Number Concepts and Automaticity: Research in Mathematics and Technology

1. Number Conceptsand Automaticity: Research in Mathematics and Technology Arjan Khalsa Conceptual Calculations, LLC akhalsa@comcast.net

2. School District A Partnership to Raise Student Achievement Publisher Pacific Institutes for Research Research Team

3. Arjan Khalsa • Co-Founder, IntelliTools • Co-Founder, Conceptual Calculations Principle Investigator on Technology Research Projects: K-8 Reading K – 5 Math and Science Elementary School Teacher University Instructor UC Berkeley Faculty, Developing Science and Math Interactions Previously - Senior Curriculum Consultant, Cambium Learning Technologies akhalsa@comcast.net

4. And You! Interest in math What ages of students? What types of students? More?

5. The Grant • The Title: Number Concepts and Automaticity • The Source: National Institutes of Health • National Institute for Child Health and Human Development – NICHD • The Total Amount: $1.3 million • For product development, implementation, and research

6. The Software: Classroom Suite Direct instruction in a flexible tool environment for students in grades Pre K through 5. • Reading instruction aligned with national standards • Writing templates across many genres • Math instruction targeting number sense and automaticity • Creativity Tools for whole class instruction and student presentations • Early Learning activities for emergent learners

7. Research Principles • Number sense is a key for student success in math (Gersten July/August 2005; Hasselbring, Lott, and Zydney 2005) • Students need “direct retrieval” of math facts - automaticity (Geary, Hamson, and Hoard 2000) • Students benefit from an explicit computational hierarchy (Fuson 2004;Siegler and Shrager 1984; Siegler 1988; Siegler 1991; Siegler & Stern 1998) • Pedagogy should include specific conceptual models (Van De Walle 2001; Kilpatrick, J., Swafford, J., & Findell, B. (Eds.) 2001 ) • Software should incorporate universal design for learning (Woodward and Cuban 2003; Rose andMeyer 2002; Hitchcock and Stahl 2003)

8. The Promise Made to the School District • Extensive implementation support in elementary math • Careful and thorough assessments on over 600 students • Excellent, supplemental math software to support your curriculum • Clearly articulated results

9. The Intended Results • Higher math performance for students • Teachers perceiving enhanced ability to teach students • Teachers and district seeing the power of technology to raise performance in an affordable and manageable way • Research validation on: • Teaching math using these methods • The specific software program under development

10. Computational Hierarchy

11. Computational Hierarchy

12. Levels of Cognition I know this. I understand this. I can calculate this.

13. Our Goal

14. Software Demonstration

15. Learning Addition Models 4+5 9 + 6 Skip Counting Base Ten Blocks Base Ten Blocks Procedures Hundreds Grid Money Mult Arrays Mult. Number Line

16. Implementation Concept S●O●S Structure the Environment Optimize Time Support Student Learning

17. Implementation Procedures Planning meetings * Hands-on training * Co-teaching Data sharing * Newsletter

18. Research Team • Scott Baker, Ph. D. – Research Design • Ben Clarke, Ph. D. – Assessments and Observation • Carrie Hancock, Ph. D. – On-site Supervisor • John Seeley, Ph. D. – Data Analysis • Mari Strand Cary, Ph. D. – Data reporting

19. Research Questions • What is the impact of the NCA software on the mathematics achievement of students in general education 2nd grade classrooms? • What is the impact of the NCA software on students who are at-risk in mathematics? • Does the quality of teacher implementation of the NCA software mediate student mathematics achievement?

20. Research Design • Randomized Control Trial • Classrooms randomly assigned to treatment or control • Blocking on school • Matched pairs outside of school blocks on key variables (e.g. SES, ELL)

21. Research Design • Treatment: Three times per week for 20 minutes students use NCA software as part of their regular math instruction • 20 classrooms apx. 400 students • Control: Business as usual • 21 classrooms apx. 420 students • Study timeline: • August Pre-testing • September Intervention begins • February Intervention ends (apx. 20 weeks) • February Post-testing

22. Student Measures • Achievement measures: Goal is to test curriculum effectiveness • Automaticity and Fluency (Curriculum Based Measurement) • Given at pre and post test and three interim points • Proximal measure • Outcome Measure (Stanford Achievement Test – 10th Edition) • Given at post test • Distal measure • Perception measure • Student survey

23. Curriculum-Based Measures • Brief measures • Measures are of short duration and timed (2 minutes) • Assess key areas of mathematical knowledge • Basic Fact Addition • Basic Fact Subtraction • 2nd grade computation • Addition across 10 • Subtraction across 10

24. Teacher Measures • Demographics / Background Info. • Number of yrs. teaching kindergarten • Math courses taken • Perceptions of the NCA program and math instruction • Satisfaction with NCA program • Thoughts on PD provided

25. Fidelity Observations • Assess key elements of NCA implementation • Yes/no items on specific components that are part of the NCA implementation process • E.g. Lesson ends with summarizing activity • Quality ratings on overall implementation • E.g. Quality of teacher’s software expertise • Observations occurred 3 times during the course of the study

26. Data that is fully processed

27. Teacher Survey Data – Concerns

28. Teacher Survey Data – Effectiveness

29. Student Survey Data

30. Teacher and Student Survey Outcomes • Teachers had low to moderate concerns over implementing the software • Teachers had overall positive perceptions of the software being effective for students • Students had positive perceptions of using the software and the software helping them learn math.

31. Data that is still in process

32. Preliminary Results: Student Outcomes • Overall Student outcomes • How did the program work for all students? • 5 CMB measures • Pre- and post-tests • Basic facts, and “crossing ten” facts • At-risk student outcomes • Below the 25th and between the 20th and 40th percentile • SEI classrooms

33. Fidelity Outcomes • How does implementation moderate student outcomes (e.g. Do teachers that implement with high fidelity produce better outcomes?)? • Produced 3 indexes: Quality, Adherence, and Engagement • Are there positive trends favoring teachers who implemented with high fidelity? • Did students who were in classrooms where the teacher implemented with higher fidelity have better math outcomes?

34. Lessons Learned • Effective computer use takes time to achieve • Teachers change their teaching style when working with conceptual models • Second grade test scores are hard to influence

35. Next Steps – What You Can Do • Gain experience with Classroom Suite Version 4, Cambium Learning Technologies • The core team for this study is starting a new company: Conceptual Calculations, LLC • We are focusing on upper elementary math – Fractions • More presentations here at Bridges: • SOS Method for Implementing Software – videos and sample documents – lots of content • Fractions – the very latest in fractions research, fund thinking, and software innovations akhalsa@comcast.net