured equation(choose a variable, identify the operation, represent the equation in concrete, semi-concrete, or abstract method). Answer the problem, attending to relevant signs Review the solution, check your answer
Teaching Functional Math Concepts for Daily Living: calendars, clocks, writing checks, keeping banking accounts, budgeting and calculating household expenses, filling out tax forms, and paying bills.
Conclusion Many math strategies that are inclusive of special needs students are beneficial and critical for all students. Never assume a child already knows anything. Work from where they are.