Early Learning in Mathematics A Formula for Success

1. Early Learning in MathematicsA Formula for Success Kathy Jungjohann University of Oregon Ben Clarke and Mari Strand Cary Pacific Institutes for Research October 2, 2009 The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Grant R305K040081 to Pacific Institutes for Research.  The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.

2. Agenda • Overview • The ELM Curriculum • Student and Teacher Measures • Classroom Observations • ELM in a multi-tier framework • Future Plans

3. High Level of Interest in Mathematics Achievement • National Research Council: Adding it Up • National Council Teachers of Mathematics: Focal Points • National Mathematics Advisory Report

4. Increasing recognition of the importance of mathematical knowledge • “For people to participate fully in society, they must know basic mathematics. Citizens who cannot reason mathematically are cut off from whole realms of human endeavor. Innumeracy deprives them not only of opportunity but also of competence in everyday tasks”. (Adding it Up, 2001)

5. State of Mathematics • Achievement on the NAEP trending upward for 4th/8th grade and steady for 12th grade • Large numbers of students still lacking proficient skills • Persistent income and ethnicity gaps • Drop in achievement at the time algebra instruction begins • TIMSS data indicate significant lower levels of achievement between US and other nations • Relative standing of US is more discrepant at higher grades • Jobs requiring intensive mathematics and science knowledge will outpace job growth 3:1 (STEM) and everyday work will require greater mathematical understanding

6. Meaningful Differences inMath Readiness • Long term trajectories are established as early as kindergarten (Morgan & Farkas, 2009) • 70% of students exiting K below the 10th %ile remain below the 10th %ile at the end of 5th grade • Middle and high SES children come to school with much more informal instruction in numbers and quantitative concepts (Griffin, 1994) • Children lacking these opportunities require formal explicit instruction to develop this understanding

7. What to do? Our approach • Develop a kindergarten core curriculum program (ELM) based on • Critical mathematics content • Research based instructional design principles. • Develop assessments tools • Use in screening and progress monitoring • Develop an observation system • Identify and study variables that impact the effectiveness of ELM • Conduct rigorous research • Randomized Control Trials

8. What is the immediate and long-term impact of the ELM curriculum on the mathematics achievement of students in general ed. kindergarten classrooms? Does the frequency and quality of teacher instructional practices affect student mathematics achievement? Research Questions

9. The Curriculum

10. Conceptual Framework for Early Learning in Mathematics Development of Mathematical Concepts Models Mathematics-related Vocabulary and Discourse Procedural Fluency

11. Mathematical Models and Multiple Representations of Number • Goal of ELM is to help children develop multiple representations of number through a focus on number sense, a construct that refers to a child’s fluidity and flexibility with using and manipulating numbers…to look at the world and make quantitative comparisons (Berch, 1998).

12. Number Models • Number line • Hundreds chart • Finger representations • Tally marks • Five and ten frames 1 2 3 4

13. Procedural Fluency and Automaticity in ELM • Automatic and effortless recall of basic math concepts frees up cognitive resources needed to focus on more complex problems • Multiple strand instruction provides daily practice across lessons • Children are given frequent opportunities to respond in whole class, partner, and written math practice activities • Teacher checks for understanding integrated into lessons

14. Kids are Teachers (KATs)

15. Math Related Vocabulary and Discourse • Basic concepts representing quantitative and relational concepts • Before, next, last, after, more, how much • Vocabulary unique to mathematics • Equal, triangle, measure, subtract, pattern • Opportunities to engage in classroom discourse using these words

16. Math Vocabulary and Discourse

17. ELM Instructional Content • National Math Advisory Panel (2008) recommends a focused, coherent progression of mathematics learning with emphasis on proficiency with key topics • ELM focuses on key strands rather than a broad array of mathematical content • Numbers and Operations • Geometry • Measurement • Vocabulary (NCTM Process Standard, 2000) NCTM Curriculum Focal Points for K (2006)

18. Structure of the Curriculum • Daily Calendar Lessons/Activities • 15 minutes daily, whole class “circle” time • Monthly booklets with objectives and application activities • 120 Core Lessons divided into 4 quarters • 30 minutes whole class instruction • 15 minutes teacher directed written work • End of quarter assessment of progress

19. ELM Objectives inNumbers and Operations • Proficiency in numeration to 30. • Count and identify numbers to 100. • Including skip counting by 5s and 10s • Use a variety of ways to model and represent numbers (fingers, tallies, ten frame, number line, hundreds chart, base ten blocks). • Use multiple strategies to solve simple addition and subtraction problems. • Develop an understandings of fractional unit “half.”

20. Introducing Numbers 0-12 through Teacher Big Book

21. Addition Stories – Lesson 57

22. Subtraction Stories – Lesson 69

23. ELM Objectives in Geometry • Identify and describe common 2 and 3 dimensional geometric shapes. • Sort and describe objects by shape, color, size, and other attributes. • Recognize and extend simple patterns.

24. Math Practice Examples

25. ELM Objectives in Measurement • Compare and order groups of objects with various strategies (visually, 1:1 correspondence, counting). • Identify objects and groups that are more, less, or equal. • Understand concepts of time, money, and measurement. • Measure in inches, tell time to the hour, count and compare coins. • Create and interpret graphs.

26. Quantity ComparisonLesson 14

27. Quantity ComparisonLesson 37

28. Quantity ComparisonLesson 68

29. Telling time to the hour3rd Quarter

30. Graphing

31. Frequent and High Quality Instructional Practices • Key math principles and concepts are explicitly modeled followed by student application and responsive teacher feedback. • Rich and frequent opportunities to engage in essential practice of key mathematical concepts. • Opportunities for students to verbalize essential mathematical concepts.

32. Effective Instructional Delivery Strategies • Explicit and Scaffolded Teaching • Teacher modeling, guided practice, independent • High student engagement • Multiple opportunities to respond • Teacher Feedback • Specific positive confirmations • Corrective feedback on errors • Distributed Practice and Review

33. Monitoring Progress with End of Quarter Assessment • Last lesson in every quarter has end of quarter check for progress • Set up activity centers for children to rotate through while you… • Call on children to work with you • Combination of independent (math practice) and individual teacher assessment

34. Does the ELM curriculum work?

35. Pilot ELM Study - Oregon • Three year research/development project • Curriculum Development 2004-2005 • Field Tested in 2005-2006 • Treatment (ELM) Classrooms: 5 • Control Classrooms: 4 • Field Tested in 2006-2007 • Treatment (ELM) Classrooms: 9 • Control Classrooms: 5

36. Results from Pilot Study were promising • Results were close to statistical significance at p =.057 • ELM accounted for 35% of the variance in SESAT scores and resulted in a meaningful positive effect d =.26 • Results did not vary based on at-risk status (i.e. at risk children showed the same gains)

37. Efficacy Studies • Study the effectiveness of the ELM curriculum • Study the added benefit of a small group component to the ELM curriculum • Continued development of assessment tools

38. Efficacy Study - Oregon • Two-year research project • ELM vs. Non-ELM • Completed 2008-09, analysis ongoing • 66 Classrooms (split evenly) • ELM + Small Group vs. ELM only • Ongoing (2009-10) • 66 Classrooms (split evenly)

39. Efficacy Study – Texas • Intended to test efficacy of ELM curriculum in different context • Two-year research project • ELM vs. Non-ELM • Ongoing 2009-10 • 66 Classrooms (split evenly) • ELM + Small Group vs. ELM only • Next year (2010-11) • 66 Classrooms (split evenly)

40. Measuring Effectiveness • Student assessments • Teacher measures • Observations of math time

41. Student assessments • Screening and Progress Monitoring (Early Numeracy CBM) • Outcome Measure (Test of Early Mathematics Ability)

42. Early Numeracy Curriculum Based Measures (EN-CBM) • 4 measures for K & 1st grade • Used with all students to screen for risk status • Measures are of short duration and timed (1 minute) • Assess key areas of mathematical knowledge • Potential for use in progress monitoring

43. EN-CBM (cont’d) • Oral Counting Students orally count for one minute. No student materials. • Number Identification

44. 9 3 4 1 5 10 9 4 __ 8 9 6 __ 8 3 4 __ EN-CBM (cont’d) • Quantity Discrimination • Missing Number

45. Teacher Measures • Demographics / Background Survey • Number of yrs. teaching kindergarten • Education degrees, certifications, and math coursework • Typical approach to math instruction • Content Knowledge Survey • Strong relationship between student achievement and teachers’ math knowledge • Designed by D. Ball and colleagues to measure the mathematical knowledge required for teaching

46. Instructional Logs Online submission, twice a month Capturing one lesson instructional time & format math strands & sub-strands specific skills & vocabulary Perceptions of the ELM program and math instruction Satisfaction with ELM program Thoughts on PD provided Teacher Measures (cont’d)

47. Observations • Conducted approximately 200 math lesson observations • 3 per year for all classrooms (fall, winter, and spring) • Duration ranged from 15 to 60 minutes • 20% were double-coded to ensure our observers were reliable

48. Observations (cont’d) • Goal 1: Capture mediating variables • Frequency of instructional interactions between teachers and students • (e.g., teacher models, practice opportunities) • Uses CATS observation instrument • Goal 2: Assess implementation fidelity

49. Coding of Academic Teacher-Student Interactions (CATS) • Relatively simple, easy to use tool • Code behaviors in a continual, serial fashion • Captures instructional context and instructional interactions

50. CATS Context Codes • Start and Stop Times • Number of Students / Whole Class • Type of Content • Number Operations • Geometry • Measurement • Calendar • Other (non-math) • Non-Academic Engagement (NAE)