Calculating and Interpreting Slope: Implications for School Psychologists Caitlin S. Flinn, Ed.S. & Andrew E. McCrea, M.S., NCSP ASPP/PSU Conference October

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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Data1

Trendline1

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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y = x + 1

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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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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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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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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


Gresham, 2001Gresham, 20013 models of RTI3 models of RTI

predictor-criterionpredictor-criteriondual discrepancydual discrepancyapplied behavior analyticapplied behavior analytic


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.


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.


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.


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.”


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.


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”


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”


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

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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)


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


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%



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


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

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%


Benchmarks based on DIBELS Goals

Expected RoI at Benchmark Level


5th Grade


% 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


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

ReferencesReferencesBatsche, G. M., Castillo, J. M., Dixon, D. N., & Forde, S. (2008). Best Batsche, G. M., Castillo, J. M., Dixon, D. N., & Forde, S. (2008). Best

practices in linking assessment to intervention. In A. Thomas and J. practices in linking assessment to intervention. In A. Thomas and J. Grimes (Eds.), Grimes (Eds.), Best practices in school psychology V.Best practices in school psychology V. (pp. 177-193). (pp. 177-193). Bethesda, MD: National Association of School Psychologists.Bethesda, MD: National Association of School Psychologists.

Batsche, G. M., Elliot, J., Graden, J. L., Kovaleski, J. F., Prasse, D., et al. Batsche, G. M., Elliot, J., Graden, J. L., Kovaleski, J. F., Prasse, D., et al. (2005). (2005). Response to intervention: Policy considerations and Response to intervention: Policy considerations and implementation.implementation. Alexandria, VA: National Association of School Alexandria, VA: National Association of School Psychologists. Psychologists.

Colvin, G., Sugai, G., Good, R. H., III, & Young-Yon, L. (1997). Using active Colvin, G., Sugai, G., Good, R. H., III, & Young-Yon, L. (1997). Using active supervision and precorrection to improve transition behaviors in an supervision and precorrection to improve transition behaviors in an elementary school. elementary school. School Psychology Quarterly, 12, School Psychology Quarterly, 12, 344-363. 344-363.

Deno, S. L. (1985). Curriculum-based measurement: The emerging Deno, S. L. (1985). Curriculum-based measurement: The emerging alternative. alternative. Exceptional Children, 52,Exceptional Children, 52, 219-232. 219-232.

Deno, S. L., & Fuchs, L. S. (1987). Developing curriculum-based Deno, S. L., & Fuchs, L. S. (1987). Developing curriculum-based measurement systems for databased special education problem solving. measurement systems for databased special education problem solving. Focus on Exceptional Children, 19Focus on Exceptional Children, 19(8), 1-15.(8), 1-15.

Deno, S. L., Fuchs, L.S., Marston, D., & Shin, J. (2001). Using curriculum-Deno, S. L., Fuchs, L.S., Marston, D., & Shin, J. (2001). Using curriculum-based measurement to establish growth standards for students with based measurement to establish growth standards for students with learning disabilities. learning disabilities. School Psychology Review, 30School Psychology Review, 30, 507-524., 507-524.

ReferencesReferencesFlinn, C. S. (2008). Graphing rate of improvement for individual students. Flinn, C. S. (2008). Graphing rate of improvement for individual students. InSight, InSight,

2828(3), 10-12.(3), 10-12.Fuchs, L. S., Fuchs, D., Hamlett, C. L., Walz, L., & Germann, G. (1993). Formative Fuchs, L. S., Fuchs, D., Hamlett, C. L., Walz, L., & Germann, G. (1993). Formative

evaluation of academic progress: How much growth can we expect? evaluation of academic progress: How much growth can we expect? School School Psychology Review, 22, Psychology Review, 22, 27-48. 27-48.

Fuchs, L. S., & Fuchs, D. (1998). Treatment validity: A unifying concept for Fuchs, L. S., & Fuchs, D. (1998). Treatment validity: A unifying concept for reconceptualizing the identification of learning disabilities. reconceptualizing the identification of learning disabilities. Learning Disabilities Learning Disabilities Research and Practice, 13Research and Practice, 13, 204-219. , 204-219.

Fuchs, L. S., & Fuchs, D. (1997) Use of curriculum-based measurement in identifying Fuchs, L. S., & Fuchs, D. (1997) Use of curriculum-based measurement in identifying students with learning disabilities. students with learning disabilities. Focus on Exceptional Children, 30, Focus on Exceptional Children, 30, 1–16.1–16.

Fuchs, L. S., Fuchs, D., Hamlett, C. L., Hope, S. K., Hollenback, K. N. Capizzi, A. M., Fuchs, L. S., Fuchs, D., Hamlett, C. L., Hope, S. K., Hollenback, K. N. Capizzi, A. M., Craddock, C. F., & Brothers, R. L. (2006). Extending responsiveness-to-Craddock, C. F., & Brothers, R. L. (2006). Extending responsiveness-to-intervention to math problem-solving at third grade. intervention to math problem-solving at third grade. Teaching Exceptional Teaching Exceptional Children, 38,Children, 38, 59-63. 59-63.

Gresham, F. (2001, August). Responsiveness to intervention: An alternative Gresham, F. (2001, August). Responsiveness to intervention: An alternative approach to the identification of learning disabilities. In R. Bradley, L. Danielson, approach to the identification of learning disabilities. In R. Bradley, L. Danielson, & D. P. Hallahan (Eds.). & D. P. Hallahan (Eds.). Identification of learning disabilities: Research in practice Identification of learning disabilities: Research in practice (pp. 467–519). Mahwah, NJ: Erlbaum.(pp. 467–519). Mahwah, NJ: Erlbaum.

Individuals with Disabilities Education Improvement Act (IDEIA) of 2004, Pub. L. No. Individuals with Disabilities Education Improvement Act (IDEIA) of 2004, Pub. L. No. 108,446.108,446.

ReferencesReferencesKovaleski, J. F. (2008, September 19). Kovaleski, J. F. (2008, September 19). Pennsylvania promotes best Pennsylvania promotes best

practices in school psychology.practices in school psychology. Paper presented at the Pennsylvania Paper presented at the Pennsylvania Training and Technical Assistance Network, King of Prussia, PA.Training and Technical Assistance Network, King of Prussia, PA.

Mortenson, B. P., & Witt, J. C. (1998). The use of weekly performance Mortenson, B. P., & Witt, J. C. (1998). The use of weekly performance feedback to increase teacher implementations of a prereferral academic feedback to increase teacher implementations of a prereferral academic intervention. intervention. School Psychology Review, 27, School Psychology Review, 27, 613-628.613-628.

No Child Left Behind Act of 2001. Pub. L. No. 107-110, 115 Stat. 1425 No Child Left Behind Act of 2001. Pub. L. No. 107-110, 115 Stat. 1425 (2002). (2002).

Noell, G. H., Witt, J. C., Slider, N. J., Connell, J. E., Giatti, S. L., Williams, Noell, G. H., Witt, J. C., Slider, N. J., Connell, J. E., Giatti, S. L., Williams, K. L., et al. (2005). Treatment implementation following behavior K. L., et al. (2005). Treatment implementation following behavior consultation in schools: A comparison of three follow-up strategies. consultation in schools: A comparison of three follow-up strategies. School Psychology Review, 34School Psychology Review, 34(1), 87-106.(1), 87-106.

Shapiro, E. S. (2008). Best practices in setting progress monitoring goals Shapiro, E. S. (2008). Best practices in setting progress monitoring goals for academic skill improvement. In A. Thomas and J. Grimes (Eds.), for academic skill improvement. In A. Thomas and J. Grimes (Eds.), Best practices in school psychology V Best practices in school psychology V (Vol. 2, pp. 141-157). Bethesda, (Vol. 2, pp. 141-157). Bethesda, MD: National Association of School Psychologists.MD: National Association of School Psychologists.

Shinn, M. R. (Ed.). (1998). Shinn, M. R. (Ed.). (1998). Advanced applications of curriculum-based Advanced applications of curriculum-based measurement. measurement. New York: Guilford Press.New York: Guilford Press.

ReferencesReferences

Shinn, M. R. (2008). Best practices in using curriculum-based Shinn, M. R. (2008). Best practices in using curriculum-based measurement in a problem-solving model. In A. Thomas and J. measurement in a problem-solving model. In A. Thomas and J. Grimes (Eds.), Grimes (Eds.), Best practices in school psychology V Best practices in school psychology V (Vol. 2, pp. (Vol. 2, pp. 243-261). Bethesda, MD: National Association of School 243-261). Bethesda, MD: National Association of School Psychologists. Psychologists.

Sulzer-Azaroff, B., & Mayer, G. R. (1991). Sulzer-Azaroff, B., & Mayer, G. R. (1991). Behavior analysis for lasting Behavior analysis for lasting changechange. Fort Worth: Holt, Rinehart, & Winston.. Fort Worth: Holt, Rinehart, & Winston.

Stuebing, K., Fletcher, J., LeDoux, J., Lyon, G. R., Shaywitz, S., & Stuebing, K., Fletcher, J., LeDoux, J., Lyon, G. R., Shaywitz, S., & Shaywitz, B. (2002). Validity of IQ-discrepancy classifications of Shaywitz, B. (2002). Validity of IQ-discrepancy classifications of reading disabilities: A meta-analysis. reading disabilities: A meta-analysis. American Educational American Educational Research Journal, 39, Research Journal, 39, 469–518.469–518.

Upah, K. R. F. (2008). Best practices in designing, implementing, and Upah, K. R. F. (2008). Best practices in designing, implementing, and evaluating quality interventions. In A. Thomas and J. Grimes (Eds.), evaluating quality interventions. In A. Thomas and J. Grimes (Eds.), Best practices in school psychology V.Best practices in school psychology V. (pp. 209-221). Bethesda, MD: (pp. 209-221). Bethesda, MD: National Association of School Psychologists. National Association of School Psychologists.

Wright, J. (2008). Wright, J. (2008). Internet resources for ‘response to intervention’. Internet resources for ‘response to intervention’. Retrieved June 24, 2008, from Retrieved June 24, 2008, from http://www.jimwrightonline.com/php/rti/rti_wire.phphttp://www.jimwrightonline.com/php/rti/rti_wire.php

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Calculating and Interpreting Slope: Implications for School Psychologists Caitlin S. Flinn, Ed.S. & Andrew E. McCrea, M.S., NCSP ASPP/PSU Conference October