Rate of Improvement
Calculation and Decision Making
Caitlin S. Flinn, EdS, NCSP
Andrew E. McCrea, MS, NCSP
Why we’re here…
While there exists a wealth of convincing
research supporting the implementation of
a response-to-intervention (RtI)
framework, there are many questions yet
to be empirically answered.
 Within multi-tiered model of assessment
and instruction/intervention, how do we
know whether a student is learning?

Measuring Learning








Class tests
Quizzes
Assignment/homework completion and accuracy
Ask students questions in class
Grades/report cards
State/local assessments
Universal screening, benchmark assessments
Progress monitoring
With Progress Monitoring Data…

How do we know if a student is learning?

Look at the data points
Where are they on the graph?
 Are the data points getting closer to the goal or
benchmark?


Is there a way to measure growth?
 Make
an aimline toward goal
 Look to see where data points are compared to
aimline
 Calculate Rate of Improvement (RoI)
Today’s Objectives
Explain what RoI is, why it is important,
and how to compute it.
 Establish that Simple Linear Regression
should be the standardized procedure for
calculating RoI.
 Discuss how to use RoI within a problem
solving/school improvement model.

RoI Definition
Rate of Improvement can be described
algebraically as the slope of a line
 Slope is defined as: the vertical change
over the horizontal change on a Cartesian
plane. (x-axis and y-axis graph)

Also called: Rise over run
 Formula: m = (y2 - y1) / (x2 - x1)
 Describes the steepness of a line (Gall & Gall,
2007)

RoI Definition

Finding a student’s RoI is determining the
student’s learning


Creating a line that fits the data points, a
trendline
To find that line, we use:
Linear regression
 Ordinary Least Squares

How does Rate of
Improvement Fit into the
Larger Context?
School Improvement/Comprehensive School Reform
Response to Intervention
Dual Discrepancy: Level & Growth
Rate of Improvement
School Improvement/
Comprehensive School Reform
Grade level content expectations (ELA,
math, science, social studies, etc.).
 Work toward these expectations through
classroom instruction.
 Understand impact of instruction through
assessment.

Assessment

Formative Assessments/High Stakes
Tests


Does student have command of content
expectation (standard)?
Universal Screening using CBM

Does student have basic skills appropriate for
age/grade?
Assessment
Q: For students who are not proficient on
grade level content standards, do they
have the basic reading/writing/math skills
necessary?
 A: Look at Universal Screening; if above
criteria, intervention geared toward content
standard, if below criteria, intervention
geared toward basic skill.

Progress Monitoring
Frequent measurement of knowledge to
inform our understanding of the impact of
instruction/intervention.
 Measures of basic skills (CBM) have
demonstrated reliability & validity (see table at

www.rti4success.org).
Classroom Instruction (Content Expectations)
Measure Impact (Test)
Proficient!
Use Diagnostic
Test to Differentiate
Non Proficient
Content Need?
Basic Skill Need?
Intervention
Progress Monitor
Intervention
Progress Monitor
With CBM
If CBM is
Appropriate
Measure
Rate of Improvement
So…





Rate of Improvement (RoI) is how we
understand student growth (learning).
RoI is reliable and valid (psychometrically
speaking) for use with CBM data.
RoI is best used when we have CBM data,
most often when dealing with basic skills in
reading/writing/math.
RoI can be applied to other data (like
behavior) with confidence too!
RoI is not yet tested on typical Tier I formative
classroom data.
RoI is usually applied to…
Tier One students in the early grades at
risk for academic failure (low green kids).
 Tier Two & Three Intervention Groups.
 Special Education Students (and IEP
goals)
 Students with Behavior Plans

RoI Foundations
 Deno,
1985
 Curriculum-based
 General
measurement
outcome measures
 Technically adequate
 Short
 Standardized
 Repeatable
 Sensitive to change
RoI Foundations
 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 Foundations
 Ardoin
 Slope
& Christ, 2008
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 Foundations
 Fuchs,
Fuchs, Walz, & Germann,
1993
 Typical
weekly growth rates in oral
reading fluency and digits correct
 Needed growth to remediate skills
 Students
who had 1.5 to 2.0 times the
slope of typically performing peers were
able to close the achievement gap in a
reasonable amount of time
RoI Foundations

Deno, Fuchs, Marston, & Shin, 2001

Slope of frequently non-responsive children
approximated slope of children already
identified as having a specific learning
disability
How many data points?

10 data points are a minimum requirement
for a reliable trendline (Gall & Gall, 2007)

Is that reasonable and realistic?
How does that affect the frequency of
administering progress monitoring probes?
 How does that affect our ability to make
instructional decisions for students?

How can we show RoI?






Speeches that included visuals, especially in
color, improved recall of information (Vogel,
Dickson, & Lehman, 1990)
“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 for Which We Compute RoI

Reading



Oral Reading Fluency
Word Use Fluency
Reading Comprehension



Early Literacy Skills








MAZE
Retell
Initial Sound
Letter Naming
Letter Sound
Phoneme Segmentation
Nonsense Word
Spelling
Written Expression
Behavior

Math



Math
Computation
Math Facts
Early Numeracy




Oral Counting
Missing Number
Number
Identification
Quantity
Discrimination
Guidelines?
 Visual
inspection of slope
 Multiple
interpretations
 Instructional
 Need
services
for explicit guidelines
Ongoing Research
RoI for instructional decisions is not a
perfect process
 Research is currently addressing 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

Future Considerations

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

Visual Inspection Approaches
“Eye Ball” Approach
 Split Middle Approach
 Tukey Method


Quantitative Approaches
Last point minus First point Approach
 Split Middle & Tukey “plus”
 Linear Regression Approach

The Visual Inspection
Approaches
Eye Ball Approach
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
Split Middle Approach

Drawing “through the two points obtained
from the median data values and the
median days when the data are divided
into two sections”
(Shinn, Good, & Stein, 1989).
Split Middle
20
19
18
17
16
14
X(14)
14
14
12
10
10
8
11
X (9)
X(9)
8
7
6
4
2
0
1
2
3
4
5
6
7
8
Tukey Method
Divide scores into 3 equal groups
 Divide groups with vertical lines
 In 1st and 3rd groups, find median data
point and median week and mark with an
“X”
 Draw line between two “Xs”

(Fuchs, et. al., 2005. Summer Institute Student progress monitoring for math.
http://www.studentprogress.org/library/training.asp)
Tukey Method
20
19
18
17
16
14
X(14)
14
14
12
11
10
10
8
8
X(8)
7
6
4
2
0
1
2
3
4
5
6
7
8
The Quantitative Approaches
Last minus First

Iris Center: last probe score minus first
probe score over last administration period
minus first administration period.
Y2-Y1/X2-X1= RoI
http://iris.peabody.vanderbilt.edu/resources.html
Last minus First
20
19
18
17
16
14
14
14
12
11
10
10
8
8
7
(14-8)/(8-0)=0.75
6
4
2
0
1
2
3
4
5
6
7
8
Split Middle “Plus”
20
19
18
17
16
14
X(14)
14
14
12
11
10
10
8
X(9)
8
7
6
(14-9)/8=0.63
4
2
0
1
2
3
4
5
6
7
8
Tukey Method “Plus”
20
19
18
17
16
14
X(14)
14
14
12
11
10
10
8
8
X(8)
7
6
(14-8)/8=0.75
4
2
0
1
2
3
4
5
6
7
8
Linear Regression
20
19
18
17
16
14
14
14
12
11
10
10
8
8
7
6
y = 1.1429x + 7.3571
4
2
0
1
2
3
4
5
6
7
8
RoI Consistency?
Any Method of
Visual Inspection
???
Last minus First
0.75
Split Middle
“Plus”
Tukey “Plus”
0.63
Linear
Regression
1.10
0.75
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.
RoI Consistency?


Last minus First (Iris Center) and Linear
Regression (Shinn, etc.) only quantitative
methods discussed in CBM literature.
Study of 37 at risk 2nd graders:
Difference in RoI b/w LmF & LR
Methods
Whole Year
0.26 WCPM
Fall
Spring
0.31 WCPM
0.24 WCPM
McCrea (2010) Unpublished data
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 an 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
 Focus on Yes/No to goal acquisition, not
degree of growth
 How many of us want to calculate OLS
Linear Regression formulas (or even
remember how)?

Pros and Cons of Each
Approach
Pros
Eye Ball
Split
Middle &
Tukey
Easy
Understandable
No software needed
Compare to
Aim/Goal line
Yes/No to goal
acquisition
Cons
Subjective
No statistic
provided, no
idea of the
degree of
growth
Pros and Cons of Each
Approach
Pros
Last minus
First
Provides a growth
statistic
Easy to compute
Cons
Does not consider
all data points,
only two
Split Middle & Considers all data
Tukey “Plus” points.
Easy to compute
No support for
“plus” part of
methodology
Linear
Regression
Calculating the
statistic
All data points
Best Practice
An Easy and
Applicable Solution
Get Out Your Laptops!
Open Microsoft Excel
I love
ROI
Graphing RoI
For Individual Students
Programming Microsoft Excel to
Graph Rate of Improvement:
Fall to Winter
Setting Up Your Spreadsheet
In cell A1, type 3rd Grade ORF
 In cell A2, type First Semester
 In cell A3, type School Week
 In cell A4, type Benchmark
 In cell A5, type the Student’s Name
(Swiper Example)

Labeling School Weeks
Starting with cell B3, type numbers 1
through 18 going across row 3
(horizontal).
 Numbers 1 through 18 represent the
number of the school week.
 You will end with week 18 in cell S3.

Labeling Dates

Note: You may choose to enter the date of
that school week across row 2 to easily
identify the school week.
Entering Benchmarks
(3rd Grade ORF)

In cell B4, type 77.
This is your fall
benchmark.

In cell S4, type 92.
This is your winter
benchmark.
Entering Student Data (Sample)






Enter the following
numbers, going
across row 5, under
corresponding week
numbers.
Week 1 – 41
Week 8 – 62
Week 9 – 63
Week 10 – 75
Week 11 – 64






Week 12 – 80
Week 13 – 83
Week 14 – 83
Week 15 – 56
Week 17 – 104
Week 18 – 74
*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.

Graphing the Data
Highlight cells A4 and A5 through S4 and
S5
 Follow Excel 2003 or Excel 2007
directions from here

Graphing the Data

Excel 2003


Across the top of your
worksheet, click on
“Insert”
In that drop-down
menu, click on “Chart”

Excel 2007



Click Insert
Find the icon for Line
Click the arrow below
Line
Graphing the Data

Excel 2003

A Chart Wizard
window will appear

Excel 2007

6 graphics appear
Graphing the Data

Excel 2003


Choose “Line”
Choose “Line with
markers…”

Excel 2007

Choose “Line with
markers”
Graphing the Data

Excel 2003


“Data Range” tab
“Columns”

Excel 2007

Your graph appears
Graphing the Data

Excel 2003



“Chart Title”
“School Week” X Axis
“WPM’ Y Axis

Excel 2007

Change your labels by
right clicking on the
graph
Graphing the Data

Excel 2003

Choose where you
want your graph

Excel 2007

Your graph was
automatically put into
your data spreadsheet
Graphing the Trendline

Excel 2003


Excel 2007
Right click on any of the student data points
Graphing the Trendline

Excel 2003

Choose “Linear”

Excel 2007
Graphing the Trendline

Excel 2003


Excel 2007
Choose “Custom” and check box next to
“Display equation on chart”
Graphing the 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

Graphing the 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:
Fall to Winter
120
y = 2.5138x + 42.113
y = 0.8824x + 76.118
100
80
Benchmark
Student: Sw iper
60
RoI
Linear (Benchmark)
40
20
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
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
minute per week gained by the student.

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 Row 5 in the corresponding
school week.

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.

Programming Excel
First Semester
Calculating Needed RoI
Calculating Benchmark RoI
Calculating Student’s Actual RoI
Quick Definitions

Needed RoI


Benchmark RoI


The rate of improvement needed to “catch” up
to the next benchmark.
The rate of improvement of typically
performing peers according to the norms
Student’s Actual RoI

Based on the available data points, this is the
student’s actual rate of improvement per week
Calculating Needed RoI






In cell T3, type Needed RoI
Click on cell T5
In the fx line (at top of sheet) type this formula
=((S4-B5)/18)
Then hit enter
Your result should read: 2.83333...
This formula simply subtracts the student’s
actual beginning of year (BOY) benchmark from
the expected middle of year (MOY) benchmark,
then dividing by 18 for the first 18 weeks (1st
semester).
Calculating Benchmark RoI
In cell U3, type Benchmark RoI
 Click on cell U4
 In the fx line (at top of sheet) type this
formula =SLOPE(B4:S4,B3:S3)
 Then hit enter
 Your result should read: 0.8825...
 This formula considers 18 weeks of
benchmark data and provides an average
growth or change per week.

Calculating Student Actual RoI
Click on cell U5
 In the fx line (at top of sheet) type this
formula =SLOPE(B5:S5,B3:S3)
 Then hit enter
 Your result should read: 2.5137...
 This formula considers 18 weeks of
student data and provides an average
growth or change per week.

Graphing RoI
For Individual Students
Programming Microsoft Excel to
Graph Rate of Improvement:
Winter to Spring
Setting Up Your Spreadsheet
In cell A1, type 3rd Grade ORF
 In cell A2, type Second Semester
 In cell A3, type School Week
 In cell A4, type Benchmark
 In cell A5, type the Student’s Name
(Swiper Example)

Labeling School Weeks
Starting with cell B3, type numbers 1
through 18 going across row 3
(horizontal).
 Numbers 1 through 18 represent the
number of the school week.
 You will end with week 18 in cell S3.

Labeling Dates

Note: You may choose to enter the date of
that school week across row 2 to easily
identify the school week.
Entering Benchmarks
(3rd Grade ORF)

In cell B4, type 92.
This is your fall
benchmark.

In cell S4, type 110.
This is your winter
benchmark.
Entering Student Data (Sample)






Enter the following
numbers, going
across row 5, under
corresponding week
numbers.
Week 1 – 74
Week 3 – 85
Week 4 – 89
Week 5 – 69
Week 6 – 85






Week 7 – 96
Week 8 – 90
Week 9 – 84
Week 10 – 106
Week 11 – 94
Week 15 – 100
*CAUTION*

If a student was not assessed during a
certain week, what do you put in that cell?

Why?
Graphing the Data
Highlight cells A4 and A5 through S4 and
S5
 Follow Excel 2003 or Excel 2007
directions from here

Graphing the Data

Excel 2003


Across the top of your
worksheet, click on
“Insert”
In that drop-down
menu, click on “Chart”

Excel 2007



Click Insert
Find the icon for Line
Click the arrow below
Line
Graphing the Data

Excel 2003

A Chart Wizard
window will appear

Excel 2007

6 graphics appear
Graphing the Data

Excel 2003


Choose “Line”
Choose “Line with
markers…”

Excel 2007

Choose “Line with
markers”
Graphing the Data

Excel 2003


“Data Range” tab
“Columns”

Excel 2007

Your graph appears
Graphing the Data

Excel 2003



“Chart Title”
“School Week” X Axis
“WPM’ Y Axis

Excel 2007

Change your labels by
right clicking on the
graph
Graphing the Data

Excel 2003

Choose where you
want your graph

Excel 2007

Your graph was
automatically put into
your data spreadsheet
Graphing the Trendline

Excel 2003


Excel 2007
Right click on any of the student data points
Graphing the Trendline

Excel 2003

Choose “Linear”

Excel 2007
Graphing the Trendline

Excel 2003


Excel 2007
Choose “Custom” and check box next to
“Display equation on chart”
Graphing the 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

Graphing the 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
120
y = 1.0588x + 90.941
y = 1.8872x + 74.81
100
80
Benchmark
Student: Sw iper
60
Rate of Improvement
Expected RoI
40
20
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Challenge!
What was the first equation?
 What is the slope of that equation?

What was the second equation?
 What is the slope of that equation?


Describe the achievement gap at the end
of the school year.
Programming Excel
Second Semester
Calculating Needed RoI
Calculating Benchmark RoI
Calculating Student’s Actual RoI
Calculating Needed RoI






In cell T3, type Needed RoI
Click on cell T5
In the fx line (at top of sheet) type this formula
=((S4-B5)/18)
Then hit enter
Your result is _____ ?
This formula simply subtracts the student’s
actual middle of year (MOY) benchmark from the
expected end of year (EOY) benchmark, then
dividing by 18 for the first 18 weeks (1st
semester).
Calculating Benchmark RoI
In cell U3, type Benchmark RoI
 Click on cell U4
 In the fx line (at top of sheet) type this
formula =SLOPE(B4:S4,B3:S3)
 Then hit enter
 Your result should read: ____?
 This formula considers 18 weeks of
benchmark data and provides an average
growth or change per week.

Calculating Student Actual RoI
Click on cell U5
 In the fx line (at top of sheet) type this
formula =SLOPE(B5:S5,B3:S3)
 Then hit enter
 Your result should read: 1.89
 This formula considers 18 weeks of
student data and provides an average
growth or change per week.

Why Graph only 18
Weeks at a Time?
Assuming Linear Growth…
…Finding Curve-linear Growth
Non-Educational Example of
Curve-linear Growth
Weight Loss Chart
205
200
10 Week RoI = -2.5
First 5 Weeks RoI = -3.6
Second 5 Weeks RoI = -1.5
200
197.5
195
193
Weight
190
189.5
186
185
184
182.5
181
180
179.5
178
175
170
165
1
2
3
4
5
6
Weeks
7
8
9
10
70
Academic Example of
Curvilinear Growth
60
50
40
WCPM
MOY to EOY = 1.19
30
20
BOY to MOY = 1.60
BOY to EOY = 1.35
10
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Weeks
McCrea, 2010
Looked at Rate of Improvement in small
2nd grade sample
 Found differences in RoI when computed
for fall and spring:
 Ave RoI for fall:
1.47 WCPM
 Ave RoI for spring:
1.21 WCPM

Ardoin & Christ, 2008
Slope for benchmarks (3x per year)
 More growth from fall to winter than winter
to spring

Christ, Yeo, & Silberglitt, in
press
Growth across benchmarks (3X per year)
 More growth from fall to winter than winter
to spring
 Disaggregated special education
population

Graney, Missall, & Martinez,
2009
Growth across benchmarks (3X per year)
 More growth from winter to spring than fall
to winter with R-CBM.

Fien, Park, Smith, & Baker,
2010
Investigated relationship b/w NWF gains
and ORF/Comprehension
 Found greater NWF gains in fall than in
spring.

DIBELS
th
(6 )
ORF Change in
Criteria
2nd
Fall to
Winter
24
Winter to
Spring
22
3rd
15
18
4th
13
13
5th
11
9
6th
11
5
AIMSweb Norms
Based on 50th
Percentile
Fall to Winter
Winter to
Spring
1st
18
31
2nd
25
17
3rd
22
15
4th
16
13
5th
17
15
6th
13
12
Speculation as to why Differences
in RoI within the Year




Relax instruction after high stakes testing in
March/April; a PSSA effect.
Depressed BOY benchmark scores due to
summer break; a rebound effect (Clemens).
Instructional variables could explain differences
in Graney (2009) and Ardoin (2008) & Christ (in
press) results (Silberglitt).
Variability within progress monitoring probes
(Ardoin & Christ, 2008) (Lent).
ROI as a Decision Tool
within a Problem-Solving Model
Steps
1.
2.
3.
4.
Gather the data
Ground the data & set goals
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
1) To what will we compare our
student growth data?
2) How will we set goals?
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%
Below 80%
May Need
More
May Need
More
Needs More Needs More
Likely LD
Likely LD
Tigard-Tualatin School District (www.ttsd.k12.or.us)
Oral Reading Fluency Adequate
Response Table
Realistic Ambitiou
Growth s 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)
If Local Criteria are Not an Option
Use norms that accompany the measure
(DIBELS, AIMSweb, etc.).
 Use national norms.

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.

Is there an easy way to do all
of this?
Oral Reading Fluency
01/15/09 01/22/09 01/29/09 02/05/09 02/12/09 02/19/09 02/26/09 03/05/09 03/12/09 03/19/09 03/26/09 04/02/09 04/09/09 04/16/09 04/23/09 04/30/09 05/07/09 05/14/09
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)
1/14/2011 1/121/2011 1/28/2011 5/14/2011
% of Expected
Needed RoI Actual RoI RoI
1
2
3
18
Benchmark 68
90
1.29
Student 22
27
56 3.78 1.89 147%
Access to Spreadsheet
Templates
http://sites.google.com/site/rateofimprove
ment/home
 Click on Charts and Graphs.
 Update dates and benchmarks.
 Enter names and benchmark/progress
monitoring data.

What about Students not on
Grade Level?
Determining Instructional Level
Independent/Instructional/Frustrational
 Instructional often b/w 40th or 50th
percentile and 25th percentile.
 Frustrational level below the 25th
percentile.
 AIMSweb: Survey Level Assessment
(SLA).

Setting Goals off of Grade Level
100% of expected growth not enough.
 Needed growth only gets to instructional
level benchmark, not grade level.
 Risk of not being ambitious enough.
 Plenty of ideas, but limited research
regarding Best Practice in goal setting off
of grade level.

Possible Solution (A)
Weekly probe at instructional level and
compare to expected and needed growth
rates at instructional level.
 Ambitious goal: 200% of expected RoI

Oral Reading Fluency
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
5th Grade
2
3
4
5
6
7
8
9
10
11
12
16
17
18
124
0.53
134
128
143
1.11
2.15
407%
92
101
115
116
129
108
121
1.11
1.43
271%
94
108
95
121
135
126
109
113
1.67
1.32
248%
99
66
100
83
92
107
109
93
1.39
0.89
168%
110
97
124
113
131
132
142
0.78
2.33
440%
96
74
108
62
107
92
94
95
1.56
0.39
74%
73
93
79
114
111
112
87
116
2.83
2.03
383%
102
112
122
103
118
135
105
112
1.22
0.51
97%
111
AB
121
121
134
131
99
120
0.72
0.11
21%
110
90
118
103
119
121
122
119
0.78
1.21
228%
105
90
79
89
120
123
119
0.94
1.22
231%
91
90
105
118
60
72
80
81
43
59
76
92
120
57
0.76
47
65
4.14
-0.06
-8%
137
110
2.71
4.94
646%
115
124
85
79
2nd Grade
15
% of Expected
RoI
104
107
3rd Grade
14
115
104
4th Grade
13
Needed RoI* Actual RoI**
0.53
55
57
66
76
66
47
66
6.27
0.49
93%
72
84
92
94
82
76
82
3.25
-0.08
-15%
81
91
70
65
73
3.21
-1.41
-267%
70
104
79
79
68
4.50
-1.45
-274%
68
90
74
63
83
91
70
104
84
71
74
86
82
77
91
1.29
0.94
1.15
89%
-0.06
2.21
171%
Possible Solution (B)
Weekly probe at instructional level for
sensitive indicator of growth.
 Monthly probes (give 3, not just 1) at
grade level to compute RoI.
 Goal based on grade level growth (more
than 100% of expected).

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.
Evidence of dual discrepancy…
05/14/09
Needed Ro I*
A c tual Ro I**
18
90
% o f Expec ted
Ro I
Dual Disc repanc y?
Keep On Truckin
Keep On Truckin
1.29
95
1.61
2.17
167%
92
2.28
2.76
213%
84
2.28
2.01
156%
83
1.39
1.50
116%
83
1.94
1.58
122%
82
1.72
1.20
93%
79
1.44
1.66
129%
79
2.06
1.76
136%
78
2.22
1.45
112%
77
1.50
1.12
87%
77
2.28
1.62
125%
76
2.67
1.76
136%
74
2.06
1.17
91%
58
3.11
1.44
111%
46
2.72
0.24
19%
44
3.39
0.75
58%
38
3.33
0.79
61%
37
4.00
0.94
73%
34
3.72
0.75
58%
30
3.44
0.02
2%
BIG
BIG
BIG
BIG
BIG
BIG
PROBLEMS
PROBLEMS
PROBLEMS
PROBLEMS
PROBLEMS
PROBLEMS
Growth Criteria
>125%
85% - 125%
<85%
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)
ISIP
TRWM
(55)
4Sight
(1235)
PSSA
(1235)
Student A
115
58
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

Final Exam…
Student Data: 27, 29, 26, 34, 27, 32, 39,
45, 43, 49, 51, --, --, 56, 51, 52, --, 57.
 Benchmark Data: BOY = 40, MOY = 68.
 What is student’s RoI?
 How does RoI compare to expected and
needed RoIs?
 What steps would your team take next?
 What if Benchmarks were 68 and 90
instead?

The RoI Web Site

http://sites.google.com/site/rateofimprovement/


Caitlin Flinn Bennyhoff


CaitlinFlinn@hotmail.com
Andy McCrea


Download powerpoints, handouts, Excel graphs,
charts, articles, etc.
andymccrea70@gmail.com
Matt Ferchalk
mferchalk@norleb.k12.pa.us