Number Conceptsand Automaticity:

Research in Mathematics and Technology

Arjan KhalsaConceptual Calculations, LLC

akhalsa@comcast.net

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

akhalsa@comcast.net

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

akhalsa@comcast.net