Math Strategies for Students with Disabilities

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Math Strategies for Students with Disabilities Powered By Docstoc
					            Research-Based Math
          Interventions for Students
               with Disabilities


                                    Melissa Storm
                                  The Access Center


Adapted from
Shanon D. Hardy, Ph.D. Presentation to Information Sharing Session
Access Center October, 2004
For Some Students:

     Math is right up there
     with snakes, public
     speaking, and heights.

     Burns, M. (1998). Math: Facing an
     American phobia. New York: Math
     Solutions Publications.
Overview
   Math Standards

   Interventions for Students with Disabilities

   Effective Teaching Practices

   California Algebra I Requirement
NCTM Goals (1989, 2000)
   Learning to value mathematics
   Becoming confident in their ability to do
    mathematics
   Becoming mathematical problem solvers
   Learning to communicate mathematically
   Learning to reason mathematically
Six NCTM General Principles
for School Mathematics
   Equity
   Curriculum
   Effective Teaching
   Learning
   Assessment
   Importance of Technology
Math Difficulties
   Memory
   Language and communication disorders
   Processing Difficulties
   Poor self-esteem
   Attention
   Organizational Skills
Interventions Found Effective
for Students with Disabilities
   Manipulatives
   Concrete-Semi-concrete-Abstract Instruction
   Mnemonics
   Meta-cognitive strategies: Self-monitoring,
    Self-Instruction
   Computer-Assisted Instruction
   Explicit Instruction
Research on Using
Manipulatives
   The use of concrete materials –
    • Can produce meaningful use of notational
        systems
    •   Can increase student concept development
    •   Is positively related to increases in student
        mathematics achievement
    •   Is positively related to improved attitudes
        towards mathematics.
Issues with Manipulatives
   Teachers may not trust the usefulness or efficiency of
    manipulative objects for higher-level algebra.

   Classroom limitations: Rigid schedules; movement of students
    and teachers; organization and supply of manipulatives.

   Dominance of textbook lessons

   Confidence of teachers in their mathematics knowledge
    compared to confidence in the use of manipulatives

   One study (Howard & Perry) secondary teachers used
    manipulatives once a month; primary teachers used daily.
Concrete-Semi-concrete-Abstract
(C-S-A) Phase of Instruction
    C-S-A is an instructional sequence supporting
    students’ understanding of mathematical concepts.

   In the concrete phase, students represent the problem with
    concrete objects - manipulatives.

   In the semi-concrete or representational phase, students draw
    or use pictorial representations of the quantities

   During the abstract phase of instruction, students involve
    numeric representations, instead of pictorial displays. C-S-A is
    often integrated with meta-cognitive instruction, i.e. mnemonics
Mnemonics Star Strategy
   Search the word problem
   Translate the word into an equation in
    picture form
   Answer the problem
   Review the solution

    (Maccini & Gagnon’s article, “Preparing Students with
    Disabilities for Algebra”)
Using the Star Strategy
   Search the word problem
    •   Students read the problem carefully,
    •   Regulate their thinking through self-questions, “What facts
        do I know? “What do I need to find?” and,
    •   Write down facts.
   Translate the words into an equation in picture form
    •   Students choose a variable for the unknown
    •   Identify the operation (s)
    •   Represent the problem using CONCRETE APPLICATION
        of CSA.
    •   Draw a picture of the representation (SEMI-CONCRETE)
    •   Write an algebraic equation (ABSTRACT application)
Using the Star Strategy
   Answer the Problem
    •   Use the appropriate operations (+, -, x or / )
    •   Use rules of solving simple equations
    •   Use rules to add/subtract positive and negative
        numbers
   Review the solution
    •   Reread the problem
    •   Check the reasonableness of the answer
    •   Check the answer.
Meta-cognitive Strategies
   Self-Instruction
Strategies include:
 Advanced or Graphic Organizers

 Support from structured worksheets and strategy
   instruction
 General guidelines to direct themselves:
   •   1. Re-read information for clarity;
   •   2. Diagram representation of the problems before solving
       them;
   •   3. Write algebraic equations for solving the problems.
Examples of
Self-Monitoring Strategies
   Cue cards to ask themselves while representing
    problems (card is eventually withdrawn)

   Structured worksheet to help organize their
    problem-solving activities that contained spaces for
    goals, unknowns, knowns, and visual
    representations.

   Questions as prompts for students while solving
    problems
               Structured Worksheet




Strategy questions                 Write a check after completing each task


Search the word problem
  Read the problem carefully                 ___________________


  Ask yourself questions:
     What facts do I know?           ___________________________
     What do I need to find?         ____________________________


   Write down facts            I know I have two rates_________________



  Adapted from Maccinni & Hughes, 2000
Computer Aided Instruction
   Programs for remediation and instruction
   Demonstration of concepts visually and
    with online manipulatives
   Games
   Spreadsheets
Use Explicit Instruction
   Begin lesson by
    • Tapping prior knowledge
    • Modeling how to solve problems while
        thinking aloud
    •   Prompting students when they needed
        assistance in the activity.
Empirically Validated Components of
Effective Instruction

   Teacher-based activities –
    • C-S-A (Manipulatives)
    • Direct/Explicit instruction
    • Teaching Prerequisite Skills
   Computer Assisted Instruction
   Strategy Instruction
    • Structured Worksheets; Diagramming
    • Graphic organizers
Reinforce strategy application through
corrective positive feedback

  • Examine students’ math work noting patterns and
    evidence of strategy.
  • Meet with students individually or in small groups.
  • Makes one positive statement about students’
    work or thinking.
  • Specify error patterns.
  • Demonstrate how to complete the problem using
    one of the strategies.
  • Provide an opportunity to practice the strategy on
    a similar problem type (guided practice).
  • End with a positive comment .
Recommendations and
Conclusions
   Provide instruction in basic arithmetic.

   Use think-aloud techniques

   Allot time to teach specific strategies.

   Provide guided practice before independent practice

   Provide a physical and pictorial model

   Relate to real-life events

   Let students practice, practice, practice
California Algebra I Requirement
 In 2000 legislation was enacted to
 require students – as a condition of
 receiving a high school diploma – to
 complete Algebra I.

 The requirement applied beginning with
 students graduating in 2003-04
Algebra I Requirement Waivers
   General waivers offered 2003-04
   A student with a disability who has an
    IEP can request a waiver if:
    • They are enrolled in Algebra
    • They are provided with accommodations as
        specified by the IEP
    •   They are still unable to pass the course
Algebra I Requirement and
Students with Disabilities
   Algebra I can and should be taught to all
    students, including students with
    disabilities
   May need more than one class
   May need practical ways of
    demonstrating skills and competencies
   May need supplementary materials
 For More Information:
http://www.cde.ca.gov/be/st/ss/mthalgebra1.asp
   Algebra content standards grades 8-12


http://www.cde.ca.gov/sp/se/fp/algebra1.asp
   Guidance and resources for teaching algebra concepts to
   students with disabilities

http://www.cde.ca.gov/re/lr/wr/specialedauthority.asp
  Information about the Algebra I waiver for students with disabilities

				
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