Core Progressâ¢ for Math - Renaissance Learning

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$Accelerated Math for Interventionâ¢ - Renaissance Learning$

Phase IV: Empirical analysis of Core Progress MethodIn 2008, Renaissance Learning began Phase IV of Core Progress development: empirical analysis. The orderof skills in the learning progression was re-examined empirically through a calibration process used to analyzeassessment items. The purpose was to compare the empirically observed order of skills (i.e. where skills fallon an assessment scale) to a pedagogically determined ordering of skills (i.e. the most productive order ofskills for teaching, mastering, and learning a concept).Between June 2008 and February 2012 over 9,500 items were field tested, calibrated, and analyzed using aprocess called dynamic calibration. 5 In this process, a small number of experimental items (one to three) wereadded onto each student’s STAR Math Enterprise assessment nationwide. Response data from thousands ofstudents were collected for each of these experimental items, and the items were then calibrated by fitting alogistic regression model (the Rasch model) to the relationship between scores on each item and a student’sRasch ability scores on STAR Math. The result was to calibrate the difficulty of each new item on the sameRasch scale that is used for adaptive item selection in STAR Math.Following the calibration process, the average of the calibrated Rasch response functions for each of theitems assessing a skill was determined; the average is a “skill characteristic curve.” For each skill, a skilldifficulty parameter was then calculated: the point on the Rasch scale at which a student of the same Raschability would have an expected percent correct of 70 if tested on all of the items that measure the skill. Thisparameter is designated SD70, or Scaled Difficulty 70. Finally, the relationship between the empiricallycalibrated SD70 skill difficulties and the sequential order of STAR Math skills in the learning progressionwas evaluated, as a means of validating the Core Progress for Math learning progression.ResultsCore Progress for Math includes 1,326 skills. Figure 3 (next page) shows 626 of the skills plotted by theirdifficulty level on the STAR Math Enterprise assessment scale and their instructional order according to thelearning progression.Each datapoint in Figure 3 represents a skill on the learning progression. The difficulty value (vertical scale) ofeach skill is derived from the calibrated difficulty of the test items from STAR Math that assess that skill. Thereare several assessment items per skill, called an item-set.Best-fitting logarithmic functions relating the SD70 value of each item-set to instructional order werecalculated for each of the four domains of STAR Math. These are plotted in Figure 3 as color-coded curvedlines superimposed on the scatter plot. For each domain, the parameters of the fitted logarithmic functionare displayed, along with the correlation between the skill difficulty parameters and instructional order. Thesecorrelations range from approximately 0.90 (for the Data Analysis, Statistics and Probability domain) to 0.94for the Algebra domain. These correlations may be thought of as measures of the validity of the Core Progresslearning progression for describing the developmental sequence of the hundreds of skills that make up theSTAR Math domains.5New assessment items aligned to the Common Core will continue to be tested on an ongoing basis.10
Figure 3: Correlation of STAR Math Enterprise to Core Progress1000Core Progress Skill DifficultyScaled Difficulty 70800600400Numbers andOperationsAlgebraGeometry andMeasurementData Analysis, Statistics,and Probabilityy = 253.5Ln(x) + 324.85r = 0.9059y = 251.45Ln(x) + 333.35r = 0.9440y = 271.68Ln(x) + 313.65r = 0.9104y = 240.13Ln(x) + 334.27r = 0.89602000 2 4 6 8 10 12Grade Level OrderThe high correlation between STAR MathEnterprise and Core Progress providesempirical evidence of the bridge betweenassessment and instruction.11
Page 1 and 2: Integralcomponents ofAccelerated Ma
Page 3 and 4: ContentsExecutive Summary..........
Page 5 and 6: IntroductionOver the last decade, m
Page 7 and 8: Evolution of the Core Progress lea
Page 9 and 10: Phase II: Revised scope and sequenc
Page 11 and 12: Prerequisite mapping in Core Progre
Page 13: Figure 2 offers a different way to
Page 17 and 18: Phase V: Building a new learning pr
Page 19 and 20: Core Progress : an integral compon
Page 21 and 22: School: Pine Hill Middle SchoolClas
Page 23 and 24: ConclusionThe goal of school distri
Page 25 and 26: CORE PROGRESS FOR MATH LEARNING PRO
Page 27 and 28: CORE PROGRESS FOR MATH LEARNING PRO
Page 29 and 30: CORE PROGRESS LEARNING PROGRESSION
Page 37 and 38: Heritage, M. (2009). The case for l
Page 40: AcknowledgementsDr. Karin Hess, Sen

Core Progressâ¢ for Math - Renaissance Learning

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Core Progressâ¢ for Math - Renaissance Learning