Math Interventions

1
Math Interventions

• By Brian Stagg
• March 7, 2002
• CBC

2
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

3
Common Skills Deficits

• Mastery of Computational Skills
• Rules
• Basic Operations
• Fluency
• Mathematic Applications

4
Common Errors

• 77
• 4
• 174
• 66
• -58
• 12

• 3
• 3
• 0
• 4
• -3
• 1
• 3
• 2
• 1
• 5
• -3
• 2

5
Errors cont.

• Carrying and Borrowing
• Computation and operations
• Both effect fluency and accuracy

6
Assessment

• Norm-referenced
• WIAT
• WJ-III
• Stanford Diagnostic Mathematic Test (SDTM)
• KeyMath-Revised
• Weaknesses
• General concepts broad-based
• Too few problems for proper assessment

7
Assessment CBM

• Assess a single skill
• Two-digit addition with borrowing
• Assess multiple skills
• Two-digit addition and subtraction
• Assesses fluency and accuracy

8
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

9
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)

10
Scoring

• Digits correct
• Add, Sub. Multiply is digits below the line
• 75
• x26
• 450
• 150_
• 2850

11
Scoring cont.

• 75
• x26
• 435
• 285_
• 3415
• Division GOOD LUCK (consult a book)
• Percent Correct divide of problems correct by
  total of problems

12
Advantages of CBM

• Find systematic errors
• Specific skills deficits
• Chart progress
• Development of short and long term goals

13
Interventions

• Self-Monitoring
• Cover,Copy, and Compare
• Reciprocal Peer Tutoring (with parental
  involvement)
• Increasing Fluency with timing and reinforcement

14
Self-Monitoring

• Number of Problems completed and/or accuracy
• Student charts progress on a graph/chart (example
  in appendix)
• Cover, Copy and Compare

15
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

16
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

17
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

18
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

19
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

20
Alternative Interventions

• Cognitive Learning Strategies (Bruning, Schraw,
  Ronning, 1999)
• Focus on processes, structures and decisions, not
  on answers
• Problem-solving approaches
• Applications

21
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)

22
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

23
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.