Transcript Number Concepts and Automaticity

Number Concepts
and Automaticity:
Research in Mathematics and
Technology
Arjan Khalsa
Conceptual Calculations, LLC
[email protected]
School
District
A Partnership to Raise
Student Achievement
Pacific Institutes for
Research
Research
Team
Publisher
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
[email protected]
3
And You!
Interest in math
What ages of students?
What types of students?
More?
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
5
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
6
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)
7
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
8
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
9
Computational Hierarchy
10
Computational Hierarchy
11
Levels of Cognition
Direct
Retrieval
400+1
Conceptual
400 ÷ 99
I understand this.
I know this.
Procedural
413 ÷ 27
I can calculate this.
12
Our Goal
Raise
Conceptual
Understanding
Increase
Automaticity
Build
Procedural
Skills
13
Software Demonstration
14
Learning
Addition
Models
4+5
Base
Ten
Blocks
Skip
Counting
9+6
Base Ten
Blocks
Procedures
Hundreds
Grid
Money
Mult
Arrays
Mult.
Number
Line
Implementation Concept
S●O●S
Structure the Environment
Optimize Time
Support Student Learning
16
Implementation Procedures
Planning meetings * Hands-on training * Co-teaching
Data sharing * Newsletter
17
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


Control: Business as usual


20 classrooms apx. 400 students
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)



Outcome Measure (Stanford Achievement Test – 10th Edition)



Given at pre and post test and three interim points
Proximal measure
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


Quality ratings on overall implementation


E.g. Lesson ends with summarizing activity
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 face
4 = 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?
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
34
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
[email protected]
35