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Rate of Improvement Calculation and Decision Making Caitlin S. Flinn, EdS, NCSP Andrew E. McCrea, MS, NCSP

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Why were here… While there exists a wealth of convincing research supporting the implementation of a response-to-intervention (RtI) framework, there are many questions yet to be empirically answered. Within multi-tiered model of assessment and instruction/intervention, how do we know whether a student is learning?

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Measuring Learning Class tests Quizzes Assignment/homework completion and accuracy Ask students questions in class Grades/report cards State/local assessments Universal screening, benchmark assessments Progress monitoring

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With Progress Monitoring Data… How do we know if a student is learning? Look at the data points Where are they on the graph? Are the data points getting closer to the goal or benchmark? Is there a way to measure growth? Make an aimline toward goal Look to see where data points are compared to aimline Calculate Rate of Improvement (RoI)

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Todays Objectives Explain what RoI is, why it is important, and how to compute it. Explain what RoI is, why it is important, and how to compute it. Establish that Simple Linear Regression should be the standardized procedure for calculating RoI. Establish that Simple Linear Regression should be the standardized procedure for calculating RoI. Discuss how to use RoI within a problem solving/school improvement model. Discuss how to use RoI within a problem solving/school improvement model.

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RoI Definition Rate of Improvement can be described algebraically as the slope of a line Rate of Improvement can be described algebraically as the slope of a line Slope is defined as: the vertical change over the horizontal change on a Cartesian plane. (x-axis and y-axis graph) Slope is defined as: the vertical change over the horizontal change on a Cartesian plane. (x-axis and y-axis graph) Also called: Rise over run Also called: Rise over run Formula: m = (y 2 - y 1 ) / (x 2 - x 1 ) Formula: m = (y 2 - y 1 ) / (x 2 - x 1 ) Describes the steepness of a line (Gall & Gall, 2007) Describes the steepness of a line (Gall & Gall, 2007)

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RoI Definition Finding a students RoI is determining the students learning Finding a students RoI is determining the students learning Creating a line that fits the data points, a trendline Creating a line that fits the data points, a trendline To find that line, we use: To find that line, we use: Linear regression Linear regression Ordinary Least Squares Ordinary Least Squares

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How does Rate of Improvement Fit into the Larger Context?

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School Improvement/Comprehensive School Reform Response to Intervention Dual Discrepancy: Level & Growth Rate of Improvement

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School Improvement/ Comprehensive School Reform Grade level content expectations (ELA, math, science, social studies, etc.). Grade level content expectations (ELA, math, science, social studies, etc.). Work toward these expectations through classroom instruction. Work toward these expectations through classroom instruction. Understand impact of instruction through assessment. Understand impact of instruction through assessment.

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Assessment Formative Assessments/High Stakes Tests Formative Assessments/High Stakes Tests Does student have command of content expectation (standard)? Does student have command of content expectation (standard)? Universal Screening using CBM Universal Screening using CBM Does student have basic skills appropriate for age/grade? Does student have basic skills appropriate for age/grade?

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Assessment Q: For students who are not proficient on grade level content standards, do they have the basic reading/writing/math skills necessary? Q: For students who are not proficient on grade level content standards, do they have the basic reading/writing/math skills necessary? A: Look at Universal Screening; if above criteria, intervention geared toward content standard, if below criteria, intervention geared toward basic skill. A: Look at Universal Screening; if above criteria, intervention geared toward content standard, if below criteria, intervention geared toward basic skill.

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Progress Monitoring Frequent measurement of knowledge to inform our understanding of the impact of instruction/intervention. Frequent measurement of knowledge to inform our understanding of the impact of instruction/intervention. Measures of basic skills (CBM) have demonstrated reliability & validity (see table at Measures of basic skills (CBM) have demonstrated reliability & validity (see table at

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Classroom Instruction (Content Expectations) Measure Impact (Test) Proficient!Non Proficient Content Need?Basic Skill Need? Intervention Progress Monitor With CBM Rate of Improvement Intervention Progress Monitor If CBM is Appropriate Measure Use Diagnostic Test to Differentiate

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So… Rate of Improvement (RoI) is how we understand student growth (learning). Rate of Improvement (RoI) is how we understand student growth (learning). RoI is reliable and valid (psychometrically speaking) for use with CBM data. RoI is reliable and valid (psychometrically speaking) for use with CBM data. RoI is best used when we have CBM data, most often when dealing with basic skills in reading/writing/math. RoI is best used when we have CBM data, most often when dealing with basic skills in reading/writing/math. RoI can be applied to other data (like behavior) with confidence too! RoI can be applied to other data (like behavior) with confidence too! RoI is not yet tested on typical Tier I formative classroom data. RoI is not yet tested on typical Tier I formative classroom data.

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RoI is usually applied to… Tier One students in the early grades at risk for academic failure (low green kids). Tier One students in the early grades at risk for academic failure (low green kids). Tier Two & Three Intervention Groups. Tier Two & Three Intervention Groups. Special Education Students (and IEP goals) Special Education Students (and IEP goals) Students with Behavior Plans Students with Behavior Plans

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RoI Foundations Deno, 1985 Curriculum-based measurement General outcome measures Technically adequate Short Standardized Repeatable Sensitive to change

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RoI Foundations Fuchs & Fuchs, 1998 Hallmark components of Response to Intervention Ongoing formative assessment Identifying non-responding students Treatment fidelity of instruction Dual discrepancy model One standard deviation from typically performing peers in level and rate

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RoI Foundations Ardoin & Christ, 2008 Slope for benchmarks (3x per year) More growth from fall to winter than winter to spring Might be helpful to use RoI for fall to winter And a separate RoI for winter to spring

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RoI Foundations Fuchs, Fuchs, Walz, & Germann, 1993 Fuchs, Fuchs, Walz, & Germann, 1993 Typical weekly growth rates in oral reading fluency and digits correct Typical weekly growth rates in oral reading fluency and digits correct Needed growth to remediate skills Needed growth to remediate skills Students who had 1.5 to 2.0 times the slope of typically performing peers were able to close the achievement gap in a reasonable amount of time Students who had 1.5 to 2.0 times the slope of typically performing peers were able to close the achievement gap in a reasonable amount of time

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RoI Foundations Deno, Fuchs, Marston, & Shin, 2001 Slope of frequently non-responsive children approximated slope of children already identified as having a specific learning disability

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How many data points? 10 data points are a minimum requirement for a reliable trendline (Gall & Gall, 2007) Is that reasonable and realistic? How does that affect the frequency of administering progress monitoring probes? How does that affect our ability to make instructional decisions for students?

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How can we show RoI? Speeches that included visuals, especially in color, improved recall of information (Vogel, Dickson, & Lehman, 1990) Speeches that included visuals, especially in color, improved recall of information (Vogel, Dickson, & Lehman, 1990) Seeing is believing. Seeing is believing. Useful for communicating large amounts of information quickly Useful for communicating large amounts of information quickly A picture is worth a thousand words. A picture is worth a thousand words. Transcends language barriers (Karwowski, 2006) Transcends language barriers (Karwowski, 2006) Responsibility for accurate graphical representations of data Responsibility for accurate graphical representations of data

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Skills for Which We Compute RoI Reading Oral Reading Fluency Word Use Fluency Reading Comprehension MAZE Retell Early Literacy Skills Initial Sound Letter Naming Letter Sound Phoneme Segmentation Nonsense Word Spelling Written Expression Behavior Math Math Computation Math Facts Early Numeracy Oral Counting Missing Number Number Identification Quantity Discrimination

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Guidelines? Visual inspection of slope Visual inspection of slope Multiple interpretations Multiple interpretations Instructional services Instructional services Need for explicit guidelines Need for explicit guidelines

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Ongoing Research RoI for instructional decisions is not a perfect process RoI for instructional decisions is not a perfect process Research is currently addressing sources of error: Research is currently addressing sources of error: Christ, 2006: standard error of measurement for slope Christ, 2006: standard error of measurement for slope Ardoin & Christ, 2009: passage difficulty and variability Ardoin & Christ, 2009: passage difficulty and variability Jenkin, Graff, & Miglioretti, 2009: frequency of progress monitoring Jenkin, Graff, & Miglioretti, 2009: frequency of progress monitoring

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Future Considerations Questions yet to be empirically answered Questions yet to be empirically answered What parameters of RoI indicate a lack of RtI? What parameters of RoI indicate a lack of RtI? How does standard error of measurement play into using RoI for instructional decision making? How does standard error of measurement play into using RoI for instructional decision making? How does RoI vary between standard protocol interventions? How does RoI vary between standard protocol interventions? How does this apply to non-English speaking populations? How does this apply to non-English speaking populations?

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How is RoI Calculated? Which way is best?

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Multiple Methods for Calculating Growth Visual Inspection Approaches Visual Inspection Approaches Eye Ball Approach Eye Ball Approach Split Middle Approach Split Middle Approach Tukey Method Tukey Method Quantitative Approaches Quantitative Approaches Last point minus First point Approach Last point minus First point Approach Split Middle & Tukey plus Split Middle & Tukey plus Linear Regression Approach Linear Regression Approach

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The Visual Inspection Approaches

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Eye Ball Approach

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Split Middle Approach Drawing through the two points obtained from the median data values and the median days when the data are divided into two sections Drawing through the two points obtained from the median data values and the median days when the data are divided into two sections (Shinn, Good, & Stein, 1989).

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Split Middle X(9) X(14) X (9)

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Tukey Method Divide scores into 3 equal groups Divide scores into 3 equal groups Divide groups with vertical lines Divide groups with vertical lines In 1 st and 3 rd groups, find median data point and median week and mark with an X In 1 st and 3 rd groups, find median data point and median week and mark with an X Draw line between two Xs Draw line between two Xs (Fuchs, et. al., Summer Institute Student progress monitoring for math.

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Tukey Method X(8) X(14)

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The Quantitative Approaches

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Last minus First Iris Center: last probe score minus first probe score over last administration period minus first administration period. Iris Center: last probe score minus first probe score over last administration period minus first administration period. Y2-Y1/X2-X1= RoI

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Last minus First

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Split Middle Plus X(9) X(14) (14-9)/8=0.63

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Tukey Method Plus X(8) X(14) (14-8)/8=0.75

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Linear Regression

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RoI Consistency? Any Method of Visual Inspection ??? Last minus First 0.75 Split Middle Plus 0.63 Tukey Plus 0.75 Linear Regression 1.10

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RoI Consistency? If we are not all using the same model to compute RoI, we continue to have the same problems as past models, where under one approach a student meets SLD criteria, but under a different approach, the student does not. If we are not all using the same model to compute RoI, we continue to have the same problems as past models, where under one approach a student meets SLD criteria, but under a different approach, the student does not. Hypothetically, if the RoI cut-off was 0.65 or 0.95, different approaches would come to different conclusions on the same student. Hypothetically, if the RoI cut-off was 0.65 or 0.95, different approaches would come to different conclusions on the same student.

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RoI Consistency? Last minus First (Iris Center) and Linear Regression (Shinn, etc.) only quantitative methods discussed in CBM literature. Last minus First (Iris Center) and Linear Regression (Shinn, etc.) only quantitative methods discussed in CBM literature. Study of 37 at risk 2 nd graders: Study of 37 at risk 2 nd graders: Difference in RoI b/w LmF & LR Methods Whole Year 0.26 WCPM Fall 0.31 WCPM Spring 0.24 WCPM McCrea (2010) Unpublished data

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Technical Adequacy Without a consensus on how to compute RoI, we risk falling short of having technical adequacy within our model. Without a consensus on how to compute RoI, we risk falling short of having technical adequacy within our model.

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So, Which RoI Method is Best?

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Literature shows that Linear Regression is Best Practice Students daily test scores…were entered into a computer program…The data analysis program generated slopes of improvement for each level using an Ordinary-Least Squares procedure (Hayes, 1973) and the line of best fit. Students daily test scores…were entered into a computer program…The data analysis program generated slopes of improvement for each level using an Ordinary-Least Squares procedure (Hayes, 1973) and the line of best fit. This procedure has been demonstrated to represent CBM achievement data validly within individual treatment phases (Marston, 1988; Shinn, Good, & Stein, in press; Stein, 1987). This procedure has been demonstrated to represent CBM achievement data validly within individual treatment phases (Marston, 1988; Shinn, Good, & Stein, in press; Stein, 1987). Shinn, Gleason, & Tindal, 1989

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Growth (RoI) Research using Linear Regression Christ, T. J. (2006). Short-term estimates of growth using curriculum based measurement of oral reading fluency: Estimating standard error of the slope to construct confidence intervals. School Psychology Review, 35, Christ, T. J. (2006). Short-term estimates of growth using curriculum based measurement of oral reading fluency: Estimating standard error of the slope to construct confidence intervals. School Psychology Review, 35, Deno, S. L., Fuchs, L. S., Marston, D., & Shin, J. (2001). Using curriculum based measurement to establish growth standards for students with learning disabilities. School Psychology Review, 30, Deno, S. L., Fuchs, L. S., Marston, D., & Shin, J. (2001). Using curriculum based measurement to establish growth standards for students with learning disabilities. School Psychology Review, 30, Good, R. H. (1990). Forecasting accuracy of slope estimates for reading curriculum based measurement: Empirical evidence. Behavioral Assessment, 12, Good, R. H. (1990). Forecasting accuracy of slope estimates for reading curriculum based measurement: Empirical evidence. Behavioral Assessment, 12, Fuchs, L. S., Fuchs, D., Hamlett, C. L., Walz, L. & Germann, G. (1993). Formative evaluation of academic progress: How much growth can we expect? School Psychology Review, 22, Fuchs, L. S., Fuchs, D., Hamlett, C. L., Walz, L. & Germann, G. (1993). Formative evaluation of academic progress: How much growth can we expect? School Psychology Review, 22,

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Growth (RoI) Research using Linear Regression Jenkins, J. R., Graff, J. J., & Miglioretti, D.L. (2009). Estimating reading growth using intermittent CBM progress monitoring. Exceptional Children, 75, Jenkins, J. R., Graff, J. J., & Miglioretti, D.L. (2009). Estimating reading growth using intermittent CBM progress monitoring. Exceptional Children, 75, Shinn, M. R., Gleason, M. M., & Tindal, G. (1989). Varying the difficulty of testing materials: Implications for curriculum-based measurement. The Journal of Special Education, 23, Shinn, M. R., Gleason, M. M., & Tindal, G. (1989). Varying the difficulty of testing materials: Implications for curriculum-based measurement. The Journal of Special Education, 23, Shinn, M. R., Good, R. H., & Stein, S. (1989). Summarizing trend in student achievement: A comparison of methods. School Psychology Review, 18, Shinn, M. R., Good, R. H., & Stein, S. (1989). Summarizing trend in student achievement: A comparison of methods. School Psychology Review, 18,

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So, Why Are There So Many Other RoI Models? Ease of application Ease of application Focus on Yes/No to goal acquisition, not degree of growth Focus on Yes/No to goal acquisition, not degree of growth How many of us want to calculate OLS Linear Regression formulas (or even remember how)? How many of us want to calculate OLS Linear Regression formulas (or even remember how)?

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Pros and Cons of Each Approach ProsCons Eye Ball EasyUnderstandableSubjective Split Middle & Tukey No software needed Compare to Aim/Goal line Yes/No to goal acquisition No statistic provided, no idea of the degree of growth

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Pros and Cons of Each Approach ProsCons Last minus First Provides a growth statistic Easy to compute Does not consider all data points, only two Split Middle & Tukey Plus Considers all data points. Easy to compute No support for plus part of methodology Linear Regression All data points Best Practice Calculating the statistic

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An Easy and Applicable Solution

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Get Out Your Laptops! Open Microsoft Excel I love ROI

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Graphing RoI For Individual Students Programming Microsoft Excel to Graph Rate of Improvement: Fall to Winter

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Setting Up Your Spreadsheet In cell A1, type 3rd Grade ORF In cell A1, type 3rd Grade ORF In cell A2, type First Semester In cell A2, type First Semester In cell A3, type School Week In cell A3, type School Week In cell A4, type Benchmark In cell A4, type Benchmark In cell A5, type the Students Name (Swiper Example) In cell A5, type the Students Name (Swiper Example)

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Labeling School Weeks Starting with cell B3, type numbers 1 through 18 going across row 3 (horizontal). Starting with cell B3, type numbers 1 through 18 going across row 3 (horizontal). Numbers 1 through 18 represent the number of the school week. Numbers 1 through 18 represent the number of the school week. You will end with week 18 in cell S3. You will end with week 18 in cell S3.

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Labeling Dates Note: You may choose to enter the date of that school week across row 2 to easily identify the school week. Note: You may choose to enter the date of that school week across row 2 to easily identify the school week.

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) Entering Benchmarks (3rd Grade ORF) In cell B4, type 77. This is your fall benchmark. In cell B4, type 77. This is your fall benchmark. In cell S4, type 92. This is your winter benchmark. In cell S4, type 92. This is your winter benchmark.

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Entering Student Data (Sample) Enter the following numbers, going across row 5, under corresponding week numbers. Enter the following numbers, going across row 5, under corresponding week numbers. Week 1 – 41 Week 1 – 41 Week 8 – 62 Week 8 – 62 Week 9 – 63 Week 9 – 63 Week 10 – 75 Week 10 – 75 Week 11 – 64 Week 11 – 64 Week 12 – 80 Week 12 – 80 Week 13 – 83 Week 13 – 83 Week 14 – 83 Week 14 – 83 Week 15 – 56 Week 15 – 56 Week 17 – 104 Week 17 – 104 Week 18 – 74 Week 18 – 74

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*CAUTION* If a student was not assessed during a certain week, leave that cell blank If a student was not assessed during a certain week, leave that cell blank Do not enter a score of Zero (0) it will be calculated into the trendline and interpreted as the student having read zero words correct per minute during that week. Do not enter a score of Zero (0) it will be calculated into the trendline and interpreted as the student having read zero words correct per minute during that week.

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Graphing the Data Highlight cells A4 and A5 through S4 and S5 Highlight cells A4 and A5 through S4 and S5 Follow Excel 2003 or Excel 2007 directions from here Follow Excel 2003 or Excel 2007 directions from here

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Graphing the Data Excel 2003 Excel 2003 Across the top of your worksheet, click on Insert Across the top of your worksheet, click on Insert In that drop-down menu, click on Chart In that drop-down menu, click on Chart Excel 2007 Excel 2007 Click Insert Click Insert Find the icon for Line Find the icon for Line Click the arrow below Line Click the arrow below Line

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Graphing the Data Excel 2003 Excel 2003 A Chart Wizard window will appear A Chart Wizard window will appear Excel 2007 Excel graphics appear 6 graphics appear

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Graphing the Data Excel 2003 Excel 2003 Choose Line Choose Line Choose Line with markers… Choose Line with markers… Excel 2007 Excel 2007 Choose Line with markers Choose Line with markers

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Graphing the Data Excel 2003 Excel 2003 Data Range tab Data Range tab Columns Columns Excel 2007 Excel 2007 Your graph appears Your graph appears

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Graphing the Data Excel 2003 Excel 2003 Chart Title Chart Title School Week X Axis School Week X Axis WPM Y Axis WPM Y Axis Excel 2007 Excel 2007 Change your labels by right clicking on the graph Change your labels by right clicking on the graph

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Graphing the Data Excel 2003 Excel 2003 Choose where you want your graph Choose where you want your graph Excel 2007 Excel 2007 Your graph was automatically put into your data spreadsheet Your graph was automatically put into your data spreadsheet

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Graphing the Trendline Excel 2003 Excel 2003 Right click on any of the student data points Right click on any of the student data points Excel 2007 Excel 2007

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Graphing the Trendline Excel 2003 Excel 2003 Choose Linear Choose Linear Excel 2007 Excel 2007

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Graphing the Trendline Excel 2003 Excel 2003 Choose Custom and check box next to Display equation on chart Choose Custom and check box next to Display equation on chart Excel 2007 Excel 2007

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Graphing the Trendline Clicking on the equation highlights a box around it Clicking on the equation highlights a box around it Clicking on the box allows you to move it to a place where you can see it better Clicking on the box allows you to move it to a place where you can see it better

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Graphing the Trendline You can repeat the same procedure to have a trendline for the benchmark data points You can repeat the same procedure to have a trendline for the benchmark data points Suggestion: label the trendline Expected ROI Suggestion: label the trendline Expected ROI Move this equation under the first Move this equation under the first

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Individual Student Graph: Fall to Winter

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Individual Student Graph The equation indicates the slope, or rate of improvement. The equation indicates the slope, or rate of improvement. The number, or coefficient, before "x" is the average improvement, which in this case is the average number of words per minute per week gained by the student. The number, or coefficient, before "x" is the average improvement, which in this case is the average number of words per minute per week gained by the student.

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Individual Student Graph The rate of improvement, or trendline, is calculated using a linear regression, a simple equation of least squares. The rate of improvement, or trendline, is calculated using a linear regression, a simple equation of least squares. To add additional progress monitoring/benchmark scores once youve already created a graph, enter additional scores in Row 5 in the corresponding school week. To add additional progress monitoring/benchmark scores once youve already created a graph, enter additional scores in Row 5 in the corresponding school week.

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Individual Student Graph The slope can change depending on which week (where) you put the benchmark scores on your chart. The slope can change depending on which week (where) you put the benchmark scores on your chart. Enter benchmark scores based on when your school administers their benchmark assessments for the most accurate depiction of expected student progress. Enter benchmark scores based on when your school administers their benchmark assessments for the most accurate depiction of expected student progress.

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Programming Excel First Semester Calculating Needed RoI Calculating Benchmark RoI Calculating Students Actual RoI

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Quick Definitions Needed RoI The rate of improvement needed to catch up to the next benchmark. Benchmark RoI The rate of improvement of typically performing peers according to the norms Students Actual RoI Based on the available data points, this is the students actual rate of improvement per week

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Calculating Needed RoI In cell T3, type Needed RoI Click on cell T5 In the fx line (at top of sheet) type this formula =((S4-B5)/18) Then hit enter Your result should read: This formula simply subtracts the students actual beginning of year (BOY) benchmark from the expected middle of year (MOY) benchmark, then dividing by 18 for the first 18 weeks (1st semester).

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Calculating Benchmark RoI In cell U3, type Benchmark RoI Click on cell U4 In the fx line (at top of sheet) type this formula =SLOPE(B4:S4,B3:S3) Then hit enter Your result should read: This formula considers 18 weeks of benchmark data and provides an average growth or change per week.

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Calculating Student Actual RoI Click on cell U5 In the fx line (at top of sheet) type this formula =SLOPE(B5:S5,B3:S3) Then hit enter Your result should read: This formula considers 18 weeks of student data and provides an average growth or change per week.

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Graphing RoI For Individual Students Programming Microsoft Excel to Graph Rate of Improvement: Winter to Spring

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Setting Up Your Spreadsheet In cell A1, type 3rd Grade ORF In cell A2, type Second Semester In cell A3, type School Week In cell A4, type Benchmark In cell A5, type the Students Name (Swiper Example)

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Labeling School Weeks Starting with cell B3, type numbers 1 through 18 going across row 3 (horizontal). Numbers 1 through 18 represent the number of the school week. You will end with week 18 in cell S3.

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Labeling Dates Note: You may choose to enter the date of that school week across row 2 to easily identify the school week.

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Entering Benchmarks (3rd Grade ORF) In cell B4, type 92. This is your fall benchmark. In cell S4, type 110. This is your winter benchmark.

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Entering Student Data (Sample) Enter the following numbers, going across row 5, under corresponding week numbers. Week 1 – 74 Week 3 – 85 Week 4 – 89 Week 5 – 69 Week 6 – 85 Week 7 – 96 Week 8 – 90 Week 9 – 84 Week 10 – 106 Week 11 – 94 Week 15 – 100

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*CAUTION* If a student was not assessed during a certain week, what do you put in that cell? Why?

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Graphing the Data Highlight cells A4 and A5 through S4 and S5 Follow Excel 2003 or Excel 2007 directions from here

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Graphing the Data Excel 2003 Across the top of your worksheet, click on Insert In that drop-down menu, click on Chart Excel 2007 Click Insert Find the icon for Line Click the arrow below Line

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Graphing the Data Excel 2003 A Chart Wizard window will appear Excel graphics appear

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Graphing the Data Excel 2003 Choose Line Choose Line with markers… Excel 2007 Choose Line with markers

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Graphing the Data Excel 2003 Data Range tab Columns Excel 2007 Your graph appears

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Graphing the Data Excel 2003 Chart Title School Week X Axis WPM Y Axis Excel 2007 Change your labels by right clicking on the graph

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Graphing the Data Excel 2003 Choose where you want your graph Excel 2007 Your graph was automatically put into your data spreadsheet

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Graphing the Trendline Excel 2003 Right click on any of the student data points Excel 2007

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Graphing the Trendline Excel 2003 Choose Linear Excel 2007

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Graphing the Trendline Excel 2003 Choose Custom and check box next to Display equation on chart Excel 2007

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Graphing the Trendline Clicking on the equation highlights a box around it Clicking on the box allows you to move it to a place where you can see it better

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Graphing the Trendline You can repeat the same procedure to have a trendline for the benchmark data points Suggestion: label the trendline Expected ROI Move this equation under the first

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Individual Student Graph

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Challenge! What was the first equation? What is the slope of that equation? What was the second equation? What is the slope of that equation? Describe the achievement gap at the end of the school year.

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Programming Excel Second Semester Calculating Needed RoI Calculating Benchmark RoI Calculating Students Actual RoI

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Calculating Needed RoI In cell T3, type Needed RoI Click on cell T5 In the fx line (at top of sheet) type this formula =((S4-B5)/18) Then hit enter Your result is _____ ? This formula simply subtracts the students actual middle of year (MOY) benchmark from the expected end of year (EOY) benchmark, then dividing by 18 for the first 18 weeks (1st semester).

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Calculating Benchmark RoI In cell U3, type Benchmark RoI Click on cell U4 In the fx line (at top of sheet) type this formula =SLOPE(B4:S4,B3:S3) Then hit enter Your result should read: ____? This formula considers 18 weeks of benchmark data and provides an average growth or change per week.

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Calculating Student Actual RoI Click on cell U5 In the fx line (at top of sheet) type this formula =SLOPE(B5:S5,B3:S3) Then hit enter Your result should read: 1.89 This formula considers 18 weeks of student data and provides an average growth or change per week.

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Assuming Linear Growth… …Finding Curve-linear Growth Why Graph only 18 Weeks at a Time?

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Non-Educational Example of Curve-linear Growth

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Academic Example of Curvilinear Growth

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McCrea, 2010 Looked at Rate of Improvement in small 2 nd grade sample Looked at Rate of Improvement in small 2 nd grade sample Found differences in RoI when computed for fall and spring: Found differences in RoI when computed for fall and spring: Ave RoI for fall:1.47 WCPM Ave RoI for fall:1.47 WCPM Ave RoI for spring:1.21 WCPM Ave RoI for spring:1.21 WCPM

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Ardoin & Christ, 2008 Slope for benchmarks (3x per year) Slope for benchmarks (3x per year) More growth from fall to winter than winter to spring More growth from fall to winter than winter to spring

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Christ, Yeo, & Silberglitt, in press Growth across benchmarks (3X per year) Growth across benchmarks (3X per year) More growth from fall to winter than winter to spring More growth from fall to winter than winter to spring Disaggregated special education population Disaggregated special education population

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Graney, Missall, & Martinez, 2009 Growth across benchmarks (3X per year) Growth across benchmarks (3X per year) More growth from winter to spring than fall to winter with R-CBM. More growth from winter to spring than fall to winter with R-CBM.

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Fien, Park, Smith, & Baker, 2010 Investigated relationship b/w NWF gains and ORF/Comprehension Investigated relationship b/w NWF gains and ORF/Comprehension Found greater NWF gains in fall than in spring. Found greater NWF gains in fall than in spring.

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DIBELS (6 th ) ORF Change in Criteria Fall to Winter Winter to Spring 2 nd rd th th th 115

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AIMSweb Norms Based on 50 th Percentile Fall to Winter Winter to Spring 1 st nd rd th th th 1312

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Speculation as to why Differences in RoI within the Year Relax instruction after high stakes testing in March/April; a PSSA effect. Relax instruction after high stakes testing in March/April; a PSSA effect. Depressed BOY benchmark scores due to summer break; a rebound effect (Clemens). Depressed BOY benchmark scores due to summer break; a rebound effect (Clemens). Instructional variables could explain differences in Graney (2009) and Ardoin (2008) & Christ (in press) results (Silberglitt). Instructional variables could explain differences in Graney (2009) and Ardoin (2008) & Christ (in press) results (Silberglitt). Variability within progress monitoring probes (Ardoin & Christ, 2008) (Lent). Variability within progress monitoring probes (Ardoin & Christ, 2008) (Lent).

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ROI as a Decision Tool within a Problem-Solving Model

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Steps 1. Gather the data 2. Ground the data & set goals 3. Interpret the data 4. Figure out how to fit Best Practice into Public Education

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Step 1: Gather Data Universal Screening Progress Monitoring

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Common Screenings in PA DIBELS DIBELS AIMSweb AIMSweb MBSP MBSP 4Sight 4Sight PSSA PSSA

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Validated Progress Monitoring Tools DIBELS DIBELS AIMSweb AIMSweb MBSP MBSP

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Step 2: Ground the Data 1) To what will we compare our student growth data? 2) How will we set goals?

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Multiple Ways to Look at Growth Needed Growth Needed Growth Expected Growth & Percent of Expected Growth Expected Growth & Percent of Expected Growth Fuchs et. al. (1993) Table of Realistic and Ambitious Growth Fuchs et. al. (1993) Table of Realistic and Ambitious Growth Growth Toward Individual Goal* Growth Toward Individual Goal* *Best Practices in Setting Progress Monitoring Goals for Academic Skill Improvement (Shapiro, 2008)

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Needed Growth Difference between students BOY (or MOY) score and benchmark score at MOY (or EOY). Difference between students BOY (or MOY) score and benchmark score at MOY (or EOY). Example: MOY ORF = 10, EOY benchmark is 40, 18 weeks of instruction (40-10/18=1.67). Student must gain 1.67 wcpm per week to make EOY benchmark. Example: MOY ORF = 10, EOY benchmark is 40, 18 weeks of instruction (40-10/18=1.67). Student must gain 1.67 wcpm per week to make EOY benchmark.

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Expected Growth Difference between two benchmarks. Difference between two benchmarks. Example: MOY benchmark is 20, EOY benchmark is 40, expected growth (40- 20)/18 weeks of instruction = 1.11 wcpm per week. Example: MOY benchmark is 20, EOY benchmark is 40, expected growth (40- 20)/18 weeks of instruction = 1.11 wcpm per week.

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Tigard-Tualatin School District (www.ttsd.k12.or.us) Looking at Percent of Expected Growth Tier ITier IITier III Greater than 150% Between 110% & 150% Possible LD Between 95% & 110% Likely LD Between 80% & 95% May Need More Likely LD Below 80%Needs More Likely LD

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Fuchs, Fuchs, Hamlett, Walz, & Germann (1993) Oral Reading Fluency Adequate Response Table Realistic Growth Ambitiou s Growth 1 st nd rd th th

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Fuchs, Fuchs, Hamlett, Walz, & Germann (1993) Digit Fluency Adequate Response Table Realistic Growth Ambitious Growth 1 st nd rd th th

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If Local Criteria are Not an Option Use norms that accompany the measure (DIBELS, AIMSweb, etc.). Use norms that accompany the measure (DIBELS, AIMSweb, etc.). Use national norms. Use national norms.

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Making Decisions: Best Practice Research has yet to establish a blue print for grounding student RoI data. Research has yet to establish a blue print for grounding student RoI data. At this point, teams should consider multiple comparisons when planning and making decisions. At this point, teams should consider multiple comparisons when planning and making decisions.

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Making Decisions: Lessons From the Field When tracking on grade level, consider an RoI that is 100% of expected growth as a minimum requirement, consider an RoI that is at or above the needed as optimal. When tracking on grade level, consider an RoI that is 100% of expected growth as a minimum requirement, consider an RoI that is at or above the needed as optimal. So, 100% of expected and on par with needed become the limits of the range within a student should be achieving. So, 100% of expected and on par with needed become the limits of the range within a student should be achieving.

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Is there an easy way to do all of this?

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Access to Spreadsheet Templates ment/home ment/home ment/home ment/home Click on Charts and Graphs. Click on Charts and Graphs. Update dates and benchmarks. Update dates and benchmarks. Enter names and benchmark/progress monitoring data. Enter names and benchmark/progress monitoring data.

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What about Students not on Grade Level?

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Determining Instructional Level Independent/Instructional/Frustrational Independent/Instructional/Frustrational Instructional often b/w 40 th or 50 th percentile and 25 th percentile. Instructional often b/w 40 th or 50 th percentile and 25 th percentile. Frustrational level below the 25 th percentile. Frustrational level below the 25 th percentile. AIMSweb: Survey Level Assessment (SLA). AIMSweb: Survey Level Assessment (SLA).

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Setting Goals off of Grade Level 100% of expected growth not enough. 100% of expected growth not enough. Needed growth only gets to instructional level benchmark, not grade level. Needed growth only gets to instructional level benchmark, not grade level. Risk of not being ambitious enough. Risk of not being ambitious enough. Plenty of ideas, but limited research regarding Best Practice in goal setting off of grade level. Plenty of ideas, but limited research regarding Best Practice in goal setting off of grade level.

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Possible Solution (A) Weekly probe at instructional level and compare to expected and needed growth rates at instructional level. Weekly probe at instructional level and compare to expected and needed growth rates at instructional level. Ambitious goal: 200% of expected RoI Ambitious goal: 200% of expected RoI

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Possible Solution (B) Weekly probe at instructional level for sensitive indicator of growth. Weekly probe at instructional level for sensitive indicator of growth. Monthly probes (give 3, not just 1) at grade level to compute RoI. Monthly probes (give 3, not just 1) at grade level to compute RoI. Goal based on grade level growth (more than 100% of expected). Goal based on grade level growth (more than 100% of expected).

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Step 3: Interpreting Growth

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What do we do when we do not get the growth we want? When to make a change in instruction and intervention? When to make a change in instruction and intervention? When to consider SLD? When to consider SLD?

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When to make a change in 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 growth). Not on track to make benchmark (needed growth). Not on track to reach individual goal. Not on track to reach individual goal.

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? When to consider SLD? Continued inadequate response despite: Fidelity with Tier I instruction and Tier II/III intervention. Fidelity with Tier I instruction and Tier II/III intervention. Multiple attempts at intervention. Multiple attempts at intervention. Individualized Problem-Solving approach. Individualized Problem-Solving approach. Evidence of dual discrepancy…

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Three Levels of Examples Whole Class Whole Class Small Group Small Group Individual Student Individual Student - Academic Data - Behavior Data

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Whole Class Example

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3 rd Grade Math Whole Class Whos responding? Whos responding? Effective math instruction? Effective math instruction? Who needs more? Who needs more? N=19 N=19 4 > 100% growth 4 > 100% growth 15 < 100% growth 15 < 100% growth 9 w/ negative growth 9 w/ negative growth

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Small Group Example

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Intervention Group Intervention working for how many? Intervention working for how many? Can we assume fidelity of intervention based on results? Can we assume fidelity of intervention based on results? Who needs more? Who needs more?

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Individual Kid Example

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Individual Kid Making growth? Making growth? How much (65% of expected growth). How much (65% of expected growth). Atypical growth across the year (last 3 data points). Atypical growth across the year (last 3 data points). Continue? Make a change? Need more data? Continue? Make a change? Need more data?

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RoI and Behavior?

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Step 4: Figure out how to fit Best Practice into Public Education

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Things to Consider Who is At-Risk and needs progress monitoring? Who is At-Risk and needs progress monitoring? Who will collect, score, enter the data? Who will collect, score, enter the data? Who will monitor student growth, when, and how often? Who will monitor student growth, when, and how often? What changes should be made to instruction & intervention? What changes should be made to instruction & intervention? What about monitoring off of grade level? What about monitoring off of grade level?

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? Who is At-Risk and needs progress monitoring? Below level on universal screening Below level on universal screening Entering 4 th Grade Example DORF (110) ISIP TRWM (55) 4Sight (1235) PSSA (1235) Student A Student B Student C

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Who will collect, score, and enter the data? Using MBSP for math, teachers can administer probes to whole class. Using MBSP for math, teachers can administer probes to whole class. DORF probes must be administered one- on-one, and creativity pays off (train and use art, music, library, etc. specialists). DORF probes must be administered one- on-one, and creativity pays off (train and use art, music, library, etc. specialists). Schedule for progress monitoring math and reading every-other week. Schedule for progress monitoring math and reading every-other week.

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Week 1Week 2 ReadingMathReadingMath 1 st XX 2 nd XX 3 rd XX 4 th XX 5 th XX

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Who will monitor student growth, when, and how often? Best Practices in Data-Analysis Teaming (Kovaleski & Pedersen, 2008) Best Practices in Data-Analysis Teaming (Kovaleski & Pedersen, 2008) Chambersburg Area School District Elementary Response to Intervention Manual (McCrea et. al., 2008) Chambersburg Area School District Elementary Response to Intervention Manual (McCrea et. al., 2008) Derry Township School District Response to Intervention Model (http://www.hershey.k12.pa.us/ /lib/ /_files/Microsoft_Word_- _Response_to_Intervention_Overview_of_Hershey_Elementary_Model.pdf) Derry Township School District Response to Intervention Model (http://www.hershey.k12.pa.us/ /lib/ /_files/Microsoft_Word_- _Response_to_Intervention_Overview_of_Hershey_Elementary_Model.pdf)

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What changes should be made to instruction & intervention? Ensure treatment fidelity!!!!!!!! Ensure treatment fidelity!!!!!!!! Increase instructional time (active and engaged) Increase instructional time (active and engaged) Decrease group size Decrease group size Gather additional, diagnostic, information Gather additional, diagnostic, information Change the intervention Change the intervention

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Final Exam… Student Data: 27, 29, 26, 34, 27, 32, 39, 45, 43, 49, 51, --, --, 56, 51, 52, --, 57. Student Data: 27, 29, 26, 34, 27, 32, 39, 45, 43, 49, 51, --, --, 56, 51, 52, --, 57. Benchmark Data: BOY = 40, MOY = 68. Benchmark Data: BOY = 40, MOY = 68. What is students RoI? What is students RoI? How does RoI compare to expected and needed RoIs? How does RoI compare to expected and needed RoIs? What steps would your team take next? What steps would your team take next? What if Benchmarks were 68 and 90 instead? What if Benchmarks were 68 and 90 instead?

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The RoI Web Site Download powerpoints, handouts, Excel graphs, charts, articles, etc. Download powerpoints, handouts, Excel graphs, charts, articles, etc. Caitlin Flinn Bennyhoff Caitlin Flinn Bennyhoff Andy McCrea Andy McCrea Matt Ferchalk Matt Ferchalk

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