Core Progressâ¢ for Math - Renaissance Learning

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$Accelerated Math for Interventionâ¢ - Renaissance Learning$

What are learning progressions?Simply put, learning progressions are descriptions of how learning typically advances in a subject area.Specifically, Pellegrino (2011, p. 9) defines learning progressions as “descriptions of successively moresophisticated ways of thinking about key disciplinary concepts and practices across multiple grades” whichoutline “the intermediate steps toward expertise.” Leahy and Wiliam (2011, p. 1) view learning progressionsas descriptions of “what it is that gets better when someone gets better at something.” “Empirically basedlearning progressions can visually and verbally articulate a hypothesis, or an anticipated path, of how studentlearning will typically move toward increased understanding over time with good instruction” (Hess, Kurizaki,and Holt, 2009).Confrey and colleagues suggest that learning progressions assume a progression of cognitive states thatmove from simple to complex and, while not necessarily linear, the progression is not random, but rather issequenced and ordered as “expectedtendencies” or “likely probabilities” of howlearning develops (Confrey and Maloney, 2010).Masters and Forster (1996, p. 1) describeprogressions as “a picture of what it means to‘improve’ in an area of learning.”Finally, Heritage (2011, p. 3) suggests thatlearning progressions provide descriptions of“how students’ learning of important conceptsand skills in a domain develops from its mostrudimentary state through increasinglysophisticated states over a period of schooling.”“Empirically based learningprogressions can visually andverbally articulate a hypothesis, oran anticipated path, of how studentlearning will typically move towardincreased understanding over timewith good instruction.”Hess, Kurizaki, and Holt, 2009Inherent in these views of progressions is the idea of a coherent and continuous pathway along whichstudents move incrementally through states of increasing competence in a domain. Every incremental statebuilds on and integrates the previous one as students accrue new levels of expertise with each successivestep in the progression. It is important to note, however, that while progressions may provide cleardescriptions of how learning develops in a domain, they are not developmentally inevitable. Rather, theyare dependent on well-mapped curriculum and sound instruction (Duschl, Schweingruber, and Shouse, 2007;Pellegrino, 2011). It should also be noted that the strong hierarchical nature of mathematics makes suchprogressions absolutely necessary.As Herman (2006, p. 122) observes, “whether and how children are able to engage in particular learningperformances and the sequence in which they are able to do so are very much dependent on previousopportunities to learn.” The benefit of progressions is that they lay out a continuum to guide teaching andlearning over time so that student competence in the domain can be advanced coherently and continuously.Several views of how learning progressions can be developed have been set forth (for example, Alonzo andSteedle, 2008; Anderson, 2008a; Corcoran, Mosher, and Rogat, 2009; Confrey and Maloney, 2010; Hess,2010; Hess, Kurizaki, and Holt, 2009; Pellegrino, 2011; Smith, Wiser, Anderson, and Krajcik, 2006). Commonto these perspectives is the idea that the development of learning progressions is an iterative process. Itbegins with a hypothesis, informed by what we know about student learning, which undergoes empiricaltesting and subsequent refinement based on the data. Core Progress for Math was developed according tothis iterative model.2
Evolution of the Core Progress learning progression for mathematicsCore Progress began as a scope and sequence and evolved into an empirically validated learningprogression. Since its inception in 2007, Core Progress has gone through a continuous cycle of research,review, and revision.Core Progress was developed to provide a research-based framework for Accelerated Math personalizedpractice software. Once built, the Core Progress skills were field tested through the STAR Math assessment 1 .The results were noteworthy and gratifying. The order of skills in Core Progress was highly correlated withthe difficulty level of STAR Math Enterprise assessment items. With a strong correlation, the natural next stepwas to statistically link Core Progress to the STAR Math assessment. As a result, a student’s STAR Math scoreprovides insight into his/her achievement level, as well as skills he/she is ready to learn next. Core Progress isnow an integral component of both Accelerated Math Live and STAR Math Enterprise—a true bridge betweenassessment, instruction, and practice.Phase I: Scope and sequenceResearchThe origin of the Core Progress learning progression dates back to 2007. It started as a scope and sequencefor Accelerated Math Enterprise 2 , spanning grade 1 to algebra.To develop the original scope and sequence, Renaissance Learning’s mathematics team relied heavily onresearch and standards including the National Council of Teachers of Mathematics (NCTM) CurriculumFocal Points (2006), the early work of the National Mathematics Advisory Panel (2008), state and internationalmathematics standards, and the American Diploma Project Benchmarks (Achieve, Inc., 2007) which provideone of the key foundations for the Common Core State Standards.ReviewThe scope and sequence was reviewed by several experts including the Education Northwest, 3 a researchlaboratory funded by the U.S. Department of Education; a panel of mathematics teachers; and a panel ofprominent mathematicians:• Dr. Sybilla Beckmann, University of Georgia, (grade 5 review)• Dr. Richard Bisk, Worcester State College, (grade 6 review)• Dr. Tom Hogan, University of Scranton (all core objectives)• Dr. James Milgram, Stanford University (grade 3 core review)• Dr. Sharif Shakrani, Michigan State University (grade 8, Algebra 1, and Geometry review)1Over 9,500 items were field tested between June 2008 and February 2012. See pages 10-11 for more information.2 Accelerated Math enables differentiated practice in mathematics and provides daily information on every skill students master. Accelerated Math wasfirst released in 1998 with a scope and sequence that reflected the standards and curricula of the time. The second edition of Accelerated Math,developed in 2007 and released in 2008, was built on the Core Progress for Math learning progression, and Accelerated Math Live, developed in2012-2013, now includes content libraries based on the Core Progress Math built for CCSS learning progression.3Formerly the Northwest Regional Educational Laboratory3
Page 1 and 2: Integralcomponents ofAccelerated Ma
Page 3 and 4: ContentsExecutive Summary..........
Page 5: IntroductionOver the last decade, m
Page 9 and 10: Phase II: Revised scope and sequenc
Page 11 and 12: Prerequisite mapping in Core Progre
Page 13 and 14: Figure 2 offers a different way to
Page 15 and 16: Figure 3: Correlation of STAR Math
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

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Core Progressâ¢ for Math - Renaissance Learning