1. IES Practice Guide - Response to Intervention in Mathematics
Teaching Math to Low-Achieving Students
IES Practice Guide - Response to Intervention in Mathematics
Presented as a webinar for Educational Research Newsletter
October 21, 2009

2. Panelists Russell Gersten (Chair) Sybilla Beckman Ben Clarke
Anne Foegen
Laurel Marsh
Jon R. Star
Bradley Witzel

3. Search for Coherence
Panel works to develop 5 to 10 assertions that are:
Forceful and useful
And COHERENT
Do not encompass all things for all people
Do not read like a book chapter or article
Cover grades K-8
Challenges for the panel:
State of math research
Paucity of rigorous research on mathematics instruction
Jump start the process by using individuals with topical expertise and complementary views

4. The Research Evidence
The body of evidence considered in developing the recommendations included:
evaluations of mathematics interventions for low-performing students and students with learning disabilities.
The panel considered:
High quality experimental and quasi-experimental studies.
Also examined studies of screening and progress monitoring measures for recommendations relating to assessment.

5. Evidence Rating
Each recommendation receives a rating based on the strength of the research evidence.
Strong
Moderate
Low

6. Key Principles of RTI
Incorporate prevention and early intervention rather than waiting until grades 2-3
Include universal screening to identify student needs
Effective practices implemented class-wide in general education (primary intervention or Tier 1)
Successive levels of support increasing in intensity and specificity provided to students as needed (secondary/tertiary intervention) 6

7. Relevance for Mathematics
Early intervention in K-2 is important:
As with reading, students differ with a wide range of knowledge and skill involving number
Leveling the playing field is really important: kids at lowest percentile at end of K tend to remain there by grade 4. (Duncan et al, Morgan & Farkas)
Probably equally important to initiate preventative interventions so students succeed in algebra beginning in grades 4, 5 or 6

8. RTI Model
TIER I
TIER II
TIER III 8

9. TIER I: CORE CLASS INSTRUCTION
Tier I is defined differently by experts.
Only common feature:
Universal screening of all students
Other possible components:
Ongoing professional development for classroom teachers on how to use research
Differentiated instruction
High quality mathematics instruction
Scientifically based mathematics instruction
TIER I 9

10. Level of Scientific Evidence
Recommendation
Level of Scientific Evidence
Universal screening (Tier I)
Moderate
Focus instruction on whole number for grades k-5 and rational number for grades 6-8
Low
Systematic instruction
Strong
Solving word problems
Visual representations
Building fluency with basic arithmetic facts
Progress monitoring
Use of motivational strategies

11. Recommendation 1
Screen all students to identify those at risk for potential mathematics difficulties and provide interventions to students identified as at risk. Level of Evidence: Moderate

12. Evidence Technical evidence solid for early grades Content of Measures
Single aspect of number sense (e.g. strategic counting, magnitude comparison) for K/1
For grades 2 and up: Probably measures reflecting major state standards, National Mathematics Panel Benchmarks, Core Standards when they evolve etc. (A lot of work to do here)

13. Roadblocks
Resistance may be encountered in allocating time resources to the collection of screening data.
Suggested Approach: Use data collection teams to streamline the data collection and analysis process.
It takes a significant amount of time to establish district-specific benchmarks. By the time district-specific benchmarks are established, a year could pass before at-risk readers are identified and appropriate instructional interventions begin.

14. Roadblocks
Questions may arise about testing students who are “doing fine”.
Screening may identify students as at-risk who do not need services and miss students who do.
Screening may identify large numbers of students who need support beyond the current resources of the school or district.

15. TIER II: SMALL GROUP INTERVENTION
Tier II is individual or small-group intervention in addition to the time allotted for core mathematics instruction.
Tier II includes curriculum, strategies, and procedures designed to supplement, enhance, and support core classroom instruction.
Can backtrack and/or elaborate/reinforce classroom curriculum.
TIER II 15

16. Recommendation 2 What to Teach in Intervention
Instructional materials for students receiving interventions should focus in-depth on:
whole numbers in kindergarten through grade 5
rational numbers in grades 4 through 8
Applications to geometry and measurement
Level of Evidence: Low

17. Evidence
Consensus across mathematicians, professional organizations, and research panels
National Council Teachers of Mathematics (NCTM) and National Mathematics Advisory Panel (NMAP)
International comparisons
We made the leap to nature of intervention curricula………

18. Roadblocks
Concern about alignment between the intervention and the core classroom instruction.
Intervention materials may cover topics that are not essential to building basic competencies such as data/probability, measurement, and time.

19. Dilemmas in designing or evaluating intervention materials: Teaching fractions as part of a whole
Pros
easy to visualize – easier for students to understand the concept of 1 whole pizza
link to real world examples
e.g. ¼ of an apple

20. Teaching fractions as part of a whole
Cons
Pretty abstract for 3rd graders
Difficulty for students to shift to improper fractions >1 (e.g. 7/5)

21. Teaching fractions as part of a set
Problem X – “Fred has 16 marbles. He gave one fourth of those away…”
No sense of “betrayal” as with Problem X
The idea of 1 whole pizza versus 1 whole set of 20 pretzels is complex

22. Fractions Defined
Fractions arise naturally whenever we want to consider one or more parts of an object or quantity that is divided into pieces.
⅛ of a pizza
⅔ of the houses in the neighborhood
¾ of a cup or water
All of these examples use the word of, and all the fractions represent part of some object, collection of objects, or quantity.
Dilemma: how to convey this to kids
Precursor: teacher must understand all this so that she or he can teach it
Source: Beckmann, 2008 Mathematics for Elementary Teachers (2nd Ed.)

23. Converting Fractions to Word Problems
Fraction Problem : 1 and ¾ divided by ½

24. Incorrect Solution 1 and ¾ divided by ½ = 3 and ½
Incorrect translation of the fraction problem into a word problem:
There are 1 ¾ pizzas left. Tran eats half of the pizza that is left. How many pieces of pizza did Tran eat?

25. Questions

26. Recommendation 3 Level of Evidence: Strong
Instruction during the intervention should be systematic. This includes providing models of proficient problem-solving, verbalization of though processes, guided practice, corrective feedback, and frequent cumulative review.
Level of Evidence: Strong

27. Evidence Six randomized controlled trials met standards Key themes
Extensive practice with feedback
Let students provide rationale for their decisions
Instructors and fellow students model how approaches to problem solving

28. Roadblocks
Interventionists may not have training in implementing interventions with explicit instruction and may underestimate the amount of practice and review needed by tier 2 and 3 students.
Suggested Approach: Districts and schools should provide professional development that allows interventionists to observe, discuss, and practice lesson delivery. PD should emphasize the importance of practice and cumulative review.

29. Explicit instruction helps with understanding of fractions

30. Recommendation 4 Level of Evidence: Strong
Interventions should include instruction on solving word problems that is based on common underlying structures.
Level of Evidence: Strong

31. Suggestions
Teach students about the structure of various problem types, how to categorize problems, and how to determine appropriate solutions.

32. Change Problems (temporal)

33. Compare Problems (quantity)

34. Teach for transfer
Teach students to recognize the common underlying structure between familiar and unfamiliar problems and to transfer known solution methods from familiar to unfamiliar problems.

35. Solving similar problems that appear different
Difficulties encountered by some students
Extraneous information
Different wording
Even though the problems have a common underlying structure
Creates problems for any student who needs intervention
Fuchs et al. (2007)

36. Recommendation 5
Intervention materials should include opportunities for the student to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas.
Level of Evidence: Moderate

37. Strip diagrams can help students make sense of fractions.

38. Division with fractional answers (adapted from Witzel, 2004 : CRA)
Say, “How many sets of three go into 8?”
8 sticks
3 cups
Distribute sticks into cups evenly and ask, “Are there an equal number of sticks per cup? How many sticks per cup?”
2 sticks per cup with 2 more sticks that need to be divided into 3 cups.
2 sticks more sticks
cup cups

40. Suggestions
Use visual representations such as number lines, arrays, and strip diagrams.
If necessary consider expeditious use of concrete manipulatives before visual representations. The goal should be to move toward abstract understanding.

41. Roadblocks
Interventionists may not fully understand the mathematical ideas that underline representations.
Suggested Approach: Districts can partner with local universities, high school mathematics instructors, and math specialists to provide relevant mathematics instruction to interventionists. Professional development should focus on ways to explain concepts in terms students will understand.
Express that experienced teachers should teach new skills and volunteers should reinforce them.

42. Recommendation 6
Interventions at all grades should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts.
Level of Evidence: Moderate
Evidence: Seven studies met WWC standards or met with reservation

43. Suggestions
Provide 10 minutes per session of instruction to build quick retrieval of basic facts.
For student in K-2 grade explicitly teach strategies for efficient counting to improve the retrieval of math facts.
Teach students in grades 2-8 how to use their knowledge of math properties to derive facts in their heads.
Provide 10 minutes per session of instruction to build quick retrieval of basic facts. Consider the use of technology, flash cards, and other materials to facilitate automatic retrieval.

44. Questions

45. Recommendation 7
Monitor the progress of students receiving supplemental instruction and other students who are at risk
Level of evidence: Low

46. Evidence
Non-experimental studies demonstrating the technical adequacy of progress monitoring measures.
General outcome measures reflecting concepts and computation objectives for the grade level.
Greater evidence in elementary grades

47. Suggestions
Monitor the progress of tier 2, tier 3 and borderline tier 1 students at least once a month using grade appropriate general outcome measures.
Use curriculum-embedded assessments in intervention materials
Frequency of measures can vary - every day to once every week.
Use curriculum-embedded assessments in intervention materials to determine whether students are learning from the intervention. Measures can be used as frequently as every day or infrequently as once every week

48. Recommendation 8
Include motivational strategies in tier 2 and tier 3 interventions.
Level of Evidence: Low

49. Roadblocks
Rewards can reduce genuine interest in mathematics by directing student attention to gathering rewards rather than learning math.
Suggested Approach: Rewards have not shown to reduce intrinsic interest. As students become more successful rewards can be faded so student success becomes an intrinsic reward.

50. Resources
Center on Instruction (COI)
National Center for Learning Disabilities (NCLD) RTI Action Network
Glover, T. A., & Vaughn, S. (in press). The promise of response to intervention: Evaluating current science and practice. New York: Guilford Press.
WWC Practice Guide
Note on COI website: There is a RTI link on the left of the page under – Hot Topics. The hot topic takes you to 4 pages of resources.
Book will be out March 2010

51. For more information, contact Jo Kerr
Thank you
For more information, contact Jo Kerr