Graphing, Calculating, and
Interpreting Rate of
Improvement
Caitlin S. Flinn, Ed.S., N.C.S.P.
Andrew E. McCrea, M.S., N.C.S.P.
NASP Convention
March 3, 2010
Objectives
There needs to be a standardized
procedure for calculating RoI
 We’re proposing a method using Simple
Linear Regression

Overview




Importance of RoI
RoI Research
A Need for
Consistency
Calculating RoI


Individual Student
Graphs
Programming Excel



Decision Making
Grounding the Data
Interpreting Growth




Individual Student
Student Groups
Considerations
Resources
Importance of Graphs

Vogel, Dickson, & Lehman, 1990

Speeches that included visuals, especially in
color, improved:
 Immediate
recall by 8.5%
 Delayed recall (3 days) by 10.1%
Importance of Graphs
“Seeing is believing.”
 Useful for communicating large amounts
of information quickly
 “A picture is worth a thousand words.”
 Transcends language barriers (Karwowski,
2006)
 Responsibility for accurate graphical
representations of data

Skills Typically Graphed

Reading



Oral Reading Fluency (ORF)
Word Use Fluency (WUF)
Reading Comprehension








Math Computation
Math Facts
Early Numeracy
Early Literacy Skills






Math
MAZE
Retell Fluency



Initial Sound Fluency (ISF)
Letter Naming Fluency (LNF)
Letter Sound Fluency (LSF)
Phoneme Segmentation Fluency
(PSF)
Nonsense Word Fluency (NWF)
Spelling
Written Expression
Behavior


Oral Counting
Missing Number
Number Identification
Quantity
Discrimination
Importance of RoI
Multi-tiered model
 Progress monitoring
 Data for decision-making
 Goal setting (Shapiro, 2008)

Importance of RoI
Visual inspection of slope
 Multiple interpretations
 Instructional services
 Need for explicit guidelines

RoI Research

Deno, 1985

Curriculum-based measurement
 General
outcome measures
 Short
 Standardized
 Repeatable
 Sensitive
to change
RoI Research

Fuchs & Fuchs, 1998

Hallmark components of Response to
Intervention
 Ongoing
formative assessment
 Identifying non-responding students
 Treatment fidelity of instruction

Dual discrepancy model
 One
standard deviation from typically performing
peers in level and rate
RoI Research

Ardoin & Christ, 2008
Slope for benchmarks (3x per year)
 More growth from fall to winter than winter to
spring
 Might be helpful to use RoI for fall to winter
 And a separate RoI for winter to spring

RoI Research

Fuchs, Fuchs, Walz, & Germann, 1993
Typical weekly growth rates
 Needed growth

 1.5

to 2.0 times typical slope to close gap
Example
Bob is below benchmark on ORF
 Typical slope is 1 wcpm per week growth
 Bob would need slope of 1.5 to 2 to close gap
in a reasonable amount of time

RoI Research

Deno, Fuchs, Marston, & Shin, 2001

Slope of frequently non-responsive children
approximated slope of children already
identified as having a specific learning
disability
RoI Research

Algebraic term: Slope of a line
Vertical change over the horizontal change
 Rise over run
 m = (y2 - y1) / (x2 - x1)
 Describes the steepness of a line (Gall & Gall,
2007)

RoI Research

Finding a student’s RoI = finding the slope
of a line


Using two data points on that line
Finding the line itself
Linear regression
 Ordinary Least Squares

RoI Research

Gall & Gall, 2007


10 data points are a minimum requirement for
a reliable trendline
How does that affect the frequency of
administering progress monitoring probes?
RoI Research
Using RoI for instructional decisions is not
a perfect process
 Research is currently looking to address
sources of error:

Christ, 2006 – standard error of measurement
for slope
 Ardoin & Christ, 2009 – passage difficulty and
variability
 Jenkin, Graff, & Miglioretti, 2009 – frequency
of progress monitoring

RoI Research

Questions yet to be empirically answered
What parameters of RoI indicate a lack of RtI?
 How does standard error of measurement
play into using RoI for instructional decision
making?
 How does RoI vary between standard
protocol interventions?
 How does this apply to non-English speaking
populations?

How is RoI Calculated?
Which way is best?
Multiple Methods for
Calculating Growth
“Eye ball” Approach
 Last point minus First point Approach
 Split Middle Approach
 Linear Regression Approach

Eye Ball
20
19
18
17
16
14
14
14
12
11
10
10
8
8
7
6
4
2
0
1
2
3
4
5
6
7
8
Last minus First
20
14 - 8 = 6; 6/ 8 weeks = 0.75 words per week
19
18
17
16
14
14
14
12
11
10
10
8
8
7
6
4
2
0
1
2
3
4
5
6
7
8
Split Middle
18
14.5-10.5 = 4; 4/8 weeks = 0.5 words per week
16
14.5
14
12
10.5
10
8
6
4
2
0
1
2
3
4
5
6
7
8
9
10
Linear Regression
20
18
16
19
y = 1.1429x + 7.3571
1.1 Words Per Week
17
14
14
14
12
11
10
10
8
8
7
6
4
2
0
1
2
3
4
5
6
7
8
RoI Consistency?
Eye Ball
???
Last minus First
0.75
Split Middle*
0.50
Linear
Regression
1.10
RoI Consistency?


If we are not all using the same model to
compute RoI, we continue to have the same
problems as past models, where under one
approach a student meets SLD criteria, but
under a different approach, the student does not.
Hypothetically, if the RoI cut-off was 0.65 or
0.95, different approaches would come to
different conclusions on the same student.
Technical Adequacy

Without a consensus on how to compute
RoI, we risk falling short of having
technical adequacy within our model.
So, Which RoI Method is Best?
Literature shows that Linear
Regression is Best Practice


Student’s daily test scores…were entered into a
computer program…The data analysis program
generated slopes of improvement for each level
using and Ordinary-Least Squares procedure
(Hayes, 1973) and the line of best fit.
This procedure has been demonstrated to
represent CBM achievement data validly within
individual treatment phases (Marston, 1988;
Shinn, Good, & Stein, in press; Stein, 1987).
Shinn, Gleason, & Tindal, 1989
Growth (RoI) Research
using Linear Regression




Christ, T. J. (2006). Short-term estimates of growth using
curriculum based measurement of oral reading fluency:
Estimating standard error of the slope to construct confidence
intervals. School Psychology Review, 35, 128-133.
Deno, S. L., Fuchs, L. S., Marston, D., & Shin, J. (2001). Using
curriculum based measurement to establish growth standards
for students with learning disabilities. School Psychology
Review, 30, 507-524.
Good, R. H. (1990). Forecasting accuracy of slope estimates for
reading curriculum based measurement: Empirical evidence.
Behavioral Assessment, 12, 179-193.
Fuchs, L. S., Fuchs, D., Hamlett, C. L., Walz, L. & Germann, G.
(1993). Formative evaluation of academic progress: How much
growth can we expect? School Psychology Review, 22, 27-48.
Growth (RoI) Research
using Linear Regression



Jenkins, J. R., Graff, J. J., & Miglioretti, D.L. (2009).
Estimating reading growth using intermittent CBM
progress monitoring. Exceptional Children, 75, 151-163.
Shinn, M. R., Gleason, M. M., & Tindal, G. (1989).
Varying the difficulty of testing materials: Implications for
curriculum-based measurement. The Journal of Special
Education, 23, 223-233.
Shinn, M. R., Good, R. H., & Stein, S. (1989).
Summarizing trend in student achievement: A
comparison of methods. School Psychology Review, 18,
356-370.
So, Why Are There So Many
Other RoI Models?
Ease of application
 How many of us want to calculate OLS
Linear Regression formulas (or even
remember how)?

An Easy and
Applicable Solution
Get Out Your Laptops!
Or Kindly Look Over Your
Neighbor’s Shoulder!
I love
ROI
Open Microsoft Excel
Microsoft Office 2003 for PCs
 Microsoft Office 2007 for PCs
 Microsoft Office for Macs

Graphing RoI
For Individual Students
Setting Up Your Spreadsheet
In cell B2, type School Week
 In cell C2, type Benchmark
 In cell D2, type WPM (or Student Scores)

Labeling School Weeks
In cell B3, type 1
 Continue entering numbers
through 36 in column B
 Week 36 will be in cell B38

Entering Benchmarks
In cell C3, type the fall benchmark 77
 In cell C20, type the winter benchmark 92
 In cell C38, type the spring benchmark 110

Entering Student Data Points
Student data points are entered between
cells D3 and D38.
 Type the student’s score next to the
corresponding week that it was
administered.

Entering Student Data Points
Week 1 – 41
 Week 8 – 62
 Week 9 – 63
 Week 10 – 75
 Week 11 – 64
 Week 12 – 80
 Week 13 – 83
 Week 14 - 83

Entering Student Data Points
Week 15 – 56
 Week 17 – 104
 Week 18 – 74
 Week 20 – 85
 Week 21 – 89
 Week 22 – 69
 Week 23 – 85

Entering Student Data Points
Week 24 – 96
 Week 25 – 90
 Week 26 – 84
 Week 27 – 106
 Week 28 – 94
 Week 32 – 100

*CAUTION*
If a student was not assessed during a
certain week, leave that cell blank
 Do not enter a score of Zero (0) it will be
calculated into the trendline and
interpreted as the student having read
zero words correct per minute during that
week.

Creating a Graph
Highlight the
data in Columns
C and D
 Include cells
C2 and D2 through
cells C38 and D38
 Include any
blank cells

Creating a Graph

Excel 2003/Macs


Click Insert
Click Chart

Excel 2007



Click Insert
Find the icon for Line
Click the arrow below
Line
Creating a Graph

Excel 2003/Macs

A Chart Wizard
window will appear

Excel 2007

6 graphics appear
Creating a Graph

Excel 2003/Macs


Choose Line
Choose Line with
markers

Excel 2007

Choose Line with
markers
Creating a Graph

Excel 2003/Macs


Data Range tab
Columns

Excel 2007

Your graph appears
Creating a Graph

Excel 2003/Macs



Chart Title
School Week (X Axis)
WPM (Y Axis)

Excel 2007

Change your labels by
clicking on the graph
Creating a Graph

Excel 2003/Macs

Choose where you
want your graph

Excel 2007

Your graph was
automatically put into
your data spreadsheet
Creating a Graph

Excel 2003/Macs

Excel 2007
Adding a Trendline

Excel 2003/Macs


Excel 2007
Right click on any of the student data points
Adding a Trendline

Excel 2003/Macs

Choose Linear

Excel 2007
Adding a Trendline

Excel 2003/Macs


Excel 2007
Choose Custom and check box next to
Display equation on chart
Adding a Trendline
Clicking on the equation highlights a box
around it
 Clicking on the box allows you to move it
to a place where you can see it better

Adding a Trendline
You can repeat the same procedure to
have a trendline for the benchmark data
points
 Suggestion: label the trendline Expected
ROI
 Move this equation under the first

Individual Student Graph
Diego's Rate of Improvement
y = 1.6317x + 50.928
Words Per Minute
120
y = 0.9434x + 75.704
100
Benchmark (3rd)
80
Diego's Scores (3rd)
60
Diego's ROI
40
Goal Slope
20
0
1
4 7 10 13 16 19 22 25 28 31 34
School Week
Individual Student Graph
The equation indicates the slope, or rate of
improvement.
 The number, or coefficient, before "x" is
the average improvement, which in this
case is the average number of words per
Improvement
minute per week gained by the student.

y = 1.6317x + 50.928
y = 0.9434x + 75.704
Individual Student Graph
The rate of improvement, or trendline, is
calculated using a linear regression, a
simple equation of least squares.
 To add additional progress
monitoring/benchmark scores once you’ve
already created a graph, enter additional
scores in Column D in the corresponding
school week.

Individual Student Graph
Remember to leave cells blank for the
weeks that no score was obtained.
 The graph will incorporate that score into
the set of data points and into the
trendline.

Individual Student Graph
The slope can change depending on
which week (where) you put the
benchmark scores on your chart.
 Enter benchmark scores based on when
your school administers their benchmark
assessments for the most accurate
depiction of expected student progress.

Options for the Graph
Resizing
 Coloring
 Data Labels

Programming Excel
To Calculate RoI
A Formula
RoI Formula

Type RoI in cell B39 below the last week
of school
Calculate Expected Slope
Click on cell C39
 Put your cursor at the top next to the fx
 Type
=SLOPE(C3:C38,B3:B38)
 Hit Enter/Return

Calculate Actual Slope
Click on cell D39
 Put your cursor at the top next to the fx
 Type
=SLOPE(D3:D38,B3:B38)
 Hit Enter/Return

ROI as a Decision Tool
within a Problem-Solving Model
Steps
1.
2.
3.
4.
Gather the data
Ground the data
Interpret the data
Figure out how to fit Best Practice into
Public Education
Step 1: Gather Data
Universal Screening
Progress Monitoring
Common Screenings in PA
DIBELS
 AIMSweb
 MBSP
 4Sight
 PSSA

Validated Progress
Monitoring Tools
DIBELS
 AIMSweb
 MBSP
 www.studentprogress.org

Step 2: Ground the Data
To what will we compare our
student growth data?
Multiple Ways to
Look at Growth
Needed Growth
 Expected Growth & Percent of Expected
Growth
 Fuchs et. al. (1993) Table of Realistic and
Ambitious Growth
 Growth Toward Individual Goal*

*Best Practices in Setting Progress Monitoring Goals for Academic Skill Improvement (Shapiro, 2008)
Needed Growth
Difference between student’s BOY (or
MOY) score and benchmark score at MOY
(or EOY).
 Example: MOY ORF = 10, EOY
benchmark is 40, 18 weeks of instruction
(40-10/18=1.67). Student must gain 1.67
wcpm per week to make EOY benchmark.

Expected Growth
Difference between two benchmarks.
 Example: MOY benchmark is 20, EOY
benchmark is 40, expected growth (4020)/18 weeks of instruction = 1.11 wcpm
per week.

Looking at Percent of
Expected Growth
Tier I
Tier II
Tier III
Greater than
150%
Between
110% & 150%
Possible LD
Between 95%
& 110%
Likely LD
Between 80%
& 95%
May Need
More
May Need
More
Likely LD
Below 80%
Needs More
Needs More
Likely LD
Tigard-Tualatin School District
(www.ttsd.k12.or.us)
Oral Reading Fluency Adequate
Response Table
Realistic
Growth
Ambitious
Growth
1st
2.0
3.0
2nd
1.5
2.0
3rd
1.0
1.5
4th
0.9
1.1
5th
0.5
0.8
Fuchs, Fuchs, Hamlett, Walz, & Germann
(1993)
Digit Fluency Adequate
Response Table
Realistic
Growth
Ambitious
Growth
1st
0.3
0.5
2nd
0.3
0.5
3rd
0.3
0.5
4th
0.75
1.2
5th
0.75
1.2
Fuchs, Fuchs, Hamlett, Walz, & Germann
(1993)
Making Decisions: Best Practice
Research has yet to establish a blue print
for ‘grounding’ student RoI data.
 At this point, teams should consider
multiple comparisons when planning and
making decisions.

Making Decisions: Lessons
From the Field
When tracking on grade level, consider an
RoI that is 100% of expected growth as a
minimum requirement, consider an RoI
that is at or above the needed as optimal.
 So, 100% of expected and on par with
needed become the limits of the range
within a student should be achieving.

Oral Reading Fluency
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1
Benchmark
Aiden
Ava
Noah
Olivia
Liam
Hannah
Gavin
Grace
Oliver
Peyton
Josh
Riley
Mason
Zoe
Ian
Faith
David
Alexa
Hunter
Caroline
2
3
4
5
6
7
8
9
10
11
12
13
14
68
40
49
43
49
48
65
17
18
Needed RoI* Actual RoI** % of Expected
RoI
49
45
60
71
95
1.61
2.17
167%
77
57
54
87
92
2.28
2.76
213%
69
61
54
84
2.28
2.01
156%
57
70
79
83
1.39
1.50
116%
36
54
70
83
1.94
1.58
122%
52
60
82
1.72
1.20
93%
67
68
84
79
1.44
1.66
129%
46
60
74
79
2.06
1.76
136%
51
51
57
78
2.22
1.45
112%
53
54
64
64
69
40
53
48
44
63
46
68
50
49
38
42
49
53
1.29
52
49
55
50
16
90
61
59
15
47
58
75
77
1.50
1.12
87%
55
48
36
67
77
2.28
1.62
125%
54
69
67
50
76
2.67
1.76
136%
49
50
64
74
2.06
1.17
91%
34
38
42
68
55
51
58
3.11
1.44
111%
41
31
45
49
47
30
46
2.72
0.24
19%
29
36
35
36
36
29
45
44
3.39
0.75
58%
30
23
44
52
43
19
63
38
3.33
0.79
61%
18
19
25
33
33
23
28
37
4.00
0.94
73%
23
23
48
38
32
34
3.72
0.75
58%
28
20
40
37
19
30
3.44
0.02
2%
* Needed RoI based on difference betw een w eek 1 score and
Benchmark score for w eek 18 divided by 18 w eeks
53
24
28
Expected RoI at Benchmark Level
25
Oral Reading Fluency Adequate Response Table
** Actual RoI based on linear regression of all data points
Benchmarks based on DIBELS Goals
60
Realistic Grow thAmbitious Grow th
1st Grade
2.0
3.0
2nd Grade
1.5
2.0
3rd Grade
1.0
1.5
4th Grade
0.9
1.1
5th Grade
0.5
0.8
(Fuchs, Fuchs, Hamlett, Walz, & Germann 1993)
Step 3: Interpreting Growth
What do we do when we do not
get the growth we want?
When to make a change in instruction and
intervention?
 When to consider SLD?

When to make a change in
instruction and intervention?
Enough data points (6 to 10)?
 Less than 100% of expected growth.
 Not on track to make benchmark (needed
growth).
 Not on track to reach individual goal.

When to consider SLD?
Continued inadequate response despite:
 Fidelity with Tier I instruction and Tier
II/III intervention.
 Multiple attempts at intervention.
 Individualized Problem-Solving
approach.
Three Levels of Examples
Whole Class
 Small Group
 Individual Student
- Academic Data
- Behavior Data

Whole Class Example
Computation
01/15/10 01/22/10 01/29/10 02/05/10 02/12/10 02/19/10 02/26/10 03/05/10 03/12/10 03/19/10 03/26/10 04/02/10 04/09/10 04/16/10 04/23/10 04/30/10 05/07/10 05/14/10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Needed RoI* Actual RoI** % of Expected
RoI
0.35
50th Percentile
25
31
25th Percentile
19
23
Student
6.5
9
8
Student
6
7.5
8.5
Student
4.5
Student
13
Student
8.5
0.24
5.5
11
13
1.72
0.61
5
11
11.5
1.72
0.57
161%
5.5
6.5
9.5
10.5
1.72
1.06
300%
173%
8
9.3
8
5.6
9.6
9.6
1.72
-0.23
-66%
8
10.5
10.5
5.6
9.3
9
1.72
-0.03
-7%
9
8
4
8
9
1.72
0.07
21%
6
10.5
9
1.72
0.43
122%
6
8
1.72
0.07
20%
7
1.72
-0.25
-71%
-119%
Student
8.5
5.5
Student
6.5
5.5
Student
6.5
9
4.5
Student
8
10.5
4.5
6.5
4
Student
9
10
5.6
6.6
5
4.6
6.6
1.72
-0.42
8
8
8.5
4
8
6.6
1.72
-0.18
-51%
3.5
6.5
1.72
-0.24
-67%
26%
Student
Student
9
4.5
4.5
4
3.5
Student
6.5
5
6.5
9
7.5
6.5
1.72
0.09
Student
5.5
3
8
4
6.5
6.3
1.72
0.19
55%
Student
7.5
10
6.6
3.3
3
6.3
1.72
-0.46
-130%
Student
5
5.5
6.5
6
5
6
1.72
0.04
11%
Student
5
4
8
8.5
10
8
6
1.72
0.25
71%
Student
4.5
3.5
5.5
1.72
-0.03
-8%
5
5.3
1.72
-0.14
-40%
Student
6
5
2.5
5.5
4.5
10.5
* Needed RoI based on difference betw een w eek 1 score and Benchmark score for w eek 18 divided by 18 w eeks
11
Digit Fluency Adequate Response Table
** Actual RoI based on linear regression of all data points
Percentiles based on AIMSw eb Grow th Tables
Expected RoI at 50th Percentile
Expected RoI at 25th Percentile
Realistic Grow thAmbitious Grow th
1st Grade
0.3
0.5
2nd Grade
0.3
0.5
3rd Grade
0.3
0.5
4th Grade
0.75
1.2
5th Grade
0.75
1.2
(Fuchs, Fuchs, Hamlett, Walz, & Germann 1993)
3rd Grade Math Whole Class
Who’s responding?
 Effective math
instruction?
 Who needs more?

N=19
 4 > 100% growth
 15 < 100% growth
 9 w/ negative
growth

Small Group Example
Oral Reading Fluency
09/11/09 09/18/09 09/25/09 10/02/09 10/09/09 10/16/09 10/23/09 10/30/09 11/06/09 11/13/09 11/20/09 11/27/09 12/04/09 12/11/09 12/18/09 01/01/10 01/08/10 01/15/10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Needed RoI* Actual RoI** % of Expected
RoI
68
1.41
Benchmark
44
Student
35
39
41
45
42
45
52
57
62
1.83
1.49
106%
Student
28
38
42
40
50
55
64
72
74
2.22
2.77
196%
Student
26
28
32
31
27
29
35
34
38
2.33
0.57
41%
Student
31
35
39
45
42
47
53
58
65
2.06
1.90
135%
Student
40
44
38
48
52
64
72
74
78
1.56
2.62
186%
* Needed RoI based on dif ference between week 1 score
and Benchmark score for week 18 divided by 18 weeks
Oral Reading Fluency Adequte Response Table
** Actual RoI based on linear regression of all data points
Benchmarks based on DIBELS Goals
Expected RoI at Benchmark Level
Realistic GrowthAmbitious Growth
1st Grade
2.0
3.0
2nd Grade
1.5
2.0
3rd Grade
1.0
1.5
4th Grade
0.9
1.1
5th Grade
0.5
0.8
(Fuchs, Fuchs, Hamlett, Walz, & Germann 1993)
Intervention Group
Intervention working for how many?
 Can we assume fidelity of intervention
based on results?
 Who needs more?

Individual Kid Example
2nd Grade Reading Progress
100
y = 1.5333x + 42.8
90
90
80
79
Words Read Correct Per Minute
74
70
68
60
60
56
53
y = 0.9903x + 36.873
53
50
48
46
45
44
40
31
30
20
10
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
09/12/08 09/19/0809/26/0810/03/08 10/10/08 10/17/08 10/24/08 10/31/08 11/07/08 11/14/08 11/21/08 11/28/08 12/05/08 12/12/08 12/19/08 01/16/09 01/23/09 01/30/09 02/06/0902/13/09 02/20/0902/27/0903/06/09 03/13/0903/20/0903/27/0904/03/09 04/10/09 04/17/0904/24/09 05/01/09
Benchmark
Linear (Benchmark)
Linear
Individual Kid
Making growth?
 How much (65% of expected growth).
 Atypical growth across the year (last 3
data points).
 Continue? Make a change? Need more
data?

RoI and Behavior?
Percent of Time Engaged in Appropriate Behavior
100
90
y = 7.2143x - 1.5
80
70
y = 3.9x + 19.8
Percent
60
50
40
y = 2x + 22
30
20
10
0
1
2
Baseline
3
4
Condition 1
5
6
Condition 2
7
8
9
Linear (Baseline)
10
11
12
Linear (Condition 1)
13
14
Linear (Condition 2)
15
16
17
Linear (Condition 2)
18
Step 4: Figure out how to fit
Best Practice into Public
Education
Things to Consider
Who is At-Risk and needs progress
monitoring?
 Who will collect, score, enter the data?
 Who will monitor student growth, when,
and how often?
 What changes should be made to
instruction & intervention?
 What about monitoring off of grade level?

Who is At-Risk and needs
progress monitoring?

Below level on universal screening
Entering 4th Grade Example
DORF
(110)
Student A
115
ISIP
TRWM
(55)
58
4Sight
(1235)
PSSA
(1235)
1255
1232
Student B
85
48
1216
1126
Student C
72
35
1056
1048
Who will collect, score, and
enter the data?
Using MBSP for math, teachers can
administer probes to whole class.
 DORF probes must be administered oneon-one, and creativity pays off (train and
use art, music, library, etc. specialists).
 Schedule for progress monitoring math
and reading every-other week.

Week 1
Reading
1st
Reading
X
X
X
X
X
Math
X
X
4th
5th
Math
X
2nd
3rd
Week 2
X
X
Who will monitor student
growth, when, and how often?



Best Practices in Data-Analysis Teaming
(Kovaleski & Pedersen, 2008)
Chambersburg Area School District Elementary
Response to Intervention Manual (McCrea et.
al., 2008)
Derry Township School District Response to
Intervention Model
(http://www.hershey.k12.pa.us/56039310111408/lib/56039310111408/_files/Microsoft_Word__Response_to_Intervention_Overview_of_Hershey_Elementary_Model.pdf)
What changes should be made
to instruction & intervention?
Ensure treatment fidelity!!!!!!!!
 Increase instructional time (active and
engaged)
 Decrease group size
 Gather additional, diagnostic, information
 Change the intervention

When Instructional Level is Not
the Same as Grade Level

Understand needed and expected RoI
within broader context:


Needed growth will only get student to next
level by next benchmark (as opposed to on
level).
100% of expected growth may not be an
acceptable minimum (not enough growth b/c
level is so low).
Grounding RoI When Monitoring
Off of Grade Level: Two Options
Best Practices in Setting Progress
Monitoring Goals for Academic Skill
Improvement (Shapiro, 2008).
 Tigard-Tualatin SD Chart: 150% instead of
100% as minimum RoI requirement???

Questions? & Comments!
Resources
 www.interventioncentral.com
 www.aimsweb.com
 http://dibels.uoregon.edu
 www.nasponline.org
Resources
www.fcrr.org
Florida Center for Reading Research
 http://ies.ed.gov/ncee/wwc//
What Works Clearinghouse
 http://www.rti4success.org
National Center on RtI

Flinn & McCrea’s RoI Web Site

http://sites.google.com/site/rateofimprove
ment/


Caitlin Flinn


Download powerpoints, handouts, Excel
graphs, charts, articles, etc.
c.s.flinn@iup.edu
Andrew McCrea

mccreand@chambersburg.k12.pa.us
References
Ardoin, S. P., & Christ, T. J. (2009). Curriculumbased measurement of oral reading: Standard
errors associated with progress monitoring
outcomes from DIBELS, AIMSweb, and an
experimental passage set. School Psychology
Review, 38(2), 266-283.
Ardoin, S. P. & Christ, T. J. (2008). Evaluating
curriculum-based measurement slope estimates
using triannual universal screenings. School
Psychology Review, 37(1), 109-125.
References
Christ, T. J. (2006). Short-term estimates of
growth using curriculum-based measurement
of oral reading fluency: Estimating standard
error of the slope to construct confidence
intervals. School Psychology Review, 35(1),
128-133.
Deno, S. L. (1985). Curriculum-based
measurement: The emerging alternative.
Exceptional Children, 52, 219-232.
References
Deno, S. L., Fuchs, L.S., Marston, D., &
Shin, J. (2001). Using curriculum-based
measurement to establish growth
standards for students with learning
disabilities. School Psychology Review,
30, 507-524.
Flinn, C. S. (2008). Graphing rate of
improvement for individual students.
InSight, 28(3), 10-12.
References
Fuchs, L. S., & Fuchs, D. (1998). Treatment
validity: A unifying concept for reconceptualizing
the identification of learning disabilities. Learning
Disabilities Research and Practice, 13, 204-219.
Fuchs, L. S., Fuchs, D., Hamlett, C. L., Walz, L., &
Germann, G. (1993). Formative evaluation of
academic progress: How much growth can we
expect? School Psychology Review, 22, 27-48.
References
Gall, M.D., & Gall, J.P. (2007). Educational
research: An introduction (8th ed.). New
York: Pearson.
Jenkins, J. R., Graff, J. J., & Miglioretti, D.L.
(2009). Estimating reading growth using
intermittent CBM progress monitoring.
Exceptional Children, 75, 151-163.
References
Karwowski, W. (2006). International
encyclopedia of ergonomics and human
factors. Boca Raton, FL: Taylor & Francis
Group, LLC.
Shapiro, E. S. (2008). Best practices in setting
progress monitoring goals for academic skill
improvement. In A. Thomas and J. Grimes
(Eds.), Best practices in school psychology V
(Vol. 2, pp. 141-157). Bethesda, MD: National
Association of School Psychologists.
References
Vogel, D. R., Dickson, G. W., & Lehman, J.
A. (1990). Persuasion and the role of
visual presentation support. The UM/3M
study. In M. Antonoff (Ed.), Presentations
that persuade. Personal Computing, 14.