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. 77 + 4 174 66 -58 12 3 +3 0 4 -3 1 3 +2 1 5 -3 2 Common Errors

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.