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Predicting High-Stakes Tests of Math Achievement using a Group-Administered RTI Instrument PDF

176 Pages·2017·2.47 MB·English
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UUnniivveerrssiittyy ooff TTeennnneesssseeee,, KKnnooxxvviillllee TTRRAACCEE:: TTeennnneesssseeee RReesseeaarrcchh aanndd CCrreeaattiivvee EExxcchhaannggee Doctoral Dissertations Graduate School 8-2014 PPrreeddiiccttiinngg HHiigghh--SSttaakkeess TTeessttss ooff MMaatthh AAcchhiieevveemmeenntt uussiinngg aa GGrroouupp-- AAddmmiinniisstteerreedd RRTTII IInnssttrruummeenntt:: VVaalliiddaattiinngg SSkkiillllss MMeeaassuurreedd bbyy tthhee MMoonniittoorriinngg IInnssttrruuccttiioonnaall RReessppoonnssiivveenneessss:: MMaatthh Jeremy Thomas Coles University of Tennessee - Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Applied Statistics Commons, Educational Assessment, Evaluation, and Research Commons, Longitudinal Data Analysis and Time Series Commons, Quantitative Psychology Commons, and the School Psychology Commons RReeccoommmmeennddeedd CCiittaattiioonn Coles, Jeremy Thomas, "Predicting High-Stakes Tests of Math Achievement using a Group-Administered RTI Instrument: Validating Skills Measured by the Monitoring Instructional Responsiveness: Math. " PhD diss., University of Tennessee, 2014. https://trace.tennessee.edu/utk_graddiss/2811 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Jeremy Thomas Coles entitled "Predicting High-Stakes Tests of Math Achievement using a Group-Administered RTI Instrument: Validating Skills Measured by the Monitoring Instructional Responsiveness: Math." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with a major in School Psychology. R. Steve McCallum, Major Professor We have read this dissertation and recommend its acceptance: Sherry M. Bell, William L. Seaver, Jennifer A. Morrow, Brian E. Wilhoit Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official student records.) Predicting High-Stakes Tests of Math Achievement using a Group-Administered RTI Instrument: Validating Skills Measured by the Monitoring Instructional Responsiveness: Math A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Jeremy Thomas Coles August 2014 i Copyright 2014© by Jeremy Thomas Coles All rights reserved. ii Dedication To my fiancée, Mackenzie, I cannot express how important your love and support was throughout graduate school; you gave me purpose and clarity when I needed it most. To Steve, Susan, and Ashley, you are already family to me. To my parents, Brian and Valerie, you believed in me before I believed in myself. To my best friend and little brother, Braden, now it’s your turn to follow your dreams. iii Acknowledgements This dissertation would not have been possible without the help of Dr. Steve McCallum. His critical analysis and suggestions ensured that each idea was carefully evaluated and focused. I would like to thank Dr. Sherry Bell. Her extensive knowledge of education and psychology helped me bridge ideas across disciplines. I would like to thank Dr. Morrow and Dr. Seaver for their knowledge and assistance in statistical methodology. I would like to thank Dr. Wilhoit for his ability to put everything into perspective. I would like to thank Dr. Michael Hopkins and Dr. Angela Hilton-Prillhart who, along with Drs. McCallum and Bell, helped created the MIR probes. I would like to thank Dr. Scott Graves, Dr. Christopher Skinner, and Dr. Jerry Morton. I would not be where I am today without their guidance and support as I navigated graduate school and internship. Most importantly, their reassurance provided clarity during the most uncertain and difficult times along this path. Finally,I would like to thank the members of the research group who helped organize the probes and enter data. Specifically, I would like to thank Elizabeth Hayes, Lakmal Walpitage, Kelly Smyth, Brooke Browarnik, and Emily Taylor. I cannot express how grateful I am for the time you spent assisting me with this project. iv Abstract Three universal screeners and nine progress monitoring probes from the Monitoring Instructional Responsiveness: Math (MIR:M), a silent, group-administered math assessment designed for implementation with an RTI Model, were administered to 223 fifth-grade students. The growth parameters of the overall MIR:M composite and two global composites (math calculation and math reasoning) identified significant variation in student growth, within significant linear and quadratic trajectories. However, there were significant differences in the nature of the growth trajectories that have applied educational implications. In addition, growth parameters across the three composites provided significant predictive potential when using the Tennessee Comprehensive Assessment Program (TCAP) Achievement Test, a high-stakes, end of the year assessment of academic achievement, as the criterion measures (p < .001). Furthermore, these parameters were predictive at the classroom and student level. Differential predictive potential of the parameters and the composites provide additional information about the nature of the MIR:M data. Altogether, the growth modeling and the predictive modeling provide evidence to support two practical uses of the MIR:M. v Table of Contents CHAPTER I LITERATURE REVIEW .......................................................................................1 High Stakes Assessment ..................................................................................................2 Curriculum-Based Measurement ......................................................................................9 Student Growth with CBMs ........................................................................................... 23 Growth as a Predictor of High-Stakes Assessment ......................................................... 33 Growth and High-Stakes Predictive Potential of a Multidimensional M-CBM ............... 37 Statement of the Problem ............................................................................................... 39 Research Questions ....................................................................................................... 41 CHAPTER II METHOD ........................................................................................................... 42 Participants .................................................................................................................... 42 Instruments .................................................................................................................... 42 Procedures ..................................................................................................................... 48 Data Cleaning ................................................................................................................ 50 Data Analyses ................................................................................................................ 51 CHAPTER III RESULTS.......................................................................................................... 58 Descriptive Statistics for MIR:M Scores ........................................................................ 58 Modeling Parameters of MIR:M .................................................................................... 59 Predicting TCAP Scores ................................................................................................ 65 CHAPTER IV DISCUSSION ................................................................................................... 76 Modeling of Initial Skills and Growth ............................................................................ 77 Global Composite Differences in Growth ...................................................................... 81 Variables Impacting Common Applied Modeling Procedures ........................................ 87 Predictive Validity ......................................................................................................... 90 vi Summary ..................................................................................................................... 103 Limitations .................................................................................................................. 107 Future Research ........................................................................................................... 110 REFERENCES ....................................................................................................................... 112 APPENDIX ............................................................................................................................ 136 MIR: M EXAMPLE PROBE ....................................................................................... 137 TCAP MATH PROCESSES ITEM SAMPLE ............................................................. 139 TCAP NUMBERS AND OPERATIONS ITEM SAMPLES ........................................ 140 TCAP ALGEBRA ITEM SAMPLES .......................................................................... 144 TCAP MEASUREMENT AND GEOMETRY ITEM SAMPLES ................................ 146 TCAP DATA ANALYSIS, STATISTICS AND PROBABILITY ITEM SAMPLES ... 148 TABLES ................................................................................................................................. 149 VITA ...................................................................................................................................... 166 vii List of Tables Table 1 Descriptive Statistics of MIR:M Total by Probe.......................................................... 149 Table 2 Descriptive Statistics of MIR:M Math Calculation by Probe ....................................... 150 Table 3 Descriptive Statistics of MIR:M Math Reasoning by Probe ........................................ 151 Table 4 Correlations of MIR:M Total by Probe ....................................................................... 152 Table 5 Correlations of MIR:M Math Calculation by Probe .................................................... 153 Table 6 Correlations of MIR:M Math Reasoning by Probe ...................................................... 154 Table 7 MIR:M Total Growth Models ..................................................................................... 155 Table 8 MIR:M Math Calculation Growth Models .................................................................. 156 Table 10 Descriptive Statistics of TCAP Scales ....................................................................... 158 Table 11 Correlations of TCAP Scales .................................................................................... 159 Table 12 Correlations of TCAP Scales by MIR:M Components .............................................. 160 Table 13 Correlations of TCAP Scales by MIR:M Predicted Values at TCAP Administration . 161 Table 14 Percentage of Variance by MIR:M Components, MIR:M Scale, and Hierarchical Levels ........................................................................................................................................ 162 Table 15 Best Predictive Model for Total Composite, MR Global, and MC Global Scores ...... 163 Table 16 Comparison of Common Modeling Procedures of Growth ........................................ 164 Figure 1 Mean Total Score by Probe Administration ............................................................... 165 viii

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Validating Skills Measured by the Monitoring Instructional Responsiveness: Math. A Dissertation sections provide a framework of the modeling and the specific information about the parameters and their notation. Modeling MIR:M Growth. In order to provide the most useful analysis of the MIR: M.
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