Number Conceptsand Automaticity:
Research in Mathematics and Technology
Arjan KhalsaConceptual Calculations, LLC
Pacific Institutes for Research
A Partnership to Raise Student Achievement
School District
Research Team
Publisher
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Arjan Khalsa
Co-Founder, IntelliToolsCo-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
And You!
Interest in math
What ages of students?
What types of students?
More?
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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
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The Software: Classroom Suite
Direct instruction in a flexible tool environment for students in grades Pre K through 5.
Reading instruction aligned with national standardsWriting templates across many genresMath instruction targeting number sense and automaticityCreativity Tools for whole class instruction and student presentationsEarly Learning activities for emergent learners
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Research Principles
1. Number sense is a key for student success in math(Gersten July/August 2005; Hasselbring, Lott, and Zydney 2005)
2. Students need “direct retrieval” of math facts - automaticity(Geary, Hamson, and Hoard 2000)
3. Students benefit from an explicit computational hierarchy(Fuson 2004;Siegler and Shrager 1984; Siegler 1988; Siegler 1991; Siegler & Stern
1998)
4. Pedagogy should include specific conceptual models(Van De Walle 2001; Kilpatrick, J., Swafford, J., & Findell, B. (Eds.) 2001 )
5. Software should incorporate universal design for learning(Woodward and Cuban 2003; Rose and
Meyer 2002; Hitchcock and Stahl 2003)
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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
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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
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Computational Hierarchy
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Computational Hierarchy
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Levels of Cognition
I know this.
I understand this. I can calculate this.
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Our Goal
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Software Demonstration
Learning Addition Models
4+5 9 + 6Skip
Counting
Base Ten
Blocks
Base Ten Blocks
Procedures
HundredsGrid
Money
MultArrays
Mult.Number
Line
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Implementation Concept
S●O●S
Structure the Environment
Optimize Time
Support Student Learning
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Implementation Procedures
Planning meetings * Hands-on training * Co-teachingData sharing * Newsletter
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
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?
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)
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
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
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
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
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
Data that is fully processed
Teacher Survey Data – Concerns
1= not true now; 7=very true now
Question PRE Mean POST Mean
I am concerned about how the software affects students.
3.58(range 1-7, n=12,
SD=1.78)
2.93(range 1-6, n=15,
SD=1.7)
I am concerned about my ability to manage all that the software requires.
3.31(range 1-7, n=13,
SD=1.89)
2.93(range 1-7, n=14,
SD=2.24)
I am concerned about time spent working with nonacademic problems related to the software.
3.25(range 1-7, n=12,
SD=1.87)
3.43(range 1-7, n=14,
SD=2.14)
Teacher Survey Data – Effectiveness
1 = not true now 7 = very true now
Question POST Mean
I believe the software is effective.
5.00(range 3-7 , n=15, SD=1.25)
I believe the software is effective for at-risk students.
5.00(range 3-7, n=15, SD=1.31)
I will continue to use the software next year.
5.08(range 4-7, n=15, SD=1.12)
Student Survey Data
1 = frown face4 = very happy face
Question Mean
Classroom Suite helped me to learn math.
3.49 (SD=.74)
I can add better than I did before Classroom Suite.
3.38 (SD=.82)
Classroom Suite was fun to use. 3.36 (SD=.85)
Classroom Suite was easy to use.
3.26 (SD=.90)
Subtraction was easier after using Classroom Suite.
2.95 (SD=1.08)
Classroom Suite made me faster with math problems.
3.44 (SD=.88)
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.
Data that is still in process
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
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?
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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
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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