the research foundation for accelerated math™

WHITE PAPER | AUGUST 2017

The Research Foundation for Accelerated Math®

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RENAISSANCEP.O. Box 8036Wisconsin Rapids, WI 54495-8036(800) [email protected]

08/17

Accelerated Math has “strong evidence of effectiveness” for

prevention and intervention at all grade levels according to the National Dropout Prevention Center/Network.

Accelerated Math is endorsed by the Council of Administrators of

Special Education.

Accelerated Math is highly rated for progress monitoring mastery

measurement by the National Center on Intensive Intervention.

Contents1 Introduction

1 Why math practice is essential

4 Accelerated Math software provides solutions for educators’ biggest challenges

8 High-quality progress monitoring and mastery measurement with Accelerated Math

8 Bridging assessment and instruction with Accelerated Math

10 Accelerated Math accolades

11 Efficacy: Key research support for Accelerated Math

19 Appendix A. Accelerated Math meets key components of effective instruction

20 Appendix B. Fidelity of implementation

21 References

Figures

2 Figure 1. Practice thickens myelin sheath

7 Figure 2. Greater math subskill mastery per week boosts achievement

9 Figure 3. Core Progress skill difficulty highly correlates with Star Math items

11 Figure 4. The better Accelerated Math is used, the more students grow and meet key benchmarks

12 Figure 5. Star Math reports higher increases for students using Accelerated Math

13 Figure 6. Accelerated Math students perform better on AIMS test than peers

13 Figure 7. High Accelerated Math implementation leads to greater TerraNova gains

14 Figure 8. Accelerated Math achievement gains by subgroup

14 Figure 9. High Accelerated Math implementers outperform low on CRCT

15 Figure 10. Title I students using Accelerated Math achieve more growth

15 Figure 11. GT students make greater gains with Accelerated Math

16 Figure 12. Students using Accelerated Math outpace district average on NALT

16 Figure 13. Students at all levels increase NALT scores with Accelerated Math

17 Figure 14. SAT-9 gains greater for Accelerated Math students

17 Figure 15. Accelerated Math use results in higher NALT growth

18 Figure 16. EL students make greater strides on NALT with Accelerated Math than peers

18 Figure 17. Pretest to posttest change on ITBS is largest for students using Accelerated Math

Tables

5 Table 1. Accelerated Math provides solutions for common barriers to practice and progress monitoring

6 Table 2. Accelerated Math accomplishes key components of effective practice

19 Table A1. How Accelerated Math addresses research-based instructional practices

©Copyright 2016 Renaissance Learning, Inc. All rights reserved. 1

IntroductionExtensive research has determined which instructional practices have the greatest impact on student achievement. Providing students time for appropriately challenging math practice, ensuring students receive feedback on this practice, setting goals with students, and frequently monitoring their progress toward set goals are all components of effective instruction and supported by a well-confirmed knowledge base (e.g., Christenson & Ysseldyke, 1989; Ysseldyke & Christenson, 1987; see Appendix A, p. 19).

Practice is a non-negotiable part of the learning process; this is especially true in mathematics. Time spent intensively practicing a skill—not initial ability—is the single most important shared characteristic of mathematicians as well as world-class chess players and musicians (Coyle, 2009; Ericsson, Charness, Feltovich, & Hoffman, 2006). Per cognitive scientist Dan Willingham, “It is virtually impossible to become proficient at a mental task without extended practice” (2009, p. 81).

In addition to practice, progress monitoring with formative assessment is necessary to continuously check the effectiveness of classroom instruction, identify students struggling with math skills, and measure students’ growth toward personal goals. “Only by keeping a very close eye on emerging learning through formative assessment can teachers be prospective, determining what is within the students’ reach, and providing them experiences to support and extend learning” (Heritage, 2010, p. 8).

The purpose of formative assessment is to provide feedback to students that will help close the gap between current academic performance and goal performance. To do this, “teachers need to have in mind a continuum of how learning develops in any particular knowledge domain so that they are able to locate students’ current learning status and decide on pedagogical action to move students’ learning forward” (Heritage, 2008, p. 2). Clearly articulated learning progressions can support instructional planning and formative assessment.

Though the need for practice and progress monitoring in building various skills is clear, these instructional practices are not always implemented in the classroom. The National Mathematics Advisory Panel (National Math Panel [NMP], 2008b) report states that “few curricula in the United States provide sufficient practice” (p. 26). Additionally, research on classroom-level monitoring and assessment reveals that “many teachers do not: assign homework frequently or regularly, record completion assignments, monitor seat work and check on students’ progress, or conduct the kind of questioning that helps to monitor learning” (Khairo, 2014, p. 35). As for learning progressions, Heritage (2008) notes that “teachers need to understand the pathways along which students are expected to progress....despite a plethora of standards and curricula, many teachers are unclear about how learning progresses in specific domains” (p. 2).

Effective, personalized practice requires continuous daily—even hourly—instruction, practice, and assessment within a formative assessment process. Renaissance Accelerated Math® facilitates student math practice and equips teachers with data to monitor progress, adjust instruction and curriculum, and provide feedback.

Why math practice is essential Mathematical proficiency is of critical importance, both to succeed academically and ultimately in life beyond schooling. The National Research Council (2001) uses this term to describe “five interrelated strands of knowledge, skills, abilities, and beliefs that allow for mathematics manipulation and achievement across all mathematical domains (e.g., conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition)” (Steedly, Dragoo, Arefeh, & Luke, 2008, p. 10). For students to learn successfully, these interconnected strands must work together. “For example, as a student gains conceptual understanding,

Practice is a non-negotiable part of the learning process.

Accelerated Math facilitates student math practice and equips teachers with data to monitor progress, adjust instruction and curriculum, and provide feedback.


computational procedures are remembered better and used more flexibly to solve problems. In turn, as a procedure becomes more automatic, the student is enabled to think about other aspects of a problem and to tackle new kinds of problems, which leads to understanding” (National Research Council, 2002, p. 17).

Students are capable of learning mathematics, but it does not just happen—it takes time, effort, and practice (Willingham, 2009–10). Practice is an essential part of learning and is often what makes the difference between successfully learning a skill or not: “It is intuitively obvious that practice is necessary for learning knowledge of any type. It’s not surprising then that research indicated that practice significantly enhances learning….The effect of practice on learning can be substantial” (Marzano, Gaddy, & Dean, 2000, p. 66).

Brain research explains why practice is universally important for learning. Practice helps build neurological connections, evidenced by increased white matter in the brain, which is the result of a process called myelination (see figure 1). These connections help people solve higher order problems faster and more efficiently, using less area of the brain and with less overall brain activity. Once a skill is taught, repeated practice alters the neurons in a part of the brain specific to that skill, so a skill can be performed automatically, seemingly without thought (Coyle, 2009; Hill & Schneider, 2006). “Practice allows students to achieve automaticity of basic skills—the fast, accurate, and effortless processing of content information—which frees up working memory for more complex aspects of problem solving” (NMP, 2008b, p. 30; Sousa, 2006).

Figure 1. Practice thickens myelin sheath

Research shows practice increases neurological connections, specifically the thickness of insulating myelin sheath, which vastly improves overall brain efficiency and higher-order thinking ability.

Researchers say we forget much of what we learn, and that the forgetting is rapid, though continued practice can protect against forgetting (Willingham, 2009). In one study, researchers found that a student who achieved a C in his first algebra course but went on to take several more math courses remembered his algebra, whereas a student who got an A in algebra but did not continue in math courses forgot what he learned (Bahrick & Hall, 1991). Taking additional math courses ensures students continue to think about and practice what they have learned.

Research also shows that in order to develop competence in skills, students need to adapt or “shape” them as they are learning. Appropriately challenging personalized practice with feedback is the primary means of doing this. The timing of feedback is of key importance, as students should have the opportunity to grapple with a problem and self-correct, finding any missteps through additional practice and error analysis. According to Marzano et al. (2000):

Students are capable of learning mathematics, but it does not just happen—it takes time, effort, and practice. (Willingham, 2009–10)


During this shaping phase, learners modify the way they use the skill, become aware of potential problem areas as well as variations in how the skill can be used, and learn to use the skill in different situations. The importance of this shaping phase cannot be overstated, yet this crucial stage of learning is often not given the necessary time and attention. Skipping or shortchanging this stage of learning can result in students’ internalizing errors that are difficult to correct. It can also mean that students will not gain the conceptual understanding that is essential to truly mastering a skill or process. (p. 67)

Academic learning time (ALT)—the amount of time students spend on actual learning activities—has long been identified as a critical contributor to academic growth (Batsche, 2007; Berliner, 1990; Gettinger & Stoiber, 1999; Karweit, 1982). An important, but often underemphasized aspect of ALT is time for practice of learned skills—which is as important as explicit instruction (Szadokierski & Burns, 2008). Since ALT is the time when most learning actually takes place, increasing ALT is a powerful tool for improving academic results (Aronson, Zimmerman, & Carlos, 1998; Berliner, 1978; Smith, 1998).

Four components distinguish ALT from simple measures of classroom time or “time on task”:

• Students are engaged with material

• Material is at the proper level of challenge

• Students experience high rates of success

• Both students and teacher receive regular feedback about performance

The challenge is that to increase ALT it is necessary to directly manage it, which is exceedingly difficult, especially in diverse classrooms where learners are working at many different levels at the same time.

The role of practice within college- and career-readiness standardsThe role of practice in learning mathematics is especially crucial in light of college- and career-readiness standards, which require “students to demonstrate deeper conceptual understanding through the application of content knowledge and skills to new situations and sustained tasks” (Hess, Carlock, Jones, & Walkup, 2009, p. 1). The rigor required of the new standards demands pedagogical shifts (Engage NY, 2012) that relate to researcher Norman Webb’s widely accepted measure of cognitive rigor, the four depths of knowledge (DOK) levels: Level 1: Recall & Reproduction, Level 2: Basic Skills & Concepts, Level 3: Strategic Thinking & Reasoning, and Level 4: Extended Thinking. The four levels each play an important role in students’ learning and do not represent a linear progression.

Integrating deeper levels of knowledge is important, so that students are able to strategically apply concepts learned to other problems. However, it is a common misconception that students should be spending all or most of their time on higher-order thinking skills and less time on learning and practicing foundational skills. Particularly in mathematics, there should be strong emphasis on foundational skills so that students can successly move on to application of these skills.

Descriptive analyses of the Common Core State Standards prepared for the Smarter Balanced Assessment Consortium show the following breakdown of DOK levels assigned to the new mathematics standards (each standard can cover a range of DOK levels): 89% were assigned DOK Level 1, 79% were assigned DOK Level 2, 21% were assigned DOK Level 3, and less than 1% were assigned DOK Level 4 (Sato, Lagunoff, & Worth, 2011). And practice guru and author Doug Lemov argues that although many educators perceive “drilling” students with foundational skills is the enemy of higher-order thinking, cognitive psychology research shows this is not true (Lemov, Woolway, & Yezzi, 2012). Establishing a strong foundation in basic skills paves the way for future understanding, application, and analysis of concepts learned. According to Willingham (2009), basic processes that initially are demanding of working memory become automatic with practice, and by making these low-level processes automatic, room is made for more high-level concerns.

Establishing a strong foundation in basic skills paves the way for future understanding, application, and analysis of concepts learned.


Accelerated Math® software provides solutions for educators’ biggest challengesAccelerated Math provides efficient progress monitoring and management of students’ personalized daily math practice for grades K–12 within a formative assessment process. Accelerated Math can be used successfully as the essential student practice component of existing classroom mathematics curricula (Ysseldyke & Betts, 2010; Ysseldyke & Bolt, 2007), supplying libraries of math problems from kindergarten math to calculus, algebra, geometry, and probability and statistics, as well as libraries aligned to various state standards, national guidelines, and textbook series. The program assists teachers with

• Creating personalized assignments and tests at an appropriate level for each student

• Scoring student practice and assessments automatically, and recording results in a grade book

• Providing informative feedback to help educators differentiate instruction and monitor progress

• Encouraging mathematical discourse and collaboration

• Motivating students with immediate feedback after assignments or tests are completed

• Promoting practices that ensure fidelity of implementation, which include recommendations for optimal growth and appropriate goal-setting practices (see Appendix B, p. 20)

The Accelerated Math libraries were first published in 1998, with a scope and sequence based on commonalities between the 1989 National Council of Teachers of Mathematics (NCTM) standards and leading publisher textbooks, National Assessment of Educational Progress (NAEP) editions, and math editor teaching experience from the 1990s. Then in 2006, the Accelerated Math libraries went through a thorough review and update to create what we termed the Second-Edition Libraries. To ensure the content in the second edition met the highest standards of the day, Renaissance developed a new scope and sequence for early numeracy, grades 1 through 8, algebra 1, and geometry that included core objectives, learning progressions, and prerequisite skills.

Several resources informed the new scope and sequence: extensive research by Renaissance on the NCTM Curriculum Focal Points (2006), the final report of the National Mathematics Advisory Panel (2008a, 2008b), and state and international standards; convening of a reviewer panel of mathematicians and researchers including Dr. Sybilla Beckmann (University of Georgia), Dr. Richard Bisk (Worcester State College), Dr. Tom Hogan (University of Scranton), Dr. R. James Milgram (Stanford University), Dr. Sharif M. Shakrani (private consultant/researcher), and Dr. Amanda VanDerHeyden (private consultant/researcher); and consultation with the US Department of Education’s Northwest Regional Educational Laboratory and mathematics teachers in several states.

Then in 2013, a significant addition to Accelerated Math came in the form of custom-built libraries built specifically aligned to college and career-readiness standards. Renaissance’s content development team created the brand-new content following constructs in the K–8 and High School Publishers’ Criteria for the Common Core State Standards for Mathematics, including identifying and analyzing skills, developing a coherent progression (validated with data on student performance), ensuring content adhered to CCSS expectations, and engaging with mathematics experts for input. Dr. VanDerHeyden (grades K–2), Dr. Karen Hess, private consultant/researcher (grades 3–5), and Dr. Milgram (grades 6–high school) provided expert review of the libraries prior to publication.

Since that time, further refinements to Accelerated Math have helped teachers balance math practice both for students working on grade-level standards and for those striving to catch up on foundational skills. Students are grouped according to Renaissance Star Math® data, and the Accelerated Math program then schedules standards coverage and dynamic practice for the entire school year. Teachers monitor student progress and manage assignments, which helps them determine tactics for differentiated instruction and move each student toward deep standards mastery.

Content aligned with key math recommendations Accelerated Math facilitates formative assessment defined by McManus (2008) as “a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students’ achievement of intended instructional outcomes” (p. 3). Likewise, the software helps educators meet recommendations in the National Math Panel’s final report (2008b) by

Accelerated Math meets five criteria identified by the FAST SCASS for effective formative assessment (McManus, 2008):

1. Learning progressions

2. Learning goals and criteria for success

3. Descriptive feedback

4. Self- and peer-assessment

5. Collaboration


Accelerated Math® software provides solutions for educators’ biggest challengesAccelerated Math provides efficient progress monitoring and management of students’ personalized daily math practice for grades K–12 within a formative assessment process. Accelerated Math can be used successfully as the essential student practice component of existing classroom mathematics curricula (Ysseldyke & Betts, 2010; Ysseldyke & Bolt, 2007), supplying libraries of math problems from kindergarten math to calculus, algebra, geometry, and probability and statistics, as well as libraries aligned to various state standards, national guidelines, and textbook series. The program assists teachers with

• Creating personalized assignments and tests at an appropriate level for each student

• Scoring student practice and assessments automatically, and recording results in a grade book

• Providing informative feedback to help educators differentiate instruction and monitor progress

• Encouraging mathematical discourse and collaboration

• Motivating students with immediate feedback after assignments or tests are completed

• Promoting practices that ensure fidelity of implementation, which include recommendations for optimal growth and appropriate goal-setting practices (see Appendix B, p. 20)

The Accelerated Math libraries were first published in 1998, with a scope and sequence based on commonalities between the 1989 National Council of Teachers of Mathematics (NCTM) standards and leading publisher textbooks, National Assessment of Educational Progress (NAEP) editions, and math editor teaching experience from the 1990s. Then in 2006, the Accelerated Math libraries went through a thorough review and update to create what we termed the Second-Edition Libraries. To ensure the content in the second edition met the highest standards of the day, Renaissance developed a new scope and sequence for early numeracy, grades 1 through 8, algebra 1, and geometry that included core objectives, learning progressions, and prerequisite skills.

Several resources informed the new scope and sequence: extensive research by Renaissance on the NCTM Curriculum Focal Points (2006), the final report of the National Mathematics Advisory Panel (2008a, 2008b), and state and international standards; convening of a reviewer panel of mathematicians and researchers including Dr. Sybilla Beckmann (University of Georgia), Dr. Richard Bisk (Worcester State College), Dr. Tom Hogan (University of Scranton), Dr. R. James Milgram (Stanford University), Dr. Sharif M. Shakrani (private consultant/researcher), and Dr. Amanda VanDerHeyden (private consultant/researcher); and consultation with the US Department of Education’s Northwest Regional Educational Laboratory and mathematics teachers in several states.

Then in 2013, a significant addition to Accelerated Math came in the form of custom-built libraries built specifically aligned to college and career-readiness standards. Renaissance’s content development team created the brand-new content following constructs in the K–8 and High School Publishers’ Criteria for the Common Core State Standards for Mathematics, including identifying and analyzing skills, developing a coherent progression (validated with data on student performance), ensuring content adhered to CCSS expectations, and engaging with mathematics experts for input. Dr. VanDerHeyden (grades K–2), Dr. Karen Hess, private consultant/researcher (grades 3–5), and Dr. Milgram (grades 6–high school) provided expert review of the libraries prior to publication.

Since that time, further refinements to Accelerated Math have helped teachers balance math practice both for students working on grade-level standards and for those striving to catch up on foundational skills. Students are grouped according to Renaissance Star Math® data, and the Accelerated Math program then schedules standards coverage and dynamic practice for the entire school year. Teachers monitor student progress and manage assignments, which helps them determine tactics for differentiated instruction and move each student toward deep standards mastery.

Content aligned with key math recommendations Accelerated Math facilitates formative assessment defined by McManus (2008) as “a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students’ achievement of intended instructional outcomes” (p. 3). Likewise, the software helps educators meet recommendations in the National Math Panel’s final report (2008b) by

Accelerated Math meets five criteria identified by the FAST SCASS for effective formative assessment (McManus, 2008):

1. Learning progressions

2. Learning goals and criteria for success

3. Descriptive feedback

4. Self- and peer-assessment

5. Collaboration

• Presenting “a focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics” (pp. xvi, 20–22)

• Supplying “sufficient and appropriate practice” that fosters “computational proficiency with whole number operations….fluency with the standard algorithms….[and] a solid understanding of core concepts” (pp. xix, 26–29)

• Focusing on effort rather than ability, which “increases [student] engagement in mathematics learning [and] improves mathematics outcomes” (pp. xx, 31–32)

• Promoting “regular use of formative assessment,” which “improves…students’ learning” (pp. xxiii, 46–48)

• Providing “tools that inform teachers about specific ways of using formative assessment information to provide differentiated instruction” (pp. 46–48)

Accelerated Math also meets five criteria identified by the Formative Assessment for Students and Teachers (FAST) State Collaborative on Assessment and Student Standards (SCASS) for effective formative assessment: (1) learning progressions, (2) learning goals and criteria for success, (3) descriptive feedback, (4) self- and peer-assessment, and (5) collaboration (McManus, 2008). Even though personalized practice and progress monitoring are key to student success in mathematics, classrooms may lack these routines due to three common barriers (see table 1). Accelerated Math can help educators meet these challenges.

Table 1. Accelerated Math® provides solutions for common barriers to practice and progress monitoring

Challenge for educators How Accelerated Math® helps

Effectively and efficiently personalizing student practice

Accelerated Math helps teachers analyze individual skills deficiencies and fill gaps in learning progressions as well as increase student practice of specific standards-linked skills. The National Math Panel describes Accelerated Math as a “mathematics program with assessment of skill level, tailoring of the instruction to match skill level, individual pacing and goal setting, ample practice, and immediate feedback to student and teacher on performance” (2008a, p. 160).

Consistently monitoring student progress

As a technology-enhanced, continuous progress-monitoring system (Ysseldyke & Burns, 2009; Ysseldyke & McLeod, 2007), Accelerated Math can be used for practice progress monitoring—the measuring of performance by underlying tasks (such as math problems) that contribute to growth in math skills or benchmarks.

Bridging assessment and instruction

The Renaissance Core Progress® Math learning progression (see pp. 8–10, also Renaissance, 2013) reveals intermediate steps and prerequisite skills needed to reach the level of expertise required by college- and career-readiness standards. Core Progress skills and understandings range from early numeracy to competencies required in college and the workplace.

Facilitates efficient and effective personalized student practice Accelerated Math helps educators facilitate academic learning time by supporting key aspects of effective student practice (see table 2).


Table 2. Accelerated Math® accomplishes key components of effective practice

Characteristics of effective practice What Accelerated Math® does

Fully engaging with the materialAs Berliner (1990) noted, “A synonym for engaged time is ‘attention’” (p. 4), which is the time students spend focused on materials/presentations with instructional goals. This implies a mental attitude in which attention “is given voluntarily and steadily by all during the entire instruction” (Currie, 1884, p. 224).

The Accelerated Math classroom is structured so that students are always using time productively, by working on assignments or tests, submitting work to be scored, or conferring with the teacher for additional instruction and intervention or with other students for peer-learning opportunities. Student routines and expectations are clearly communicated in an Accelerated Math classroom, so students always know where efforts should be focused. If guidance is needed, the teacher (and classroom signage) is available to provide direction.

Working at an optimal level of challengeAccording to Csikszentmihalyi (1991), the appropriate level of difficulty should result in a state of flow, “a sense that one’s skills are adequate to cope with the challenges at hand, in a goal-directed, rule-bound action system that provides clear clues as to how well one is performing” (p. 71).

Star Math assessments coupled with ongoing measurement of results from the Accelerated Math program ensure assignments are tailored to each student’s individualized level, which is continuously recalculated as the student progresses.

Students experiencing a high rate of successHigh levels of success are necessary to maintain engagement and student motivation. If students are not highly successful, their will to continue working will be threatened (Ericsson, Krampe, & Tesch-Römer, 1993).

With Accelerated Math, teachers help students become highly successful math learners by ensuring they maintain an average percent correct of 75% or above on assignments and 85% or above on tests.

Receiving immediate informative feedbackTo monitor and manage math skills practice, frequent feedback on student results is essential, so teachers can intervene as necessary and assure each student is successful at a high level (above 85–90% in the case of reading and math) (Ericsson et al., 1993; Topping & Sanders, 2000). Per the Institute of Education Sciences, teachers should “provide feedback to students that is timely, specific, well formatted, and constructive,” which may improve academic achievement (Hamilton et al., 2009, p. 9).

Instant feedback is provided to both students and teachers in Accelerated Math, making it possible for students to know exactly which subskills need more practice and for teachers to monitor progress and adjust assignments according to student needs. By design, feedback is shared after completed assignments and tests, rather than after each item, to give students an opportunity to self-correct, either through repeated practice or error analysis.

Evidence of the positive effect of time spent by students engaged in learning activities (i.e., academic learning time) on student growth is revealed in an analysis of the Accelerated Math database. Figure 2 (next page) shows that students who master more math subskills per week have higher student growth percentiles (SGPs), a measure that compares a student’s growth to that of academic peers nationwide (i.e., students in the same grade with a similar score history).


Figure 2. Greater math subskill mastery per week boosts achievement

99

50

1

Fall-to-spring growth (SGP)

Sprin

g ac

hiev

emen

t (PR

)

Low achievement, high growthLow achievement, low growth

High achievement, low growth High achievement, high growth

1 50 99

Math subskills mastered/week

(Volume)

Median SGP: student growth

percentile(Growth)

Median PR: percentile rank

(Spring achievement)

Number of students

< = .5 46 48 59,753

0.51 - 1 50 56 68,077

1.01 - 1.5 52 61 47,657

1.51 - 2 55 65 33,351

2.01 - 2.5 56 68 23,350

2.51 - 3 58 72 16,713

> 3 60 76 37,171

Encourages student collaboration Talking about math encourages students to take ownership of their practice and reflect on new math concepts. Encouraging mathematical discourse in the classroom allows students to make sense of and critique their peers’ ideas, creating deep, connected math knowledge that will prepare them for the rigors of college and the workplace.

Students’ Accelerated Math assignments are an ideal jumping off point for students to talk with their classmates about the math skills they are learning. The work they do on paper while solving unique problem sets creates a record of their reasoning they can reference while speaking with their peers. Students can share the steps they took to solve a particular problem and share points of confusion or road blocks they encountered while completing their work.


High-quality progress monitoring and mastery measurement with Accelerated Math®

Accelerated Math can be thought of as an assessment for daily practice monitoring, meaning it is designed to provide feedback regarding both student completion of important tasks known to improve achievement outcomes (such as math problem solving) and student comprehension of direct instruction. Assessments at this level provide the majority of the information necessary to inform instruction and personalize student practice that will improve performance. Integrated assessment technology is a practical way to administer daily assessments and benefit from the wealth of data they provide (Renaissance, 2016).

Given the strong connection between teacher monitoring of student progress and subsequent academic performance for students, it is critical teachers receive thorough training in progress monitoring. However, a meta-analysis of classroom-level monitoring and assessment research reveals that this is not always the case (Cotton, 1988):

• Many teachers do not assign homework frequently or regularly, record completion assignments, monitor seatwork and check students’ progress, or conduct questioning that helps to monitor learning.

• Teachers do not receive adequate preservice training in conducting formal or informal assessments.

• Administrative support for and in-service training in the skills associated with assessment and monitoring are extremely insufficient.

• Many teachers are aware their monitoring skills are inadequate and desire training to expand their capabilities; others are unaware of the importance of close monitoring of student progress and of their own need for skill development.

Research on teachers’ decision-making processes suggests a lack of progress monitoring. According to the research, “a great many teachers are reluctant to make changes in the instructional strategy or pacing of lessons once these are planned, even when instruction and learning are progressing poorly” (Cotton, 1988, p. 6).

Accelerated Math provides continuous, differentiated student practice within a difficulty range that is neither too hard, and thus frustrating, nor so easy that no new knowledge and skills are learned. In order to customize student practice and ensure kids are working at appropriate levels of challenge, the teacher determines each student’s beginning placement in Accelerated Math using results from a reliable and valid standardized math assessment, such as Star Math, and/or an Accelerated Math Diagnostic Test. Based on their results, students begin personalized practice/test cycles that proceed through mastery and review of each needed subskill. In mastery measurement systems such as this, students work through a hierarchical sequence of skills and demonstrate mastery of each before proceeding to the next skill (www.rti4success.org).

With Accelerated Math, student math practice and teacher monitoring take place each day. This continuous daily stream of data shows how students are performing and provides feedback long before progress can be measured by other methods, such as weekly or monthly progress monitoring. The program tracks the status of each student’s practice assignments and tests, including the subskills a student or group has been assigned, are ready to test on, or may be struggling with. Also tracked are students’ percent correct on assignments and tests, number of subskills mastered, and academic growth and achievement. These insights provide a quick but holistic view of students’ overall math progress, which helps teachers evaluate instruction, identify student needs, and intervene quickly and effectively to give all students help exactly when needed. Immediate feedback is much more useful to inform and adapt instruction and student practice than waiting for mid-year or end-of-year scores when it is too late to make changes that could impact a student’s growth.

Bridging assessment and instruction with Accelerated Math®

Renaissance’s trusted Accelerated Math software has positively impacted student mathematics learning and provided a way for teachers to measure mastery of math skills for more than 15 years. As described by the National Math Panel, Accelerated Math is a “mathematics program with assessment of skill level, tailoring of the


instruction to match skill level, individual pacing and goal setting, ample practice, and immediate feedback to student and teacher on performance” (2008a, p. 160).

Learning progressionsNew standards for teaching and learning abound in education today; however, as Duschl, Schweingruber, and Shouse (2007) note, “many standards and curricula contain too many disconnected topics that are given equal priority. The way many standards and curricula are conceived limits their utility for planning instruction and assessing learning. Too little attention is given to how students’ understanding of a topic can be supported from grade to grade” (p. 231). Explicit learning progressions can provide clarity for teachers by describing a pathway of learning for each student to assist with instruction.

Learning progressions describe how learning usually advances in a subject area. “Empirically based learning progressions can visually and verbally articulate a hypothesis, or an anticipated path, of how student learning will typically move toward increased understanding over time with good instruction” (Hess, Kurizaki, & Holt, 2009). This pathway anchors both instruction and assessment because “when teachers understand the continuum of learning in a domain and have information about current status relative to learning goals (rather than to the activity they have designed to help students meet the goal), they are better able to make decisions about what the next steps in learning should be” (Heritage, 2008, p. 2).

Recent enhancements to Star Math and Accelerated Math seamlessly integrate assessment with instruction and practice. A student takes a Star Math test, and the resulting score helps teachers determine the level of understanding of particular skills and the type of practice needed. Accelerated Math then generates personalized practice assignments based on the skills the student is ready to learn next or to review. The order of the subskills assigned to each student is based on an interconnected web of prerequisite skills in the Core Progress Math learning progression.

Core Progress was developed to provide a research-based framework for Accelerated Math (Renaissance, 2013). Once built, Core Progress skills were field tested through the Star Math assessment, with remarkable results. As illustrated in figure 3, the order of skills in the learning progression was highly correlated with the difficulty level of Star Math items. With this strong correlation, the natural next step was to statistically link Core Progress to Star Math.

Figure 3. Core Progress® skill difficulty highly correlates with Star Math® items

0 2 4 6 8 10 12200

400

600

800

1000

Data Analysis, Statistics, and Probability

Geometry and Measurement

Algebra

Numbers and Operations

Core Progress Skill Difficulty

Scal

ed D

iffic

ulty

70

Grade Level Order

y = 240.13Ln(x) + 334.27r = 0.8960

y = 271.68Ln(x) + 313.65r = 0.9104

y = 251.45Ln(x) + 333.35r = 0.9440

y = 253.5Ln(x) + 324.85r = 0.9059

As a result of this linking, a student’s Star Math score provides insight into both achievement level and the skills and understandings the student is ready to develop next. Core Progress is now an integral component of Accelerated Math and Star Math, helping to seamlessly bridge assessment, instruction, and practice.


Can be used with any curriculumNo matter the curriculum used in a classroom, Accelerated Math is an excellent means for providing and monitoring student math practice. Teachers deliver instruction using a given textbook, and can then have students use Accelerated Math to practice what they have learned.

A study by Ysseldyke and Betts (2010) compared students using specific textbook curricula—both traditional and reform (enVision Math, Everyday Mathematics, Holt McDougal, Macmillan/McGraw-Hill, and Saxon Math)—with and without Accelerated Math. Results showed students using Accelerated Math outperformed their peers who did not use the software.

Content aligned to college- and career-readiness standardsTo help students achieve deep standards mastery, Accelerated Math’s K–12 content libraries were built to meet the rigors of college and career expectations and differentiated by depth. The program provides students with a solid base in foundational skills and practice with higher-order thinking skills.

Using the Core Progress learning progression as a guide, Accelerated Math automatically schedules assignments covering appropriate standards and exposing students to varying levels of practice. The learning progression provides information about which intermediate steps and prerequisite skills are necessary to reach the level of expertise identified through the standards, beginning with early numeracy and progressing through what is required in college and the workplace.

Use with Response to Intervention (RTI) and differentiated instruction A guiding principle of Response to Intervention is differentiated instruction—at all tiers—with personalized goal setting that allows teachers to accurately monitor students’ growth in a timely manner and make changes to instruction as necessary. Differentiated instruction in RTI should not be limited to students formally designated to receive interventions—it should apply within the core (Tier 1) classroom as well. It is true that differentiated instruction is difficult—because inherently it implies setting, and monitoring, individual goals.

After a student’s starting point in Accelerated Math is determined using the results from the program’s Diagnostic Test, a Star Math assessment, or both, the software automatically creates assignments geared to that student’s individual level and appropriate subskills. This process works well in an RTI framework, as it’s engaging and motivating for students and frees teacher time to work with students experiencing difficulties. Because Accelerated Math automatically scores assignments, the teacher can immediately and effectively act upon that data to ensure students are making progress toward goals.

Accelerated Math allows teachers to make true differentiation—the key to RTI—a reality, by processing performance data to inform differentiated assignments, by helping the teacher create those assignments, and by automatically ng a flow of data to the teacher, student, and parent(s) that explains at a glance whether individual goals are being met.

Accelerated Math® accoladesAccelerated Math is a reliable, valid, efficient, and cost-effective continuous progress-monitoring system. Several experts have determined that this program meets high scientific standards of quality, making it a perfect fit for screening and progress monitoring.

In 2016, Accelerated Math was endorsed by the Council of Administrators of Special Education. In several reviews since 2012, Accelerated Math has been highly rated for progress monitoring by the National Center on Intensive Intervention (NCII, 2016). In 2010, the National Dropout Prevention Center/Network determined Accelerated math has “strong evidence of effectiveness” for prevention and intervention at all grade levels.

In 2009, Accelerated Math was the first progress-monitoring tool to be highly rated as a mastery measure by the National Center on Response to Intervention (NCRTI). In 2007, the National Center on Student Progress Monitoring—the predecessor to the NCRTI—determined that Accelerated Math met all criteria for scientifically based progress-monitoring tools.

Students using Accelerated Math with traditional and reform curricula outperformed peers who used only these curricula (Ysseldye & Betts, 2010):

• enVision Math

• Everyday Mathematics

• Holt McDougal

• Macmillan/McGraw-Hill

• Saxon Math


Efficacy: Key research support for Accelerated Math®

When used with integrity, Accelerated Math has been shown to accelerate math achievement for all students. To ensure that teachers make the most of their data and that students benefit to the greatest extent possible, fidelity of implementation is guided by research-based professional development promoting best practices in mathematics.

The large evidence base supporting Accelerated Math numbers 101 studies and reviews, including 33 experimental or quasi-experimental research studies—generally considered the strongest study designs—90 independent studies, and 22 articles published in peer-reviewed journals, and thus upheld to the highest scrutiny. A selection of this research is highlighted below.

Trends in student outcome measuresIn an analysis of data from the 2013–2014 school year, Renaissance (2017) examined patterns of growth and expected college and career readiness according to the extent of individualized math practice accomplished by students. Researchers analyzed data for grades 1–12 from over 2.7 million students and 12,000 schools nationwide to compare independent math practice, as tracked by Accelerated Math, with the typical performance of students who do not use the program. Whether examined by grade or by populations of interest (students struggling with math, English learners, and students in free or reduced lunch programs), Accelerated Math was associated with better student performance and higher levels of annual growth (see figure 4). The better the program was used, the better the outcomes were for students.

Figure 4. The better Accelerated Math® is used, the more students grow and meet key benchmarks

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Note: Program use was voluntary (students were not recruited nor randomly assigned to a particular comparison group) and results should be considered correlational, not causal. While trends presented are helpful to understand patterns of growth at a high level, educators should rely most heavily on causal evidence, which generally requires an experimental or quasi-experimental design. The balance of this section presents such evidence for Accelerated Math.

Accelerated Math® improves math performance of at-risk studentsIn a study by Lambert, Algozzine, and McGee (2014), teachers in grades 2–5 at three Midwestern elementary schools implemented Accelerated Math as a progress-monitoring mastery-measure tool with students at risk for school failure in 36 classrooms randomly assigned to either the treatment or control group. Students were tested with Star Math at the beginning of the study for placement into Accelerated Math, then mid-year and end of year to measure growth. Star Math results showed that the growth of the treatment group was significantly higher than the control group (see figure 5). In order to further evaluate the program’s effectiveness, treatment classes were categorized into either high- or low-implementation groups based on the level of implementation achieved. The researchers found that growth for the high-implementation group was significantly higher than for the low-implementation group.


Figure 5. Star Math® reports higher increases for students using Accelerated Math®

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Note: NCE scores are a way of representing percentile scores so they can be accurately averaged and compared with each other. Because NCEs are derived from percentiles, they measure growth in comparison to national norms. Positive NCE gains mean student achievement grew at a faster rate than the national average (a gain of zero).

Students, teachers, and schools as sources of variability, integrity, and sustainability in progress monitoring To examine issues of variability, implementation integrity, and sustainability when implementing a progress-monitoring program, an investigation by Bolt, Ysseldyke, and Patterson (2010) followed some of the same schools, teachers, and students as studied by Ysseldyke and Bolt in 2007 (see study, next page) for a second year as they began schoolwide impleme ntation of Accelerated Math. Bolt et al. also investigated the relationship between Accelerated Math implementation and positive student outcomes. The new study reported significant variability in intensity of implementation across all three levels studied (student, teacher, and school); however, individual teacher implementation remained stable across the two years. Students of teachers who implemented Accelerated Math with greater fidelity experienced higher math gains on standardized assessments than other students; likewise, the relationship between Accelerated Math use and achievement was significant at the student level.

More students using Accelerated Math® score proficient or higher in mathWhile studying 360 elementary schools in Florida, Minnesota, New York, and Texas, researchers Burns, Klingbeil, and Ysseldyke (2010) found more students in schools using Accelerated Math scored in the Proficient or higher categories of their respective state mathematics tests. State reading test performance was controlled for as a covariate. The researchers also discovered a positive effect related to amount of time schools used the program. Schools working in Accelerated Math for 5 years or more outperformed those using it for less time or not at all. The results also showed no racial achievement gap among treatment schools, whereas there was a gap in control schools.

Students who use Accelerated Math® make gains regardless of instructional approach Ysseldyke and Betts (2010) examined math curriculum data for nearly 2,000 classrooms assessing student achievement with Star Math, some also using Accelerated Math software and some not. Researchers found that students who worked in Accelerated Math with the following curricula outperformed peers who used only the curriculum: enVision Math, Everyday Mathematics, Holt McDougal, Macmillan/McGraw-Hill, and Saxon Math. The curricula studied represent both traditional and reform approaches to teaching math. It is noteworthy that Accelerated Math use resulted in significant positive effects with both teaching methods, suggesting that the program increases student achievement no matter the instructional approach accompanying it.

Juniors at Arizona high school pass the AIMS after Accelerated Math® interventionSpringer, Pugalee, and Algozzine (2007) conducted a randomized experiment with 28 at-risk high school juniors who did not pass the Arizona Instrument to Measure Standards (AIMS) test in grade 10. The control group participated in the school’s typical math classroom, while the experimental class used Accelerated Math. Figure 6 shows that afterwards, more students in the experimental condition (57%) were able to pass the state test than those in the control condition (14%). All students in the Accelerated Math classroom demonstrated positive gains on the test.


Figure 6. Accelerated Math® students perform better on AIMS test than peers

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Implementing Accelerated Math® with fidelity is key to more growthIn a quasi-experimental study, Ysseldyke and Bolt (2007) examined the impact of Accelerated Math with nearly 2,000 elementary students from eight schools. Students from more than 100 classrooms spanning seven US states, including several in large cities, were randomly assigned to experimental (using Accelerated Math with existing curriculum) and control (using only existing curriculum) groups. Researchers discovered that students whose teachers used Accelerated Math as intended demonstrated greater gains on two standardized tests, TerraNova and Star Math, than students with limited or no implementation (see figure 7).

Figure 7. High Accelerated Math® implementation leads to greater TerraNova Gains

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Large-scale study reveals impact of Accelerated Math® on grades 3–10 and subgroupsFor this quasi-experimental study, Ysseldyke and Tardrew (2003, 2007) examined 2,200 students from 47 schools in 24 US states. They found that students using Accelerated Math in grades 3–10 achieved math gains from 7 to 18 percentile points higher than comparison students. In every grade and subgroup identified, such as eligibility for Title I and free or reduced lunch programs, students in Accelerated Math classes outperformed students not using the program (see figure 8). Students who closely followed Accelerated Math best practice recommendations by scoring higher than 85% correct and completing more subskills made even greater gains. Accelerated Math educators reported qualitative improvements too—teachers spent more time providing individualized instruction, while students spent more time academically engaged, enjoyed math more, and took responsibility for their work. In total, 80% of Accelerated Math educators reported students were learning basic math skills better with Accelerated Math.


Figure 8. Accelerated Math® achievement gains by subgroup

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Schoolwide Accelerated Math® implementation benefits Georgia studentsIn a quasi-experimental study, Holmes, Brown, and Algozzine (2006) examined the effectiveness of both Accelerated Math and Accelerated Reader with 2,287 students from four elementary schools (two rural, two urban) in central and northern Georgia. One school in each area was either a high or low implementer of Accelerated Math and Accelerated Reader. As shown in figure 9, results from the Criterion-Referenced Competency Tests (CRCT) indicated that students in the two high-implementing schools outperformed students in the two low-implementing comparison schools overall (effect size [ES]=0.65), and in math (ES=0.75), reading (ES=0.50), and language arts (ES=0.71). Teachers in all schools expressed positive attitudes toward both Renaissance programs.

Figure 9. High Accelerated Math® implementers outperform low on CRCT

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The 870 students in this quasi-experimental study (Ysseldyke, Betts, Thill, & Hannigan, 2004) were a subset of students who participated in a large national experiment by Ysseldyke and Tardrew, 2003 (see prior page). The students were in grades 3–6 from 47 schools in 24 US states. A two-group pretest/posttest comparison was used to evaluate whether students in a Title I program whose teachers used Accelerated Math would show greater gains in mathematics achievement than Title I students who received no intervention other than their regular math instruction. Star Math results show that students using Accelerated Math significantly outperformed the comparison group, gaining an average of 7.9 normal curve equivalents (NCEs) compared to the 0.3 NCEs earned by students not using Accelerated Math—a difference of 7.6 NCEs (see figure 10). Thus, evidence was found that Accelerated Math can improve the math achievement of Title I students.


Figure 10. Title I students using Accelerated Math® achieve more growth

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Gifted and talented students score even higher after Accelerated Math® practiceAs with the previous study, the 843 students (in grades 3–6 from 47 schools) who participated in this quasi-experimental study (Ysseldyke, Tardrew, Betts, Thill, & Hannigan, 2004) were a subset of the sample from a large national experiment by Ysseldyke and Tardrew, 2003 (see p. 13). All students in Accelerated Math classrooms experienced greater gains in math achievement than those in comparison classrooms. Of the 100 Gifted and Talented (GT) students in the sample, those who used Accelerated Math advanced significantly more than those who did not. The Star Math mean normal curve equivalent (NCE) gain for the experimental classrooms was 11.9 NCEs, a difference of 7.1 NCEs from the 4.8 gain in the control classrooms. As figure 11 shows, GT students using Accelerated Math also made bigger gains, obtained a higher percent correct on practice and test items, attempted more tests, and mastered more objectives than non-GT students using Accelerated Math.

Figure 11. GT students make greater gains with Accelerated Math®

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Accelerated Math® helps Minnesota students surpass district on NALTThis quasi-experimental study by Ysseldyke, Spicuzza, Kosciolek, and Boys (2003) examined the effects of Accelerated Math on math achievement and classroom behaviors known to be related to overall student achievement. Sixty-eight percent of students who participated in the study were eligible for free- or reduced-price lunch. Researchers assigned 160 students from three schools in a large, urban Midwestern district to classes that used Everyday Math (the district curriculum) with Accelerated Math or without. Students in Accelerated Math classrooms excelled in math achievement on Star Math and the Northwest Achievement Levels Test (NALT), including outperforming a district sample by 4.02 normal curve equivalents (NCEs) (see figure 12). In addition, ecological observation data indicated that Accelerated Math use resulted in increased time spent on classroom activities, which researchers identified as contributing to positive academic outcomes. The authors also found Accelerated Math automates the application of evidence-based components of effective instruction.


Figure 12. Students using Accelerated Math® outpace district average on NALT

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With Accelerated Math® practice, Midwestern students exceed national normsIn a quasi-experimental study, Ysseldyke, Spicuzza, Kosciolek, Teelucksingh, et al. (2003) examined the effect of Accelerated Math on overall student achievement at four schools in a large, urban Midwestern school district composed of approximately 75% minority students and 67% free- or reduced-price lunch eligibility. Researchers assigned 881 students in grades 3–5 to either use Accelerated Math with their regular curriculum, or just use the curriculum. Results showed that students at all ability levels who used the program demonstrated accelerated rates of improvement compared to national norms, even after beginning below norms before participating in the treatment classroom. As seen in figure 13, gains ranged from 3.4 to 10.8 NCEs on the Northwest Achievement Levels Test (NALT), and increases were similar on the Star Math assessment.

Figure 13. Students at all levels increase NALT scores with Accelerated Math®

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Kansas high school students realize higher scores with Accelerated Math®

A quasi-experimental study by Gaeddert (2001) involved 103 students at a Kansas high school who were enrolled in pre-algebra, algebra, and geometry classes. As shown in figure 14, results from the Stanford Achievement Test (SAT-9) showed the intervention (treatment) group gained, on average, 10.1 normal curve equivalents (NCEs), whereas the control group gained 3.5 NCEs. Pre- and post-study attitudinal surveys also showed improvement in opinions about math for students who used Accelerated Math and their parents.


Figure 14. SAT-9 gains greater for Accelerated Math® students

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Midwestern students at all achievement levels make greater gains with Accelerated Math®

The majority of students participating in this quasi-experimental study at four urban Midwestern schools were eligible for free- or reduced-price lunch (Spicuzza et al., 2001). The 198 fourth and fifth graders studied were assigned to classrooms to use Accelerated Math or not. At all achievement levels, students in Accelerated Math classrooms demonstrated more growth on Star Math and the Northwest Achievement Levels Test (NALT) than students in non-Accelerated Math classrooms. The Star Math adjusted mean for Accelerated Math students was 42.96 compared to 31.45 for comparison students. As seen in figure 15, on the NALT, the adjusted normal curve equivalent (NCE) mean for Accelerated Math students was 51.3, and for the comparison group it was 46.6. The same students also outperformed a district sample of students in non-Accelerated Math classrooms.

Figure 15. Accelerated Math® use results in higher NALT growth

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Accelerated Math® equals success for English learners in MinnesotaIn this quasi-experimental study, Teelucksingh, Ysseldyke, Spicuzza, and Ginsburg-Block (2001) studied 201 English learners (ELs) in grades 4 and 5 from four Minneapolis schools to compare the math performance of students using Accelerated Math following recommended best practices to a control group of students who did not receive the intervention. EL students in classrooms that used Accelerated Math in conjunction with their math curriculum gained 6.7 normal curve equivalents (NCEs) on the Northwest Achievement Levels Test (NALT) compared to EL students from the control group who gained 3.9 NCEs (see figure 16).


Figure 16. EL students make greater strides on NALT with Accelerated Math® than peers

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Accelerated Math® promotes growth in grade 8 pre-algebra classroomsZumwalt (2001) conducted a 25-week study of 350 eighth-grade pre-algebra students in six schools in Idaho. In total, 94 students received traditional instruction, 162 were instructed using Accelerated Math, and 94 students used computer-aided instruction software from either Jostens Learning Corporation or Computer Curriculum Corporation (CCC). Figure 17 shows that on the Iowa Test of Basic Skills (ITBS) students who used Accelerated Math significantly outperformed students using Jostens, CCC, or traditional instruction. The significant differences between the Accelerated Math group (mean difference score: 29.26) and the Jostens-CCC (16.13) and traditional instruction (18.70) groups equated to almost a year of typical instructional growth and more than a year of growth, respectively.1 Lower performing students, in particular, benefited more from Accelerated Math.

Figure 17. Pretest to posttest change on ITBS is largest for students using Accelerated Math®

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Appendix A. Accelerated Math® meets key components of effective instruction The Accelerated Math program is anchored by evidence-based classroom strategies that ensure guided independent math practice accompanies direct instruction, and is supported by data and management features to accelerate math growth throughout the classroom and across grade and achievement levels.

Table A1 shows key evidence-based instructional practices based on Christenson and Ysseldyke (1989, 2002), as noted in many literature analyses (e.g., Christenson, Ysseldyke, & Thurlow, 1989; Gettinger & Stoiber, 1999), and infused with additional research. The right column explains how Accelerated Math incorporates these practices.

Table A1. How Accelerated Math® addresses research-based instructional practices

Research-based instructional practice How Accelerated Math® aligns

Instructional match and relevant practice“The extent of the match between student ability and difficulty of instructional materials affects student productivity, performance, and attention. When teachers adapt instruction, students can make significant academic progress. Students will be most successful when taught at their instructional level” (NCII, 2014).

Initial placement in Accelerated Math is determined using results of a reliable and valid math assessment, such as Star Math, and/or an Accelerated Math Diagnostic Test. Teachers then monitor progress of student work on Accelerated Math assignments, which helps to inform instruction and intervention.

Instructional expectations Students respond more favorably when they can establish their own goals and are presented with “a meaningful, interesting, and reasonably demanding challenge” (Black & Wiliam, 1998)

Accelerated Math best practices recommend that teachers involve students in setting scientifically based goals with Star Math. Immediate, informative feedback keeps students aware of their progress toward goals.

Classroom environmentEffective teachers establish a positive classroom environment by letting students know they can learn from their mistakes, giving feedback that stresses the positive aspects of performance, and handling errors in a supportive way (Barbetta, Norona, & Bicard, 2005).

The teacher is at the heart of the Accelerated Math classroom, delivering daily math instruction before students practice in the program. Accelerated Math excels at classroom management, by completing administrative tasks and providing progress-monitoring information to help teachers provide timely feedback to students. Classroom routines include checking in with students to see if additional instruction and intervention are needed.

Instructional presentation and student understandingTeacher modeling of problem-solving strategies (Gersten et al., 2009) about procedures, symbols, and decision making (Jayanthi, Gersten, & Baker, 2008), including both correct and incorrect behaviors (Montague, 2004), as well as student verbalization, or think-alouds (Gersten & Clarke, 2007), which help to build understanding while providing the teacher with an opportunity to diagnose misconceptions (Gersten et al., 2009), are all effective instructional practices.

Accelerated Math supports best practices in mathematics classrooms, such as clear communication with kids about routines and expectations. The program facilitates teacher modeling and think alouds during teacher-to-student interaction, so students can hear and see the teach-er’s thought process while solving a problem. Likewise, student verbaliza-tion can be used to check understanding and provide insight into a student’s thinking.

Motivational strategiesStudent motivation can be cultivated by providing students with opportunities to experience high levels of success. If students are not highly successful, their will to continue working will be threatened (Ruiz, 2012).

With Accelerated Math, teachers motivate students by providing opportunities for successful math practice. The program keeps track of the number of subskills mastered, percent correct, completion of a library, and other metrics to use for goal setting to help motivate stu-dents to practice more.

Informed feedbackEffective teachers provide “feedback to students that is timely, specific, well formatted, and constructive,” (Hamilton et al., 2009, p. 9).

Immediate feedback is generated as students complete assignments, including corrective information about items answered incorrectly. Accelerated Math routines recommend that students rework missed problems on paper and then submit to the teacher for additional instruc-tion or intervention as needed.

Academic engaged time“The student is actively engaged in responding to academic content; the teacher monitors the extent to which the student is engaged and redirects the student when the student is unengaged” (Ysseldyke & Christenson, 2002).

The Accelerated Math classroom is structured so that students use time productively. Students are expected to work on assignments or tests, submit work to be scored, confer with the teacher for additional instruc-tion and intervention as needed, or meet with other students for peer-learning opportunities. Student routines and expectations are clearly communicated, so students always know where their efforts should be focused. If they need guidance, the teacher and classroom signage are available to provide direction.

Adaptive instruction “The curriculum is modified within reason to accommodate a student’s unique and specific instructional needs” (Ysseldyke & Christenson, 2002).

Through a specific practice, test, and review cycle, students are provided with multiple opportunities to practice and master an objective as well as ensure mastery over time through incremental review. Each assignment in Accelerated Math is based on a student’s prior work.


Appendix B. Fidelity of implementation Tools that support effective instruction must be implemented with fidelity. To ensure that teachers make the most of the data from Accelerated Math to help students benefit to the greatest extent possible, implementation integrity is guided by research-based professional development promoting best practices in mathematics.

Research shows that high implementation of Accelerated Math promotes both personalized goal setting and appropriate, personalized practice (e.g., Nunnery & Ross, 2007; Ysseldyke & Bolt, 2007). Accelerated Math supports best practices in math, which include techniques for differentiating instruction, increasing and verifying academic engaged time (AET) for math skills practice, interpreting performance data, and monitoring the application of skills during student practice. The recommendations, which underscore the critical role the teacher plays in the effective use of Accelerated Math, are taught in a flexible series of professional development sessions:

1. Math practice time—Teachers ensure students have an appropriate amount of time for guided independent mathematics practice. We recommend working toward a goal of 40 minutes of daily practice with Accelerated Math, which will put students on track to master, on average, four subskills per week.

2. Math success—Teachers ensure students are highly successful math learners, with an average percent correct of 75% or higher on practice and 85% or higher on tests.

3. Appropriate math subskills—Teachers ensure students are practicing math subskills appropriate to their achievement level.

4. Progress monitoring—Teachers obtain information for progress monitoring from three sources: (1) daily, from direct teacher observation and conferences with students; (2) daily and weekly, from completion of student work in the software; and (3) periodically, 3–10 times per year, from a reliable and valid math assessment like Star Math.

5. Personalized goals—Teachers motivate students by ensuring they are working toward personalized quality (average percent correct) and quantity (number of subskills mastered) goals.

6. Personalized instruction—Teachers use information from progress monitoring and goal setting to assess, inform, and tailor personalized instruction for each student.

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