1. Mathematics and Interventions for Learning Disabled Students Madhavi Jayanthi

2. Teaching Mathematics to Students With Learning Disabilities: A Meta-Analysis Russell Gersten David Chard Madhavi Jayanthi Scott Baker Paul Morphy Jonathan Flojo

3. A synthesis of Intervention research on instructional approaches that enhance mathematics proficiency for students with learning disabilities

4. Method  Reviewed studies from January 1971 to August 2007 Limited to RCTs and QEDs Defined LD sample as - separate outcome data for LD sample OR all LD OR over 50% of sample was LD Criteria similar to What Works Clearinghouse except no specific criteria on differential attrition/total attrition  Total 42 studies

5. Categories for Analysis  Approaches to instruction and/or curriculum design  Providing feedback to teachers on students’ mathematics performance  Providing data and feedback to students with LD on their mathematics performance  Peer-assisted mathematics instruction

6. Data Analysis  Determined effectiveness of each variable in isolation Hedges g (Mean weighted effect size with significance tests) Homogeneity statistic Q  Determined effectiveness in relative terms Series of Hierarchical Multiple Regressions Suggests combination of variables that explain outcomes Takes into account intercorrelations between some of the variables

7. Explicit Instruction  Teachers provide clear models with think alouds  Teachers use an array of carefully sequenced examples  Students practice newly learned strategies and skills.  Students have opportunities to think aloud (i.e., talk through the decisions they make and the steps they take)  Students are provided with extensive corrective feedback  Teachers include cummulative review

8. Explicit Instruction  Step-by-step demonstration of a plan (strategy) for solving the problem  Students use the same procedure/steps as teacher demonstrates (Note: Somewhat different than the definition of National Mathematics Advisory Panel) Did not include heuristics

9. Explicit Instruction  Produced consistent effects (n=11 studies) ES = 1.22 (p<.001) Q statistic = 41.68 (p<.001)  Contributes unique variance Effect increase of 0.53 (p<.05) above the average adjusted effect Note: Outcome measures often closely aligned to the strategy taught

10. Visual Representations  Use of visuals is beneficial (n=12) ES =.47 (p<.001) Q statistic = 14.13 (ns)  More effective when combined with other instructional components  Specificity of the visual matters

11. Explicitly Teaching a Visualizing Strategy  Read the problem  Draw individual circles for which you will find half  Draw a rectangle divided in half, creating two boxes  Cross out the first circle and draw it in the left box; cross out the second circle and draw it in the right box.Continue until you run out of circles. If you end up with one extra circle, draw a vertical line down the middle of the remaining circle and draw half a circle in the left box and half the circle in the right box.  Count circles in each box to make sure the same number of circles are in each box Source: Owen and Fuchs, 2002

12. Susan had eight marbles. She gave half the marbles to Becky. How many marbles did she give Becky? Source: Owen & Fuchs, 2002

13. Using Visuals  Occasional and unsystematic exposure is not helpful  Systematically teach students how to use visuals to understand abstract mathematical concepts  Transition back to abstract representations  Use concrete objects judiciously even in higher grades

14. An Effective Instructional Package  Teach explicitly, That there are several types of word problems Determine type of problem based on underlying mathematical structure Use visual to represent the critical information and mathematical procedures Translate diagram into a math sentence and solve Practice using multiple examples  Xin, Jitendra, and Deatline-Buchman (2005) (ES = 2.15)

15. Verbalizations Sequence, Range of Examples Effective when tested in isolation, but did not contribute unique variance in multiple regressions  Verbalizations (n=8 studies) ES = 1.04 (p<.001) Q statistic = 53.39 (p<.001)  Sequence and/or range of examples (n=9 studies) ES = 0.82 (p<.001) Q statistic = 19.78 (p<.01)

16. Examples of Word Problems Susan wants to buy 1 CD for each of her 10 friends. Each packet contains 6 CDs. How many packets does Susan have to buy to give 1 CD to each of her friends? Susan wants to buy 1 CD for each of her 10 friends. Becky wants to buy 5 CDs. Each bag contains 6 CDs. How many bags does Susan have to buy to give 1 CD to each of her friends?

17. Use of Heuristics  Generic approach for solving a problem  Not problem specific  Multiple heuristics expose students to multiple ways of solving a problem

18. Use of Heuristics  Appears to be beneficial (n=4) ES = 1.56 (p<.001) Q statistic = 9.10 (p<.05) Effect size increase of 1.21(p<.001) above the average adjusted effect  Verbalizations and reflections?  Cognitively demanding?

19. Providing Feedback to Teachers  Providing teacher feedback is helpful (n=7)  ES = 0.21 (p<.05)  Q statistic = 0.32 (ns)  Providing teacher feedback plus options is more helpful (n=5)  ES = 0.34 (p<.10)  Q statistic = 1.01 (ns)  More effective with special educators though rarely studied for general education teachers

20. Providing Feedback to Students  Appears to be beneficial (n=7) ES = 0.23 (p<.01) Q statistic = 3.60 (ns) Feedback on effort appears to help  However, feedback with goal setting does not appear to be beneficial (n=5) ES = 0.17 Q statistic = 12.67 (p<.01)

21. Peer-Assisted  Peer-assisted within-class does not appear to be effective (n=6) ES = 0.14 (ns) Q statistic = 2.66 (ns)  Cross-age appears to be effective (n=2) ES = 1.02; (p<.001) Q statistic = 0.68 (ns)  Not explicit enough?  Not enough discourse?

22. For more information http://www.inresg.org Gersten, R., Chard, D., Jayanthi, M., Baker, S., Morphy, P., & Flojo, J. (2009). A Meta-analysis of Mathematics Instructional Interventions for Students with Learning Disabilities: A Technical Report. Los Alamitos, CA: Instructional Research Group.