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Math Interventions. By Brian Stagg March 7, 2002 CBC. Background. Current math curriculum is sequential Skills deficits become cumulative About 5% to 6% of students are Math LD 40% of 4 th graders scored Below Basic Level Many students struggle with math especially fluency.

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math interventions

Math Interventions

By Brian Stagg

March 7, 2002

CBC

background
Background
  • Current math curriculum is sequential
    • Skills deficits become cumulative
  • About 5% to 6% of students are Math LD
  • 40% of 4th graders scored Below Basic Level
    • Many students struggle with math especially fluency
common skills deficits
Common Skills Deficits
  • Mastery of Computational Skills
    • Rules
    • Basic Operations
    • Fluency
  • Mathematic Applications
common errors
77

+ 4

174

66

-58

12

3

+3

0

4

-3

1

3

+2

1

5

-3

2

Common Errors
errors cont
Errors cont.
  • Carrying and Borrowing
  • Computation and operations
  • Both effect fluency and accuracy
assessment
Assessment
  • Norm-referenced
    • WIAT
    • WJ-III
    • Stanford Diagnostic Mathematic Test (SDTM)
    • KeyMath-Revised
  • Weaknesses
    • General concepts & broad-based
    • Too few problems for proper assessment
assessment cbm
Assessment CBM
  • Assess a single skill
    • Two-digit addition with borrowing
  • Assess multiple skills
    • Two-digit addition and subtraction
  • Assesses fluency and accuracy
other assessments
Other Assessments
  • Error analysis: looking at a common error over many problems
    • CBM can be effective in determining EA
  • Clinical Interviews
    • CI entails asking the student to talk through the steps he or she used to a solve a problem
conducting cbm
Conducting CBM
  • Use district scope and sequence list of computational skills (appendix)
  • Construct 2 to 3 probe sheets with about 30 – 35 problems
  • Directions (see appendix)
scoring
Scoring
  • Digits correct
    • Add, Sub. Multiply is digits below the line

75

x26

450

150_

2850

scoring cont
Scoring cont.

75

x26

435

285_

3415

  • Division: GOOD LUCK (consult a book)
  • Percent Correct: divide # of problems correct by total # of problems
advantages of cbm
Advantages of CBM
  • Find systematic errors
  • Specific skills deficits
  • Chart progress
  • Development of short and long term goals
interventions
Interventions
  • Self-Monitoring
  • Cover,Copy, and Compare
  • Reciprocal Peer Tutoring (with parental involvement)
  • Increasing Fluency with timing and reinforcement
self monitoring
Self-Monitoring
  • Number of Problems completed and/or accuracy
    • Student charts progress on a graph/chart (example in appendix)
  • Cover, Copy and Compare
cover copy and compare
Cover Copy and Compare
  • A sheet with about 10 problems w/answers in left column and two other columns (copy and compare)
    • Student reads problem and answer
    • Covers problem
    • Then copies the problem and answer
    • Uncover and compare answers
  • Best for basic math facts
reciprocal peer tutoring rpt
Reciprocal Peer Tutoring (RPT)
  • “Combines self-management techniques and group contingencies within a peer tutoring format” (Rathvon, 1999; pp. 195).
  • Resources
    • Paired-partners
    • Flash cards w/problems and computational steps
    • Problem drill sheets
    • Reinforcement menu
    • 30 minutes
    • 4 section paper w/ ‘Try 1’ ‘try 2’ ‘help’ and ‘try 3’
rpt cont
RPT cont.
  • Procedure
    • Partners set a team goal and individual goal for number of problems answered correct
    • One student act as teacher and gives flashcards
    • The other answers the problems on 4-section paper
      • Try 1: 1st attempt
      • Try 2: ‘teacher’ prompt from card
      • Help: ‘teacher’ models with instruction
      • Try 3: retry
    • Switch roles after 10 minutes
    • After 2nd set each person completes a problem drill sheet
    • If goals are met record on score card, and after 5 wins receive reinforcement item
rpt with parental involvement
RPT with Parental Involvement
  • Same as RPT but with a parent component
  • Procedure
    • Inform parents of the program with a letter (Rathvon, 1999. pp. 202-203)
    • Same procedure but after 3 wins send a parent notification to reward the child
      • One variation is that the parents would return the note indicating the reinforcement given
  • RPT allows you chart progress and evaluate instruction
other interventions to increase fluency and accuracy
Other Interventions to Increase Fluency and Accuracy
  • Other types of progress charts and reinforcement schedules
    • % completed in time limit
    • % accurate in time limit
    • Homework completion
      • Reinforcement schedules at home or school
alternative interventions
Alternative Interventions
  • Cognitive Learning Strategies (Bruning, Schraw, & Ronning, 1999)
  • Focus on processes, structures and decisions, not on answers
  • Problem-solving approaches
  • Applications
considerations for interventions
Considerations for Interventions
  • Do not be misguided or misdirected
  • Prevent habituating incorrect routines
  • Guarantee success (more correct answers)
  • Offer alternative ways to display proficiency in math
    • (Cawley & Parmar, 1991)
considerations for cbc
Considerations for CBC
  • Intervention at school and reinforcement at home
  • CBM measures
    • Assess
    • Chart progress
    • Data collection
  • Parents practice and model homework with the child
  • Peer tutoring
references
References
  • Bruning, R. H., Schraw, G. J., & Ronning, R. R. (1999). Cognitive Psychology and Instruction. Upper Saddle River, NJ: Prentice-Hall.
  • Cawley, J. F., & Parmar, R. S. (1991). Maximizing mathematics success in the regular classroom. In G. Stoner, M. R. Shinn, & H. M. Walker (Eds.), Interventions for achievement and behavior problems. Silver Spring, MD: NASP.
  • Fleischner, J. E., & Manheimer, M. A. (1997). Math interventions for students with learning disabilities: Myths and realities. School Psychology Review, 26, 397-413.
  • Rathvon, N. (1999). Effective school interventions: Strategies for enhancing academic achievement and social competence. New York: Guilford Press.
  • Shapiro, E. S. (1996). Academic skills problems: Direct assessment and intervention. New York: Guilford Press.
  • Shapiro, E. S., & Kratochwill, T. R. (2000). Conducting school-based assessments of child and adolescent behavior. New York: Guilford Press.