1. Mathematics
Chapter 14

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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?

10. 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

11. 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?

12. 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

13. 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

14. 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?

15. 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

16. 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

17. 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?

18. 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 you can use to teach these concepts.