Calculating and Interpreting Calculating and Interpreting Slope: Implications for Slope: Implications for School PsychologistsSchool Psychologists
Caitlin S. Flinn, Ed.S. &Caitlin S. Flinn, Ed.S. &
Andrew E. McCrea, M.S., NCSPAndrew E. McCrea, M.S., NCSP
ASPP/PSU ConferenceASPP/PSU Conference
October 8, 2009October 8, 2009
Translations…Translations…
ROI = Rate of Improvement, SlopeROI = Rate of Improvement, Slope
RTI = Response to InterventionRTI = Response to Intervention
SLD = Specific Learning DisabilitySLD = Specific Learning Disability
DD = Dually DiscrepantDD = Dually Discrepant
OverviewOverview
ConceptualizationConceptualization ImportanceImportance DefinitionsDefinitions FunctionsFunctions Graphing in ExcelGraphing in Excel
Individual GraphsIndividual Graphs Calculating ROICalculating ROI
Decision MakingDecision Making Grounding the DataGrounding the Data Interpreting GrowthInterpreting Growth
Individual StudentIndividual Student Student GroupsStudent Groups
ConsiderationsConsiderations
What is Rate of Improvement?What is Rate of Improvement?
Lines
Graphs
Improvement
Growth
Development
Progress
Slope
Graphs in EducationGraphs in Education
Core instruction efficacy Core instruction efficacy Batsche, et al., 2005Batsche, et al., 2005
Data-driven instructionData-driven instruction NCLB, 2001; IDEA, 2004NCLB, 2001; IDEA, 2004
Incremental skill growthIncremental skill growth Colvin, Sugai, Good, & Young-Yon, 1997Colvin, Sugai, Good, & Young-Yon, 1997
Intervention effectivenessIntervention effectiveness Batsche, Castillo, Dixon, & Forde, 2008Batsche, Castillo, Dixon, & Forde, 2008
Setting goalsSetting goals Shapiro, 2008Shapiro, 2008
Progress monitoringProgress monitoring Wright, 2008; Fuchs & Fuchs, 1997Wright, 2008; Fuchs & Fuchs, 1997
Graphs in EducationGraphs in Education Assessing level and rateAssessing level and rate
Batsche, Castillo, Dixon, & Forde, 2008Batsche, Castillo, Dixon, & Forde, 2008 Self monitoringSelf monitoring
Fuchs et al., 2006Fuchs et al., 2006 IEP goalsIEP goals
Shinn, 2008Shinn, 2008 Professional accountability Professional accountability
Sulzer-Asaroff & Mayer, 1991Sulzer-Asaroff & Mayer, 1991 Treatment integrityTreatment integrity
Mortenson & Witt, 1998Mortenson & Witt, 1998 Teacher performance feedbackTeacher performance feedback
Noell et al., 2005Noell et al., 2005
Why do we like graphs so much?Why do we like graphs so much?
Seeing is believing!Seeing is believing! A picture is worth a thousand words!A picture is worth a thousand words! People rememberPeople remember
Speeches that included visuals, especially in color, Speeches that included visuals, especially in color, improved immediate recall by 8.5% and delayed recall improved immediate recall by 8.5% and delayed recall (3 days) by 10.1% (Vogel, Dickson, & Lehman, 1990)(3 days) by 10.1% (Vogel, Dickson, & Lehman, 1990)
Visual aids are more effective for communicating Visual aids are more effective for communicating large amounts of information quicklylarge amounts of information quickly
Transcend language barriers (Karwowski, 2006)Transcend language barriers (Karwowski, 2006)
Is Is seeing seeing enough?enough?
If there are only two data points, basic If there are only two data points, basic slope calculation is accurate.slope calculation is accurate.
Chart Title
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y = x + 1
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Why do I need to know ROI?Why do I need to know ROI?
This is also how to calculate an aimline.This is also how to calculate an aimline.
Chart Title
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Why Bother with all the Data?Why Bother with all the Data?
If there are multiple data points, should you calculate the If there are multiple data points, should you calculate the slope between the first and last data points only?slope between the first and last data points only?
Chart Title
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ROI in Educational DecisionsROI in Educational Decisions
DataData
(slope)(slope)
InterpretationInterpretation
(progress?)(progress?)
DecisionDecision
Instructional NeedInstructional Need
Quick Stretch of the MindQuick Stretch of the Mind
DataData Benchmark: 77Benchmark: 77 Diego: 41Diego: 41
InterpretationInterpretation NOT GOOD! NOT GOOD!
DecisionDecision ??? ???
Will Diego catch up?Will Diego catch up? Do you have enough Do you have enough
info?info?
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Quick Stretch of the MindQuick Stretch of the Mind
DataData Benchmark: 77, 92Benchmark: 77, 92 Diego: 41, 62, 63Diego: 41, 62, 63
InterpretationInterpretation Slightly better Slightly better
DecisionDecision ??? ???
Will Diego catch up?Will Diego catch up? Do you have enough Do you have enough
info?info?
Diego's Progress
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Quick Stretch of the MindQuick Stretch of the Mind
DataData Benchmark: 77, 92Benchmark: 77, 92 Diego: 41 … 104Diego: 41 … 104
InterpretationInterpretation Good work Good work
DecisionDecision Cured!!!Cured!!!
Will Diego maintain Will Diego maintain that progress?that progress?
Diego's Progress
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1 4 7 10 13 16 19 22 25 28 31 34
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Quick Stretch of the MindQuick Stretch of the Mind
DataData Benchmark: 77, 92Benchmark: 77, 92 Diego: 41 … 74Diego: 41 … 74
InterpretationInterpretation UmmmUmmm
DecisionDecision Uh oh…Uh oh…
What EXACTLY IS What EXACTLY IS Diego’s Progress??Diego’s Progress??
Diego's Progress
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Now can you make a decision?Now can you make a decision?
Diego's Progress
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Diego
Diego's ROI
Goal Slope
Rationale for Importance of ROIRationale for Importance of ROI
Shift from discrepancy to RtI for SLD Shift from discrepancy to RtI for SLD eligibility determinationeligibility determination
Use of ROI to determine lack of RtIUse of ROI to determine lack of RtIQuestions to be Empirically AnsweredQuestions to be Empirically Answered
What parameters of ROI indicate lack of RtI?What parameters of ROI indicate lack of RtI?How does ROI present between SLD and How does ROI present between SLD and
non-SLD?non-SLD?What are reasonable goals using ROI?What are reasonable goals using ROI?
Rationale for Importance of ROIRationale for Importance of ROI
School School psychological psychological practices including practices including more CBM as a more CBM as a result of IDEA result of IDEA 2004 and NCLB 2004 and NCLB 20012001
CBM is great CBM is great because:because:
ComparisonsComparisons Dual discrepancyDual discrepancy EfficientEfficient Federal regulationsFederal regulations GraphGraph GOMGOM Goal settingGoal setting Instructional planningInstructional planning Multi-tiered assessmentMulti-tiered assessment Match instructional levelMatch instructional level Norms availableNorms available ParentsParents Progress monitoringProgress monitoring Survey level assessmentsSurvey level assessments Sensitive to changeSensitive to change ScreeningScreening Systems-levelSystems-level Technically adequateTechnically adequate
Rate of ImprovementRate of Improvement
Algebraic terms:Algebraic terms: slope is the change in the output because of the input, slope is the change in the output because of the input,
over timeover time a way of looking at growtha way of looking at growth
Aimline: expected performanceAimline: expected performance Trendline: actual performanceTrendline: actual performance
Definitions: Definitions: Fuchs and Fuchs (1998)Fuchs and Fuchs (1998) Batsche, Castillo, Dixon, and Forde (2008) Batsche, Castillo, Dixon, and Forde (2008)
Rate of ImprovementRate of Improvement
Shapiro (2008)Shapiro (2008) Criteria for setting reasonable, achievable, and Criteria for setting reasonable, achievable, and
ambitious goalsambitious goals
Fuchs, Fuchs, Hamlett, Walz, and Germann Fuchs, Fuchs, Hamlett, Walz, and Germann (1993)(1993) weekly rates of growth in curriculum-based weekly rates of growth in curriculum-based
measurementsmeasurements slopes between 1.5 and 2.0 times that of their peers slopes between 1.5 and 2.0 times that of their peers
were most likely to remediate skill deficits with current were most likely to remediate skill deficits with current instructioninstruction
Functions of ROIFunctions of ROI
ComparisonsComparisons
peers/classpeers/class
local norms/districtlocal norms/district
national normsnational norms
Functions of ROIFunctions of ROI
A decision toolA decision tool
Shinn’s estimate for decision-making in RTI Shinn’s estimate for decision-making in RTI trainings in Pennsylvania (Kovaleski, 2008)trainings in Pennsylvania (Kovaleski, 2008)
Slope of 2.0x or greater (than expected slope, to Slope of 2.0x or greater (than expected slope, to close the gap)close the gap)
Rate of Improvement and RTIRate of Improvement and RTI
Fuchs and Fuchs (1998)Fuchs and Fuchs (1998)hallmark components of RTIhallmark components of RTI
ongoing formative assessmentongoing formative assessmentidentifying non-responsive studentsidentifying non-responsive studentstreatment fidelity of core / supplemental instructiontreatment fidelity of core / supplemental instruction““dual discrepancy”dual discrepancy”
a student performing at or greater than one standard a student performing at or greater than one standard deviation from typically performing peers in deviation from typically performing peers in
(a) level (i.e., grade) and (a) level (i.e., grade) and (b) rate (b) rate (slope)(slope)
Eligibility and ROIEligibility and ROI
School psychologistsSchool psychologistsAdopt use of additional information (CBM!)Adopt use of additional information (CBM!) ““Snapshot” dataSnapshot” data
Good day, bad day dataGood day, bad day data
VersusVersus
Data continuously collected over timeData continuously collected over timeData that accounts for good days and bad days!Data that accounts for good days and bad days!
Eyeball the graph vs. decision guidelinesEyeball the graph vs. decision guidelines
Determining SLD in an RTI ModelDetermining SLD in an RTI Model
Gresham, 2001Gresham, 2001RTI is viable alternative for identifying learning RTI is viable alternative for identifying learning
disabilitiesdisabilitiesStuebing, Fletcher, LeDoux, Lyon, Stuebing, Fletcher, LeDoux, Lyon,
Shaywitz, & Shaywitz, 2002Shaywitz, & Shaywitz, 2002Poor reliability and validity of discrepancy Poor reliability and validity of discrepancy
modelmodel
Determining SLD in an RTI ModelDetermining SLD in an RTI Model
Gresham, 2001Gresham, 20013 models of RTI3 models of RTI
predictor-criterionpredictor-criteriondual discrepancydual discrepancyapplied behavior analyticapplied behavior analytic
Determining SLD in an RTI ModelDetermining SLD in an RTI Model
Gresham, 2001Gresham, 2001All three models involved:All three models involved:
multiple tiers of interventionmultiple tiers of interventionprogress monitoringprogress monitoringeffective instructional strategieseffective instructional strategies
support for applying the RTI model to support for applying the RTI model to identifying students for learning identifying students for learning disabilitiesdisabilities
Eligibility and ROIEligibility and ROI
Deno, Fuchs, Marston, and Shin, 2001Deno, Fuchs, Marston, and Shin, 2001slopes of children identified as frequently non-slopes of children identified as frequently non-
responsive to robust interventions responsive to robust interventions approximated the slopes of children already approximated the slopes of children already identified as having a specific learning identified as having a specific learning disabilitydisability
supportive evidence for dual-discrepancy supportive evidence for dual-discrepancy model model
Summary of ROI ResearchSummary of ROI Research
Through an RTI model, students receive Through an RTI model, students receive instruction based on data. Rate of instruction based on data. Rate of improvement, or slope, has surfaced in the improvement, or slope, has surfaced in the literature as an indicator for making literature as an indicator for making instructional decisions. instructional decisions.
Although research is expanding in terms of Although research is expanding in terms of reliability and validity for both RTI and reliability and validity for both RTI and ROI, extant studies allude to strong utility ROI, extant studies allude to strong utility for educational planning. for educational planning.
Skills Typically GraphedSkills Typically Graphed ReadingReading
Oral Reading Fluency (ORF)Oral Reading Fluency (ORF) Word Use Fluency (WUF)Word Use Fluency (WUF) Reading ComprehensionReading Comprehension
MAZEMAZE Retell FluencyRetell Fluency
Early Literacy SkillsEarly Literacy Skills Initial Sound Fluency (ISF)Initial Sound Fluency (ISF) Letter Naming Fluency (LNF)Letter Naming Fluency (LNF) Letter Sound Fluency (LSF)Letter Sound Fluency (LSF) Phoneme Segmentation Fluency Phoneme Segmentation Fluency
(PSF)(PSF) Nonsense Word Fluency (NWF)Nonsense Word Fluency (NWF)
SpellingSpelling Written Expression Written Expression BehaviorBehavior
MathMath Math ComputationMath Computation Math FactsMath Facts Early NumeracyEarly Numeracy
Oral CountingOral Counting Missing NumberMissing Number Number Number
IdentificationIdentification Quantity Quantity
DiscriminationDiscrimination
Get out your laptops!Get out your laptops!
Open Microsoft ExcelOpen Microsoft Excel
I loveROI
Setting Up Your SpreadsheetSetting Up Your Spreadsheet
Open Microsoft ExcelOpen Microsoft Excel In cell B2, type In cell B2, type School School
Week Week to represent the to represent the weeks of schoolweeks of school
In cell C2, type In cell C2, type BenchmarkBenchmark to to represent the represent the benchmarks or goals benchmarks or goals of the skill you are of the skill you are graphinggraphing
In cell D2, type In cell D2, type WPMWPM to represent Words to represent Words Per Minute (or an Per Minute (or an abbreviation the basic abbreviation the basic skill you are graphing)skill you are graphing)
Labeling School WeeksLabeling School Weeks
In cell B3, type In cell B3, type 11 to to represent the first represent the first week of schoolweek of school
Continue numbering Continue numbering to 36 in column 2to 36 in column 2
Why 36? There’s Why 36? There’s typically 36 school typically 36 school weeks per school weeks per school year.year.
Finish at cell B38Finish at cell B38
Entering Benchmarks/GoalsEntering Benchmarks/Goals In cell C3, type the In cell C3, type the
numbernumber that represents that represents the fall benchmark the fall benchmark (months 1-3) of the skill (months 1-3) of the skill you are graphing (e.g., you are graphing (e.g., 77). This score should be 77). This score should be next to school week 1.next to school week 1.
In cell C20, type the In cell C20, type the numbernumber that represents that represents the winter benchmark the winter benchmark (months 4-6) of the skill (months 4-6) of the skill you are graphing (e.g., you are graphing (e.g., 92). This score should be 92). This score should be next to school week 18. next to school week 18.
In cell C38, type the In cell C38, type the numbernumber that represents that represents the spring benchmark the spring benchmark (months 7-10) of the skill (months 7-10) of the skill you are graphing (e.g., you are graphing (e.g., 110). This score should be 110). This score should be next to school week 36.next to school week 36.
Entering Student ScoresEntering Student Scores
In cells D3 through D38 In cells D3 through D38 type the type the number number that that represents the score the represents the score the student achieved during student achieved during that week of the school that week of the school year. year.
If a student was not If a student was not assessed during a certain assessed during a certain week of the school year, week of the school year, leave that cell leave that cell blankblank**..
Entering Student ScoresEntering Student Scores
*Do NOT enter zero (0)*Do NOT enter zero (0) or a or a score of zero will be calculated score of zero will be calculated into the trend line and interpreted into the trend line and interpreted as the student having read zero as the student having read zero words correct per minute that words correct per minute that week.week.
Creating a GraphCreating a Graph Highlight the data in Highlight the data in
columns C and D.columns C and D. Left click with mouse in Left click with mouse in
cell C2. cell C2. While holding down While holding down
mouse, highlight mouse, highlight columns C and D from columns C and D from row 2 through row 38. row 2 through row 38.
These will be your data These will be your data points contributing to points contributing to your graph. your graph.
The selection should The selection should include the blank cells include the blank cells in column C.in column C.
Creating a GraphCreating a Graph
Left click “Insert” in Left click “Insert” in the tool bar (typically the tool bar (typically in the top row) while in the top row) while columns C and D are columns C and D are still highlighted.still highlighted.
Left click “Chart” in Left click “Chart” in the drop-down menu. the drop-down menu. A “Chart Wizard” A “Chart Wizard” window will appear.window will appear.
Creating a GraphCreating a Graph
In the Chart Wizard In the Chart Wizard are two tabs. Make are two tabs. Make sure you are in the sure you are in the left tab, “Standard left tab, “Standard Types.”Types.”
Next, you want to left Next, you want to left click on the “Line” click on the “Line” graph on the left side graph on the left side of your Chart Wizard.of your Chart Wizard.
Creating a GraphCreating a Graph
On the right side is On the right side is “Chart sub-type.” Choose “Chart sub-type.” Choose the graph with the the graph with the description “Line with description “Line with markers displayed at markers displayed at each data value.” This each data value.” This option is typically the first option is typically the first graph icon in the second graph icon in the second row. row.
Left click “Next” at the Left click “Next” at the bottom of your Chart bottom of your Chart Wizard. Wizard.
Creating a GraphCreating a Graph
The upper left The upper left tab says “Data tab says “Data Range.” The Range.” The bottom half of bottom half of that tab has that tab has your data range your data range and series type. and series type. You want to You want to select select “Columns.”“Columns.”
Creating a GraphCreating a Graph
The top right tab is The top right tab is labeled “Series.” Left click labeled “Series.” Left click on “Series” on “Series”
The top half of the The top half of the “Series” tab has an icon “Series” tab has an icon of your graph. The bottom of your graph. The bottom half shows you the label half shows you the label your data for the legend. your data for the legend.
Left click “Next” at the Left click “Next” at the bottom of your Chart bottom of your Chart Wizard.Wizard.
Creating a GraphCreating a Graph The next options include tabs The next options include tabs
for Titles, Axes, Gridlines, etc. for Titles, Axes, Gridlines, etc. If you would like to title your If you would like to title your
chart, left click on the “Titles” chart, left click on the “Titles” tab. Enter a title (i.e., tab. Enter a title (i.e., Diego’s Diego’s Rate of ImprovementRate of Improvement) in the ) in the first box.first box.
Enter a description in the Enter a description in the Category (X) Axis, which is Category (X) Axis, which is your number of school weeks. your number of school weeks. Suggestion: Suggestion: School Week School Week
Enter a description in your Enter a description in your Value (Y) Axis, which is the Value (Y) Axis, which is the number of the skill you are number of the skill you are graphing. Suggestion: graphing. Suggestion: Words Words Per Minute.Per Minute.
Left click “Next” at the bottom Left click “Next” at the bottom of your Chart Wizard.of your Chart Wizard.
Numerical Label to Data Points Numerical Label to Data Points
Click on “Data Labels”Click on “Data Labels” Click to put a check Click to put a check
mark next to “Value”mark next to “Value” Click on the “Next” Click on the “Next”
ButtonButton
Note: This can clutter Note: This can clutter your graph but your graph but provide useful info.provide useful info.
Creating a GraphCreating a Graph Left click the bottom circle to choose “As Left click the bottom circle to choose “As
object in: …” This will put the graph in the object in: …” This will put the graph in the worksheet you have open. worksheet you have open.
Left click “Finish” in your Chart Wizard. This Left click “Finish” in your Chart Wizard. This will place your graph in your Excel Document.will place your graph in your Excel Document.
- OR -- OR -
Creating a GraphCreating a Graph You can choose to have the graph created in a new You can choose to have the graph created in a new
worksheet within your Excel document. worksheet within your Excel document. Click next to “As new sheet…” Click next to “As new sheet…” Label the worksheet by clicking on the tab at the bottom of the Label the worksheet by clicking on the tab at the bottom of the
sheet and typing a name (i.e., sheet and typing a name (i.e., Diego’s GraphDiego’s Graph)) Left click “Finish” in your Chart Wizard. This will place your Left click “Finish” in your Chart Wizard. This will place your
graph in a new sheet in your Excel Document.graph in a new sheet in your Excel Document.
Creating a GraphCreating a Graph
Resizing the GraphResizing the Graph
You may resize the graph by clicking in You may resize the graph by clicking in any white space within your graph any white space within your graph which will bring up squares at the which will bring up squares at the corners of your graph. corners of your graph.
You can put your mouse over these You can put your mouse over these squares and drag the graph to a size squares and drag the graph to a size you prefer. you prefer.
Keep in mind that a large graph may not Keep in mind that a large graph may not print easily.print easily.
Coloring the GraphColoring the Graph
Right click in the gray Right click in the gray area and a drop down area and a drop down menu appearsmenu appears
Click on “Format Plot Click on “Format Plot Area”Area”
Coloring the GraphColoring the Graph
The Format Plot Area The Format Plot Area menu appears. menu appears.
To eliminate a color To eliminate a color border, click next to border, click next to “None”“None”
To eliminate a color To eliminate a color plot area, click next to plot area, click next to “None” or choose a “None” or choose a color.color.
Click “OK”Click “OK”
Coloring Data PointsColoring Data Points
Right click on the data Right click on the data points for which you points for which you would like to change would like to change the colorthe color
Click on “Format Data Click on “Format Data Series”Series”
Choose the Choose the foreground, foreground, background, and line background, and line colorcolor
Adding TrendlinesAdding Trendlines RIGHT click on any of the student’s scores/data RIGHT click on any of the student’s scores/data
points within your graph.points within your graph. Left click “Add Trendline” from the menu that Left click “Add Trendline” from the menu that
appears.appears.
Adding TrendlinesAdding Trendlines
Under the “Type” tab, Under the “Type” tab, click on “Linear.”click on “Linear.”
Under the “Options” tab, click Under the “Options” tab, click next to “Custom” and type next to “Custom” and type “Diego’s ROI” “Diego’s ROI”
Click by “Display Equation…”Click by “Display Equation…” Click “OK”Click “OK”
Adding TrendlinesAdding Trendlines
Left clicking on the equation will highlight a Left clicking on the equation will highlight a “box” around it, and clicking on that box “box” around it, and clicking on that box will allow you to move the equation above will allow you to move the equation above the chart legend to see it better.the chart legend to see it better.
Adding TrendlinesAdding Trendlines Repeat this process for the other set of data – your Repeat this process for the other set of data – your
benchmarks. Begin by right clicking on any of your three benchmarks. Begin by right clicking on any of your three goal data points. goal data points.
For your benchmark data, label the trendline title For your benchmark data, label the trendline title “Expected Slope”“Expected Slope”
Click next to “Display equation on chart”Click next to “Display equation on chart” Click “OK”Click “OK”
Adding TrendlinesAdding Trendlines
Move your equation under the first oneMove your equation under the first one
Lines, Lines, LinesLines, Lines, LinesDiego's Rate of Improvement
y = 1.6317x + 50.928
y = 0.9434x + 75.704
0
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Diego's Scores (3rd)
Diego's ROI
Goal Slope
Cautions in Interpreting SlopeCautions in Interpreting Slope(my disclaimer!)(my disclaimer!)
The graph depicts the actual scores as data points on The graph depicts the actual scores as data points on the graph.the graph.
You can change the size of the font for the numeric You can change the size of the font for the numeric values by right clicking on any of them and choosing a values by right clicking on any of them and choosing a smaller font size. This may reduce some of the clutter on smaller font size. This may reduce some of the clutter on your graph.your graph.
The rate of improvement, or trendline, is calculated using The rate of improvement, or trendline, is calculated using a linear regression, a simple equation of least squares. a linear regression, a simple equation of least squares. This line takes into account each score entered to This line takes into account each score entered to portray an average rate of improvement across school portray an average rate of improvement across school weeks.weeks.
The equation indicates the slope, or rate of The equation indicates the slope, or rate of improvement. The number, or coefficient,improvement. The number, or coefficient, beforebefore "x" is "x" is the average improvement, which in this case is the the average improvement, which in this case is the average number of words per minute per week gained average number of words per minute per week gained by the student. by the student.
Cautions in Interpreting SlopeCautions in Interpreting Slope(my disclaimer continued!)(my disclaimer continued!)
The slope can change depending on which week (where) The slope can change depending on which week (where) you put the benchmark scores on your chart. Enter you put the benchmark scores on your chart. Enter benchmark scores based on when your school benchmark scores based on when your school administers their benchmark assessments for the most administers their benchmark assessments for the most accurate depiction of expected student progress. accurate depiction of expected student progress.
To add additional progress monitoring/benchmark scores To add additional progress monitoring/benchmark scores once you’ve already created a graph, enter additional once you’ve already created a graph, enter additional scores in Column D in the corresponding school week. scores in Column D in the corresponding school week. Remember to leave cells blank for the weeks that no Remember to leave cells blank for the weeks that no score was obtained. The graph will incorporate that score was obtained. The graph will incorporate that score into the set of data points and into the trendline. score into the set of data points and into the trendline.
Program Excel to Calculate ROIProgram Excel to Calculate ROI
Type “ROI” in cell B39 Type “ROI” in cell B39 (below your last week (below your last week of school)of school)
Program Excel to Calculate ROIProgram Excel to Calculate ROI
To calculate the To calculate the expected slope as per expected slope as per the benchmarks:the benchmarks:
Click on cell C39Click on cell C39 Put your cursor at the Put your cursor at the
top next to the top next to the fxfx Type:Type:
=SLOPE(C3:C38,B3:B38)=SLOPE(C3:C38,B3:B38)
Hit Enter/ReturnHit Enter/Return
Program Excel to Calculate ROIProgram Excel to Calculate ROI
To calculate the To calculate the student’s slope:student’s slope:
Click on cell D39Click on cell D39 Put your cursor at the Put your cursor at the
top next to the top next to the fxfx Type:Type:
=SLOPE(D3:D38,B3:B38)=SLOPE(D3:D38,B3:B38)
Hit Enter/ReturnHit Enter/Return
ROI as a Decision ToolROI as a Decision Toolwithin a Problem-Solving Modelwithin a Problem-Solving Model
StepsSteps
1.1. Gather the dataGather the data
2.2. Ground the dataGround the data
3.3. Interpret the dataInterpret the data
4.4. Figure out how to fit Best Practice into Figure out how to fit Best Practice into Public EducationPublic Education
Step 1: Gather DataStep 1: Gather Data
Universal Screening Universal Screening
Progress MonitoringProgress Monitoring
Common Screenings in PACommon Screenings in PA
DIBELSDIBELSAIMSwebAIMSwebMBSPMBSP4Sight4SightPSSAPSSA
Validated Progress Validated Progress Monitoring ToolsMonitoring Tools
DIBELSDIBELSAIMSwebAIMSwebMBSPMBSP www.studentprogress.orgwww.studentprogress.org
Step 2: Ground the DataStep 2: Ground the Data
To what will we compare our To what will we compare our student growth data?student growth data?
Multiple Ways to Multiple Ways to Look at GrowthLook at Growth
Needed Growth Needed Growth Expected Growth & Percent of Expected Expected Growth & Percent of Expected
GrowthGrowthFuchs et. al. (1993) Table of Realistic and Fuchs et. al. (1993) Table of Realistic and
Ambitious GrowthAmbitious GrowthGrowth Toward Individual Goal*Growth Toward Individual Goal*
*Best Practices in Setting Progress Monitoring Goals for Academic Skill Improvement (Shapiro, 2008)*Best Practices in Setting Progress Monitoring Goals for Academic Skill Improvement (Shapiro, 2008)
Tigard-Tualatin School District (www.ttsd.k12.or.us)Tigard-Tualatin School District (www.ttsd.k12.or.us)
Looking at Percent of Looking at Percent of Expected GrowthExpected Growth
Tier ITier I Tier IITier II Tier IIITier III
Greater than Greater than 150%150%
Between Between 110% & 150%110% & 150%
Possible LDPossible LD
Between 95% Between 95% & 110%& 110%
Likely LDLikely LD
Between 80% Between 80% & 95%& 95%
May Need May Need MoreMore
May Need May Need MoreMore
Likely LDLikely LD
Below 80%Below 80% Needs MoreNeeds More Needs MoreNeeds More Likely LDLikely LD
Fuchs, Fuchs, Hamlett, Walz, & Germann (1993)Fuchs, Fuchs, Hamlett, Walz, & Germann (1993)
Oral Reading Fluency Adequate Oral Reading Fluency Adequate Response TableResponse Table
Realistic Realistic GrowthGrowth
Ambitious Ambitious GrowthGrowth
11stst 2.02.0 3.03.0
22ndnd 1.51.5 2.02.0
33rdrd 1.01.0 1.51.5
44thth 0.90.9 1.11.1
55thth 0.50.5 0.80.8
Fuchs, Fuchs, Hamlett, Walz, & Germann (1993)Fuchs, Fuchs, Hamlett, Walz, & Germann (1993)
Digit Fluency Adequate Digit Fluency Adequate Response TableResponse Table
Realistic Realistic GrowthGrowth
Ambitious Ambitious GrowthGrowth
11stst 0.30.3 0.50.5
22ndnd 0.30.3 0.50.5
33rdrd 0.30.3 0.50.5
44thth 0.750.75 1.21.2
55thth 0.750.75 1.21.2
Oral Reading Fluency01/15/09 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 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Benchmark 68 90 1.29
Aiden 61 40 52 60 71 95 1.61 2.17 167%
Ava 49 43 49 77 57 54 87 92 2.28 2.76 213%
Noah 49 48 45 69 61 54 84 2.28 2.01 156%
Olivia 65 49 57 70 79 83 1.39 1.50 116%
Liam 55 53 36 54 70 83 1.94 1.58 122%
Hannah 59 54 64 69 52 60 82 1.72 1.20 93%
Gavin 64 40 67 68 84 79 1.44 1.66 129%
Grace 53 48 46 60 74 79 2.06 1.76 136%
Oliver 50 44 46 68 51 51 57 78 2.22 1.45 112%
Peyton 63 50 47 58 75 77 1.50 1.12 87%
Josh 49 38 49 55 48 36 67 77 2.28 1.62 125%
Riley 42 49 54 69 67 50 76 2.67 1.76 136%
Mason 53 53 50 64 60 74 2.06 1.17 91%
Zoe 34 38 42 68 55 51 58 3.11 1.44 111%
Ian 41 31 45 49 47 30 46 2.72 0.24 19%
Faith 29 36 35 36 36 29 45 44 3.39 0.75 58%
David 30 23 44 52 43 19 63 38 3.33 0.79 61%
Alexa 18 19 25 33 33 23 28 37 4.00 0.94 73%
Hunter 23 23 24 48 38 32 34 3.72 0.75 58%
Caroline 28 20 28 40 37 19 25 30 3.44 0.02 2%
** Actual RoI based on linear regression of all data points
Benchmarks based on DIBELS Goals
Expected RoI at Benchmark Level
(Fuchs, Fuchs, Hamlett, Walz, & Germann 1993)
% of Expected RoI
Needed RoI* Actual RoI**
Realistic Grow thAmbitious Grow th
Oral Reading Fluency Adequate Response Table
1st Grade
2nd Grade
* Needed RoI based on difference betw een w eek 1 score and Benchmark score for w eek 18 divided by 18 w eeks
0.5
3rd Grade
4th Grade
5th Grade
0.9
0.8
2.0
1.5
1.0
3.0
2.0
1.5
1.1
Step 3: Interpreting GrowthStep 3: Interpreting Growth
What do we do when we do not What do we do when we do not get the growth we want?get the growth we want?
When to make a change in instruction and When to make a change in instruction and intervention?intervention?
When to considered SLD?When to considered SLD?
When to make a change in When to make a change in instruction and intervention?instruction and intervention?
Enough data points (6 to 10)?Enough data points (6 to 10)?Less than 100% of expected growth.Less than 100% of expected growth.Not on track to make benchmark (needed Not on track to make benchmark (needed
growth).growth).Not on track to reach individual goal.Not on track to reach individual goal.
When to consider SLD?When to consider SLD?
Continued inadequate response despite: Continued inadequate response despite: Fidelity with Tier I instruction and Tier II Fidelity with Tier I instruction and Tier II
intervention.intervention. Multiple attempts at intervention.Multiple attempts at intervention. Individualized Problem-Solving Individualized Problem-Solving
approach. approach.
Whole Class ExampleWhole Class ExampleComputation
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
50th P ercentile 25 31 0.35
25th P ercentile 19 23 0.24
Student 6.5 9 8 8.5 5.5 11 13 1.72 0.61 173%
Student 6 7.5 8.5 5 11 11.5 1.72 0.57 161%
Student 4.5 5.5 6.5 9.5 10.5 1.72 1.06 300%
Student 13 8 9.3 8 5.6 9.6 9.6 1.72 -0.23 -66%
Student 8 10.5 10.5 5.6 9.3 9 1.72 -0.03 -7%
Student 8.5 5.5 9 8 4 8 9 1.72 0.07 21%
Student 6.5 5.5 6 10.5 9 1.72 0.43 122%
Student 6.5 9 4.5 6 8 1.72 0.07 20%
Student 8 10.5 4.5 6.5 4 7 1.72 -0.25 -71%
Student 9 10 5.6 6.6 5 4.6 6.6 1.72 -0.42 -119%
Student 8 8 8.5 4 8 6.6 1.72 -0.18 -51%
Student 9 4.5 4.5 4 3.5 3.5 6.5 1.72 -0.24 -67%
Student 6.5 5 6.5 9 7.5 6.5 1.72 0.09 26%
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 6 5 2.5 3.5 5.5 1.72 -0.03 -8%
Student 5.5 4.5 10.5 11 5 5.3 1.72 -0.14 -40%
* Needed RoI based on difference betw een w eek 1 score and Benchmark score for w eek 18 divided by 18 w eeks
** Actual RoI based on linear regression of all data points
Percentiles based on AIMSw eb Grow th Tables
Expected RoI at 50th PercentileExpected RoI at 25th Percentile
Needed RoI* Actual RoI** % of Expected RoI
Digit Fluency Adequate Response Table
Realistic Grow thAmbitious Grow th
1st Grade 0.3 0.5
2nd Grade 0.3 0.5
3rd Grade 0.3 0.5
(Fuchs, Fuchs, Hamlett, Walz, & Germann 1993)
4th Grade 0.75 1.2
5th Grade 0.75 1.2
33rdrd Grade Math Whole Class Grade Math Whole Class
Who’s responding? Who’s responding? Effective math Effective math
instruction? instruction? Who needs more?Who needs more?
N=19N=194 > 100% growth 4 > 100% growth 15 < 100% growth15 < 100% growth9 w/ negative 9 w/ negative
growthgrowth
Small Group ExampleSmall Group ExampleOral 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
Benchmark 44 68 1.41
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%
** Actual RoI based on linear regression of all data points
Benchmarks based on DIBELS Goals
Expected RoI at Benchmark Level
(Fuchs, Fuchs, Hamlett, Walz, & Germann 1993)
5th Grade
* Needed RoI based on difference betw een w eek 1 score and Benchmark score for w eek 18 divided by 18 w eeks
% of Expected RoI
2nd Grade
0.9 1.1
3rd Grade
4th Grade
0.5 0.8
1.5 2.0
1.0 1.5
Needed RoI* Actual RoI**
2.0 3.0
Oral Reading Fluency Adequte Response Table
1st Grade
Realistic Grow thAmbitious Grow th
Intervention GroupIntervention Group
Intervention working for how many?Intervention working for how many?Can we assume fidelity of intervention Can we assume fidelity of intervention
based on results?based on results?Who needs more?Who needs more?
Individual Kid ExampleIndividual Kid Example 2nd Grade Reading Progress
44
68
90
31
56
45
53 53
4846
60
74
79
y = 1.5333x + 42.8
y = 0.9903x + 36.873
0
10
20
30
40
50
60
70
80
90
100
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 01/23/0901/30/0902/06/0902/13/0902/20/0902/27/0903/06/0903/13/0903/20/0903/27/0904/03/0904/10/0904/17/0904/24/0905/01/09
Wo
rds
Re
ad
Co
rre
ct
Pe
r M
inu
te
Benchmark Linear (Benchmark) Linear
Individual KidIndividual Kid
Making growth?Making growth?How much (65% of expected growth).How much (65% of expected growth).Atypical growth across the year (last 3 Atypical growth across the year (last 3
data points). data points). Continue? Make a change? Need more Continue? Make a change? Need more
data?data?
Step 4: Figure out how to fit Step 4: Figure out how to fit Best Practice into Public Best Practice into Public
EducationEducation
Things to ConsiderThings to Consider
Who cares about Rate of Improvement?Who cares about Rate of Improvement?Who is At-Risk and needs progress Who is At-Risk and needs progress
monitoring?monitoring?Who will collect, score, enter the data?Who will collect, score, enter the data?Who will monitor student growth, when, Who will monitor student growth, when,
and how often?and how often?What changes should be made to What changes should be made to
instruction & intervention? instruction & intervention?
Who cares about Rate of Who cares about Rate of Improvement?Improvement?
Explaining the concept of RoI.Explaining the concept of RoI.Creating buy-in with ORF, M-CBM, etc. Creating buy-in with ORF, M-CBM, etc. Defending frequent data collection (the Defending frequent data collection (the
“we spend too much time testing and not “we spend too much time testing and not enough time teaching” argument).enough time teaching” argument).
Who is At-Risk and needs Who is At-Risk and needs progress monitoring?progress monitoring?
Below level on universal screeningBelow level on universal screening
Entering 4Entering 4thth Grade Example Grade Example
DORF DORF (110)(110)
ISIP ISIP TRWM TRWM
(55)(55)
4Sight 4Sight (1235)(1235)
PSSA PSSA (1235)(1235)
Student AStudent A 115115 5858 12551255 12321232
Student BStudent B 8585 4848 12161216 11261126
Student CStudent C 7272 3535 10561056 10481048
Who will collect, score, and Who will collect, score, and enter the data?enter the data?
Using MBSP for math, teachers can Using MBSP for math, teachers can administer probes to whole class.administer probes to whole class.
DORF probes must be administered one-DORF probes must be administered one-on-one, and creativity pays off (train and on-one, and creativity pays off (train and use art, music, library, etc. specialists).use art, music, library, etc. specialists).
Schedule for progress monitoring math Schedule for progress monitoring math and reading every-other week.and reading every-other week.
Week 1Week 1 Week 2Week 2
ReadingReading MathMath ReadingReading MathMath
11stst XX XX
22ndnd XX XX
33rdrd XX XX
44thth XX XX
55thth XX XX
Who will monitor student Who will monitor student growth, when, and how often?growth, when, and how often?
Best Practices in Data-Analysis Teaming Best Practices in Data-Analysis Teaming (Kovaleski & Pedersen, 2008)(Kovaleski & Pedersen, 2008)
Chambersburg Area School District Chambersburg Area School District Elementary Response to Intervention Elementary Response to Intervention Manual (McCrea et. al., 2008)Manual (McCrea et. al., 2008)
Derry Township School District Response Derry Township School District Response to Intervention Model to Intervention Model (http://www.hershey.k12.pa.us/56039310111408/lib/56039310111408/_files/(http://www.hershey.k12.pa.us/56039310111408/lib/56039310111408/_files/Microsoft_Word_-Microsoft_Word_-_Response_to_Intervention_Overview_of_Hershey_Elementary_Model.pdf)_Response_to_Intervention_Overview_of_Hershey_Elementary_Model.pdf)
What changes should be made What changes should be made to instruction & intervention?to instruction & intervention?
Ensure treatment fidelity!!!!!!!!Ensure treatment fidelity!!!!!!!! Increase instructional time (active and Increase instructional time (active and
engaged)engaged)Decrease group sizeDecrease group sizeGather additional, diagnostic, informationGather additional, diagnostic, informationChange the intervention Change the intervention
RoI and Behavior?RoI and Behavior?
Percent of Time Engaged in Appropriate Behavior
y = 2x + 22
y = 3.9x + 19.8
y = 7.2143x - 1.5
0
10
20
30
40
50
60
70
80
90
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Per
cen
t
Baseline Condition 1 Condition 2 Linear (Baseline) Linear (Condition 1) Linear (Condition 2) Linear (Condition 2)
Check These OutCheck These Out
www.interventioncentral.comwww.interventioncentral.com
www.aimsweb.comwww.aimsweb.com
http://dibels.uoregon.eduhttp://dibels.uoregon.edu
www.nasponline.orgwww.nasponline.org
Check These OutCheck These Out
www.fcrr.orgwww.fcrr.org
Florida Center for Reading ResearchFlorida Center for Reading Research http://ies.ed.gov/ncee/wwc//http://ies.ed.gov/ncee/wwc//
What Works ClearinghouseWhat Works Clearinghouse http://sites.google.com/site/rateofimprovement/http://sites.google.com/site/rateofimprovement/
Rate of Improvement Rate of Improvement http://www.rti4success.orghttp://www.rti4success.org
National Center on RtINational Center on RtI
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