how to establish and utilize long-term growth standards gary l. williamson, ph.d
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How to Establish and Utilize Long-Term Growth Standards Gary L. Williamson, Ph.D. Director of Accountability Operations, NCDPI. Academic Growth. Strategies. Normative approach Criterion Referenced approach Judgmental approach. Normative Approach to Establishing a Growth Standard. - PowerPoint PPT PresentationTRANSCRIPT
How to Establish and Utilize Long-Term Growth Standards
Gary L. Williamson, Ph.D.Director of Accountability Operations, NCDPI
Academic Growth
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Strategies
• Normative approach• Criterion Referenced approach• Judgmental approach
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Normative Approach to Establishing a Growth Standard
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Reading Growth Curves by Cohort Panel
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Grade
Le
xil
e M
ea
su
re
1995-2000 1996-2001 1997-2002 1998-2003 1999-2004 4
Measurement of Growth
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Criterion-Referenced Context for Growth
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Measurement of Growth
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Extrapolated Growth Curvewith Median Postsecondary Text Measures
UndergraduateAdmissionsand Military
Citizenship
Workplace
Community College
University
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Grade (0=K)
Lexil
e
E(L) = 700.0 + 118.7 (Grade-3) - 6.1 (Grade-3)2
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Judgmental Approach to Setting Growth
Standards
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How to Modify an Empirical Growth Standard to Reflect
Values
• Start with the State Average Growth Curve• Change the intercept• Change the initial velocity• Change the acceleration (deceleration)• Some Combination of the above
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S tart with a B as eline G rowth C urve
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G rade
Le
xil
e
Me
as
ure
NC ref
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LEXI
LE M
EASU
RE
GRADE
Alternate Paths to a Higher Twelfth-Grade Outcome
NC ref
intercept=820
University Text(1395L)
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LEXI
LE M
EASU
RE
GRADE
Alternate Paths to a Higher Twelfth-Grade Outcome
NC ref
intercept=820
velocity=132
University Text(1395L)
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LEX
ILE
MEA
SUR
E
GRADE
Alternate Paths to a Higher Twelfth-Grade Outcome
NC ref
intercept=820
velocity=132
deceleration=-9.2
University Text(1395L)
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400
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3 4 5 6 7 8 9 10 11 12
LEXI
LE M
EASU
RE
GRADE
Alternate Paths to a Higher Twelfth-Grade Outcome
NC ref
Combined strategy
University Text(1395L)
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Numerical Comparison of the Four Strategies
Parameters (in Lexiles)
NC HigherIntercept
Higher Velocity
Lower Deceleration
Combination Strategy
Intercept 700.0 820.0 700.0 700.0 775.0
Initial velocity 118.7 118.7 132.0 118.7 122.0
Deceleration -12.2 -12.2 -12.2 -9.2 -11.8
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Four Ways to Depict a Growth Standard
• Graph• Table• Equation• Multi-Level Model
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Graphical Presentation of a Growth Standard
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CDC Growth ChartsStature-for-Age
http://www.cdc.gov/growthcharts/data/set2/chart 07.pdf
http://www.cdc.gov/growthcharts/data/set2/chart 08.pdf
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1999-2004 NC Average Reading Growth Curve
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3 4 5 6 7 8
Grade
Le
xile
Me
as
ure
Average Quadratic Fit
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Tabular Presentation of a Growth Standard(s)
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Gains Between Each Pair of GradesNC Averages (N=67,908) By Grade
rounded to nearest Lexile 700 813 913 1001 1077 1141
Grade 3 4 5 6 7 8
3 113 213 301 377 441
4 100 189 265 329
5 88 164 228
6 76 140
7 64
8 0
change between adjacent grades; i.e., year-to-year change
change across 2-year spans
change across 3-year spans
change across 4-year spans
change across 5-year span from 3 to 8
A Growth Standard Presented in Tabular Form
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Growth Standard Presented as an Equation
2201000 tititi TTL
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Growth Standard Presented as an Equation
(Example)
)(1.6)(7.118700)( 2TTLE t
Note: Use T = (Grade – 3) when applying the model
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Growth Standard Presented as a Multi-
Level Model
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Level II
ii
ii
ii
r
r
r
2202
1101
0000
titiitiiiti eTTL 2210 Level I
Multilevel Model for Unconditional Quadratic Growth
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Growth Standard Presented as a Multi-Level Model(Combined Form)
)( 2210
2201000
titiitiii
tititi
eTrTrr
TTL
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North Carolina Longitudinal Data Analyses End-of-Grade Reading in Lexiles
Six-Wave Panel, Grades 3-8, 1999-2004 N=67,908
Unconditional Quadratic Growth Model Fixed Effect Estimate SE t prob Initial status, 00 700.023 0.850 823.808 <.0001
Instantaneous rate (grade 3), 10 118.727 0.334 355.442 <.0001
Curvature, 20 -6.093 0.060 -101.801 <.0001 Random Effect Variance SE z prob Level 1 (temporal variation) Within Student, tie 8371.113 26.229 319.158 <.0001 Level 2 (between students) Initial status, ir0 42,157.328 266.974 157.908 <.0001
Instantaneous rate (grade 3), ir1 1492.703 45.322 32.935 <.0001
Curvature, ir2 19.024 1.495 12.721 <.0001 28
Instructional Response to an Intercept
• Review curriculum for K-3• Instruction for diverse performance• Early intervention initiatives (e.g., Primary Reading
Program, Smart Start, More at Four, etc.)• Realize young children are growing fast• Don’t do things that hold them back!
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Instructional Response to Initial Velocity
• Scope and Sequence• Pace of Instruction• Long-Term view
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Instructional Response to Deceleration
• Vertical articulation of curriculum• Alignment of instruction• Keep the end in mind
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1999-2004 NC Average Reading Growth Curve
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3 4 5 6 7 8
Grade
Le
xile
Me
as
ure
Average Quadratic Fit
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Questions?
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