Contemporary Research on Tier 2 Intervention: K-2 Number Sense

1. Contemporary Research on Tier 2 Intervention: K-2 Number Sense Diane P. Bryant, Ph.D. The University of Texas at Austin © 2008 Meadows Center

2. Overview • Number Sense • 3-Tier Model: Tier 2 • Tier 2 Intervention Boosters © 2008 Meadows Center

3. Number Sense • . . . Core number sense developed informally prior to starting school: “an ability to immediately identify the numerical value associated with small quantities, a facility with basic counting skills, and a proficiency in approximating the magnitudes of small numbers of objects and simple numerical operations (NMAP, 2008, p. 27). • . . . More advanced type of number sense developed through formal instruction: “understanding of place value, of how whole numbers can be composed and decomposed, and the meaning of the basic arithmetic operations. . . .understanding the commutative, associative, and distributive properties . . .” (NMAP, 2008, p. 27) © 2008 Meadows Center

4. Number Sense • . . . involves representing numbers in many ways, recognizing numerical patterns [algebraic reasoning], and understanding numerical quantities • . . . includes abilities related to subitizing, counting, number knowledge [e.g., numerical sequences, numerical magnitude comparisons] arithmetic combinations, and story problems (Berch, 2005; Jordan et al., 2006). • . . . is highly correlated with first-grade mathematics achievement (Jordan, Kaplan, Locuniak, & Ramineni, 2007; Locuniak & Jordan, 2008). © 2008 Meadows Center

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6. RTI: Tier 2: Intervention Secondary Prevention Focus For students identified with mathematics difficulties Instruction Standard research-validated intervention protocol Grouping Small group instruction (1:3, 1:4, or 1:5) 25 - 30 minutes per day/several days per week in addition to 60 - 90 minutes of mathematics instruction Time Assessment Ongoing progress monitoring during intervention Interventionist Personnel determined by the school (e.g., classroom teacher, mathematics interventionist) Fidelity Observations conducted on fidelity of implementation © 2008 Meadows Center

7. Instruction CR/VR/AR Tier 2 Types of Boosters Fluency Building AR • Concrete Representation • Visual/Pictorial Representation • Abstract/Numeric Representation Skill Building/ Practice PR/VR/AR T E K S Lower Proficiency Levels Higher © 2008 Meadows Center

8. Tier 2: Number Sense Instructional Content (Examples) Subitizing (dot patterns) Recognize number of dots quickly Number Knowledge and Relationships Count: Rote, Counting Up/Back, Skip (2, 5, 10) Read & write numbers: 0 - 20 (K); 0 – 99 (1st); 0 – 999 (2nd) Compare & order numbers Identify numbers that are one and two more than/less than Anchor Numbers to 5 & 10 frames © 2008 Meadows Center

9. Tier 2: Number Sense Instructional Content (Examples) Relationships to 10/Base 10/Place Value Use models to represent numbers: groups of tens and ones (1st grade); groups of hundreds, tens, and ones (2nd grade) Create equivalent representations of numbers Compose and decompose numbers - multi-digit numbers Solve addition & subtraction problems © 2008 Meadows Center

10. Tier 2: Number Sense Instructional Content (Examples) Addition & Subtraction Combinations Identify and apply properties (e.g., commutative, inverse relationship between addition and subtraction) Develop and apply strategies to solve facts (e.g., count on [+ 0, + 1, + 2], doubles, doubles +1, make 10 + more; count back [-0, -1, -2, -3] Word Problem Solving Solve different types of problems [part-part-whole, joining, separating, comparing, two step problems] Include extraneous information © 2008 Meadows Center

11. Features of Tier 2 Intervention • Instructional Routine: modeling, modeled practice, guided practice, independent practice (daily progress monitoring) • Lesson Design: mixed instructional content; scripted interventions; explicit, strategic, “think aloud” instruction; error correction; multiple opportunities to respond; pacing; timer • Daily components: warm-up (review), 2 lessons, cool down • Instructional Content: focuses on difficult numbers; vocabulary; (e.g., greater than/less than); procedural and conceptual knowledge; TEKS: number, operation, quantitative reasoning; patterns/relationships/algebraic thinking; problem solving; other TEKS incorporated into instructional design © 2008 Meadows Center

12. Features of Tier 2Intervention • Grouping: homogeneous grouping with 3 - 5 students per group • Duration: daily sessions for 30 minutes; PM 5th day • Representations: physical (concrete), visual (pictorial), • abstract (numbers/symbols) • Materials: number charts (100s), 5- and 10-frames, counters, cubes, number lines, base-ten materials, dot cards, fact cards, place value cards • Progress monitoring: daily checks (independent practice); aim checks • Stretch Your Skills Bubble answers option for WPS © 2008 Meadows Center

13. Results: Tier 2 Intervention • 2007-2008 [3-Tier Schools]: Based on Spring assessment results with below the 25th percentile as the cut score for Tier 2 • Kindergarten: • 41% qualified to exit Tier 2 • 25% qualified for Tier 2 • 34% qualified for Tier 3 (below the 10th percentile) • First Grade: • 52% qualified to exit Tier 2 • 24% qualified for Tier 2 • 24% qualified for Tier 3 • Second Grade: • 49% qualified to exit Tier 2 • 24% qualified for Tier 2 • 27% qualified for Tier 3 © 2008 Meadows Center

14. Results: 1st GradeExample Effect Sizes .51 TEMI-PM .20 TEMI-O .3 - .5 medium .0 - .2 small (Cohen, 1988) © 2008 Meadows Center