The Dropout Dilemma

The

Dropout

Dilemma Early Academic Intervention for Continued School Success: Catapult Learning’s Research-Based Approach

Dr. Marcella L. Bullmaster-Day, Ed.D.

Academic success, as defined by high school graduation, can be predicted with reasonable accuracy by knowing someone’s reading skill at the end of third grade. A person who is not at least a modestly skilled reader by that time is unlikely to graduate from high school.

– Snow, Burns, & Griffin, 1998, p. 21

Literacy and language develop over many years. If students fall behind, they seldom right themselves without special help. Instead, the momentum of the decline intensifies.

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– Chall, Jacobs, & Baldwin, 1990, p.150

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The

Dropout

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Early Academic Intervention for Continued School Success: Catapult Learning’s Research-Based Approach Contents

Page:

The Dropout Dilemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 New Demands on Schooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Struggling Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Early Warning Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Early Intervention Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Catapult Learning Tier 2-level Interventions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 AchieveReading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 AchieveMath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

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The Dropout Dilemma Prospects for a high school dropout in the United States today are bleaker than they have ever been. Dropouts fare much worse than graduates in terms of opportunity, financial stability, health, and life expectancy. They are less likely to be steadily employed over the course of their lives and they earn far less on average than graduates.

They are overrepresented in the prison population and more likely to be arrested or to have a child while still a teenager (National Center for Education Statistics [NCES], 2009; Northeastern University Center for Labor Market Studies, 2007; Sum, Khatiwada, McLaughlin, & Palma, 2009; Rosenbaum, 2001).

Yet nationwide well over a million students drop out of high school each year – three students in ten or about 7,000 for every school day in a year. And while the national graduation rate stands at 68.8%, closer examination reveals stark disparities across lines of class, race, gender, and school environment. More than three-quarters of Asian and White students earn their diplomas on time, compared with only 56% of Latino, 54% of African American, and 51% of American Indian students. Further, only half of male students More than three-quarters of

from these historically underserved groups graduate from high school in four years (Alliance for Excellent Education,

Asian and White students

2010; Editorial Projects in Education, 2010).

earn their diplomas on time, compared with only 56% of Latino, 54% of African American, and 51% of American Indian students.

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Early failure in reading and mathematics is a major predictor of dropout risk (MacIver & MacIver, 2009), and U.S. public school students’ test scores paint a grim picture. Only one-third of fourth (33%) and eighth (32%) graders scored at the Proficient level on the

Dropout

Dilemma

Early failure in reading and mathematics is a major predictor of dropout risk

National Assessment of Educational Progress (NAEP). The other twothirds of students could not demonstrate an overall understanding of a text by making inferences, drawing conclusions, making connections to their own experiences and to other readings, and identifying some of the devices that authors use in composing text (NCES, 2010).

Significant numbers of students—33% of fourth graders and 25% of eighth graders—performed below the Basic level, indicating that they could not consistently demonstrate an understanding of the literal meaning of what they read, much less make relatively obvious connections between the text and their own experiences. These students could not extend the ideas in a text by making simple inferences, or draw conclusions based on the text (NCES, 2010).

Meanwhile, while little has changed since 1992 in terms of the proportions of students who master reading to the level of proficiency compared with those who do not, what has changed, and continues to rise rapidly, is the level of complexity of literacy skill demanded by participation in 21st century society and today’s labor market. The opportunity gap continues to widen between those with adequate levels of literacy and those without.

The opportunity gap continues to widen between those with adequate levels of literacy and those without.

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New Demands on Schooling Changing patterns of consumption and radically altered technology infrastructures that move information, people, and goods globally have pushed us past the information age and into a conceptual, creative economy. The automation and outsourcing of both low-skilled and formerly lucrative occupations has resulted in a decrease in employment opportunities in many fields in the U.S. and an increase in rewards for innovative, non-routine work (Florida, 2002; Pink, 2005).

Compared to their counterparts in past economic eras, many more 21st-century workers will need to be able to: • access information from a wide variety of sources; • select, comprehend, organize, interpret, analyze, synthesize, and evaluate information; • communicate effectively by writing, speaking, and representing information • a ccomplish tasks using information, system technologies, and personal and interpersonal resources; • produce and apply new usable knowledge; • s hift between working independently and working collaboratively as part of a problemsolving team; • self-regulate and monitor their own thinking and learning; and • examine multiple perspectives on problems and solutions (Smith et al., 2000).

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The

Dropout

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In light of these new realities, even a military career is no longer an option for most high school dropouts (Mission: Readiness, 2009). Various estimates put the net cost in lost earnings, taxes, and productivity for every dropout at between $260,000 and $456, 354 (Northeastern University Center for Labor Market Studies, 2007; Riley & Peterson, 2008).

As school systems continue to adjust to the demands of a shifting global economy, students in middle and high school will be expected to read more difficult texts, do more with texts of different types, and handle larger amounts of reading (Smith et al., 2000). Reading to learn in the middle and high school years requires more than fluent decoding—it entails sophisticated higher-order thinking and a flexible grasp of texts that vary in style, format, vocabulary, purpose, and intended audience. In order to stem the dropout tide and ready high school graduates for college and career success, it has become imperative that they enter high school with grade-level skills and knowledge (Balfanz, 2009).

As school systems continue to adjust to the demands of a shifting global economy, students in middle and high school will be expected to read more difficult texts, do more with texts of different types, and handle larger amounts of reading.

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Struggling Students Educational trajectories, for good or ill, are set very early in life for most students (Alexander, Entwisle, & Horsey, 1997; Zarate & Gallimore, 2010).

Dropping out of school is a process of disengagement that typically begins in the elementary years and is most often characterized by early academic difficulties in reading and mathematics (Balfanz, Herzog, & Mac Iver, 2007; Janosz, Archambault, Morizot, & Pagani, 2008; Nield & Balfanz, 2006; Silver, Saunders, & Zarate, 2008).

Dropping out of school is a

In fact, research by Balfanz (2009) and his colleagues at the Everyone process of disengagement that typically begins in the elementary years and is most often characterized by early academic difficulties in reading and mathematics.

Graduates Center at Johns Hopkins University has shown that by sixth grade, a student who fails math or English/reading, or who attends school less than 80% of the time, or who has received an unsatisfactory behavior grade in a core course has only a 10 – 20% chance of graduating on time. According to Balfanz: Although these numbers are shocking initially, upon reflection they are understandable. Once a sixth grader has demonstrated that he or she lacks either the knowledge to pass tests in math or English or the ability to complete assignments, absent successful intervention, this is unlikely to change on its own.

This may be especially true in high-poverty environments, where home and community resources can be limited.

As a result, the student continues to fail courses and may not achieve on-time promotion to the next grade. The student then enters high school, overage for the grade with a history of course failure. Lacking the skills, knowledge, and self-confidence to succeed in high school and feeling distanced from his or her peers, the student continues to fail, does not earn promotion to the 10th grade, and, at this point, may well have reached the legal age for dropping out. (2009, p. 4)

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The

Dropout

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By sixth grade, a student who fails math or English/reading, or who attends school less than 80% of the time, or who has received an unsatisfactory behavior grade in a core course has only a 10 – 20% chance of graduating on time.

Other elementary-level predictors of high school dropout include frequent absences, behavior infractions, grade retention, low levels of family income and parent education, lack of parental involvement, and school mobility (Alexander, Entwisle, & Horsey, 1997; Balfanz, Bridgeland, Moore, & Fox, 2010; Balfanz, Herzog, & MacIver, 2007; Dynarski, Clarke, Cobb, Finn, Rumberger, & Smink, 2008; Rumberger & Lim, 2008; Roderick, 1994; Temple, Reynolds, & Miedel, 2000). Reading difficulties that occur in combination with aggressive behavior put elementary students at risk for adolescent delinquency, academic failure, and dropout. And each successive school failure at the middle school level has a greater negative impact on high school graduation rates than course failure at the high school level (Balfanz, Herzog, & Mac Iver, 2007; Miles & Stipek, 2006).

Among these identified risk factors for school dropout are many over which educators do have direct control. When high school dropouts were interviewed about their choice to abandon schooling (Bridgeland, Dilulio, & Morison, 2006), they reported that: • their classes were not interesting (47%); • they were not motivated or inspired to work hard (69%); • they did one hour or less of homework each day (80%); • they would have worked harder if more had been demanded of them (66%); • they could have graduated if they had tried (70%); • they started high school poorly prepared by their earlier schooling (45%); and • they were required to repeat a grade before dropping out (32%).

These same former students said that there were things that educators could have done to pull them back into schooling, including: • improving teaching and curricula to make school more relevant and engaging (71%); • enhancing the connection between school and work (81%);

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• providing more opportunities for real-world, experiential learning (81%); • providing smaller classes with more individualized instruction (75%); • doing more to help students who have problems learning (55%); • providing more tutoring, summer school, and extra time with teachers (70%); • building a school climate that fosters academics through increased supervision (62%); • doing more to help students feel safe from violence (57%); • doing more to help students with problems outside of class (62%); and • increasing parental involvement and communication between teachers, parents, and students (70%).

Since student behaviors predictive of dropping out are well established, schools and districts can systematically collect data about students’ grades, test scores, attendance, and behavior records to build early warning systems that can guide preventative measures and early interventions to keep students on track to school success and graduation (Allensworth & Easton, 2005; Hauser & Koenig, 2010; Pinkus, 2008). Mac Iver & Mac Iver (2009) warn that: No matter how good the classroom instruction and school climate, some students who exhibit one or more of the early warning indicators of dropping out—the ABCs of poor attendance, poor behavior, and course failure—will need additional supports. If not addressed, many if not most of these students will slip through the cracks in most schools. (p.15)

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Early Warning Systems The critical transition years from elementary to middle school (sixth grade) and from middle school to high school (ninth grade) function as decisive turning points for many dropouts (Kennelly & Monrad, 2007; Mac Iver & Mac Iver, 2009; Roderick, 1993). However, even before students reach these danger points, elementary schools need to establish early warning systems that track “attendance, behavior, grades in reading and math, and benchmark test scores, and regularly report this information to teachers, school counselors, administrators, and parents to identify individual students who are off track and need both moderate and more intensive interventions” (Balfanz, Bridgeland, Moore, & Fox, 2010, p. 62).

One critical and well documented phenomenon that portends the high school dropout of millions of students is the “fourth-grade slump” (Chall, Jacobs, & Baldwin, 1990). An alarmingly large percentage of children – especially low-income Black, Hispanic, and Native American students in high-poverty schools – arrive at fourth grade unprepared to make the transition from learning to read to reading to learn when they begin to encounter more complex informational texts. As students move up through the grades, texts are written with increasingly complex assumptions about what students already know. Comprehending this material relies on students’ reading fluency along with extensive vocabulary and background knowledge. In order to successfully understand and use the new information to which they are introduced, students need some prior familiarity with the topics discussed in the texts (Annie E. Casey Foundation, 2010; Chall & Jacobs, 2003; Hirsch, 2003; NCES, 2010; Recht & Leslie, 1988).

The critical transition years from elementary to middle school (sixth grade) and from middle school to high school (ninth grade) function as decisive turning points for many dropouts .

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Higher levels of content-area literacy rely on the ability to make sense of many kinds of text— texts that vary in style, format, vocabulary, purpose, and intended audience – and to read and write for meaning in many different ways. As they progress through school, students must, in ever more sophisticated ways, “go beyond the information given” to gain a flexible grasp on complex material – breaking it down for a sense of its underlying structure; organizing pieces of information into coherent wholes; and making evidence-based judgments about the validity or quality of ideas (Bransford, Brown & Cocking, 2000; Bruner, 1973; Krathwohl, 2002).

The good news is that with

The good news is that with appropriate intervention as

appropriate intervention as

students approach fourth grade, “the typical slumps found in

students approach fourth grade,

their reading achievement can be prevented” (Chall, Jacobs, & Baldwin, p. 149). Intensive academic interventions with elementary school students can play a critical role in getting students back on track to school success and graduation before they have accumulated a cycle of academic failure.

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“the typical slumps found in their reading achievement can be prevented.”

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The

Dropout

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Early Intervention Systems Research shows that children experiencing the most difficulties are also more likely to benefit the most from early explicit, systematic, intensive interventions, suggesting that targeted interventions are an appropriate and cost-effective strategy for substantially reducing risk factors (Barrera et al., 2002; Kellam et al., 1998; Ross,, Smith, Casey, & Slavin, 1995; Stoolmiller et al., 2000). For decades, early educational interventions, from the preschool years through the early elementary grades, have been shown to provide long-lasting intellectual, academic, and economic benefits to students placed at risk by poverty. These benefits include: • enhanced cognitive performance; • higher academic achievement in reading and mathematics; • significantly fewer placements into special education; • fewer grade retentions; • lower rates of juvenile arrest; and • significantly increased high school graduation rates (Campbell & Ramey, 1994; 1995; Lazar, Darlington, Murray, Royce, & Snipper, 1982; Reynolds, 1994; Reynolds & Temple, 1998; Reynolds, Temple, Robinson, & Mann, 2001; Royce, Darlington, & Murray, 1983; Temple, Reynolds, Miedel, 2000).

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Research shows that children experiencing the most difficulties are also more likely to benefit the

Based upon a combination of public health prevention-based systems models and the federal Response to Intervention (RTI) model from the 2004 Individuals with Disabilities Education Act (IDEA), experts in dropout prevention at the Everyone Graduates Center at Johns Hopkins University have called for a systematic,

most from early explicit, systematic, intensive interventions.

coherent, school-wide, three-tiered prevention/intervention model to address attendance, behavior, and academic learning needs of students identified as at risk for dropping out of school (Mac Iver & Mac Iver, 2009; Nield, Balfanz, & Herzog, 2007). Both the federal RTI model and the Johns Hopkins model combine universal preventatives – screening and high-quality instruction for all students –with interventions targeted at struggling students. The RTI model places an emphasis on identifying students for special education services (Gersten, et al., 2008), while the Johns Hopkins model stresses providing sequential interventions designed to help all students stay on track to graduate from high school, since so many students who begin to disengage early from schooling do not have physical or cognitive challenges that would require special education services (Mac Iver & Mac Iver, 2009).

The primary, foundational stage of both the RTI and Johns Hopkins dropout prevention models (Tier 1) involve systematic, explicit, whole-school, research-based, high-quality instructional practices, attendance programs, and motivational strategies for all students.

The secondary stage (Tier 2) consists of targeted, intensive smallgroup interventions (typically between three to five times per week for 20 – 40 minutes) for students who require additional focused academic and behavioral supports (Gersten et al., 2008). In the tertiary stage (Tier 3), students who do not progress satisfactorily in small-group interventions receive one-on-one attention and instruction. At each stage, timely and valid formative assessments are administered to monitor student progress.

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The empirical research base is most robust for Tier 2-level interventions. Effective Tier 2 instructional interventions: • provide increased intensive instruction to small groups of students formed on the basis of universal screening results; • are focused carefully on the most essential learning needs of the students; • are explicit, involving more teacher-student interaction; • are systematic, building skills gradually and then integrating them; • afford many more opportunities for re-teaching, review, and guided practice with specific feedback (Crawford & Torgeson, 2007; Gersten et al., 2008).

Based upon the body of research cited above, Catapult Learning has designed AchieveReading™ and AchieveMath™ supplemental instructional Tier 2-level services. AchieveReading and AchieveMath are systematic, explicit, and intensive small-group interventions for students who require additional focused academic and behavioral supports.

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In order for sustained learning to occur, students must actively engage with lesson content through various forms of supervised practice during which they receive timely, substantive feedback on their performance to help them improve.

Catapult Learning Tier 2-level Interventions AchieveReading and AchieveMath provide targeted small-group instruction that supports and enhances, but does not supplant, the core classroom curriculum in order to meet the varied needs of low-achieving students. These Catapult Learning Tier 2-level programs are systematic in that they follow a carefully designed scope and sequence of skills that build upon one another within and across grade levels, providing an organized approach to student learning. Instruction is explicit; focused on precisely articulated core skills taught directly and reinforced through targeted lesson activities that promote application of the skills. And both programs are intensive, delivering a scaffolded sequence of direct instruction, guided practice, and independent practice over multiple days, informed by preassessment, formative assessment, and summative assessment.

Direct instruction: Research shows that students achieve more in classes in which they spend much of their time being directly taught or supervised by their teacher (Good & Brophy, 2003; Dean & Kuhn,2007; Englert, 1984; Ellis & Worthington, 1994; Rosenshine, 2002). Catapult Learning teachers follow detailed lesson plans to help them introduce and support skills clearly and explicitly.

Guided and independent practice: In order for sustained learning to occur, students must actively engage with lesson content through various forms of supervised practice during which they receive timely, substantive feedback on their performance to help them improve. Effective feedback during guided and independent practice scaffolds student learning by providing a period of cognitive apprenticeship that supports the development of habitual internal procedures which enable successful performance of higher order activities (Anderson, Greeno, Reder, & Simon, 2000; Bransford, Brown, & Cocking, 2000; Collins, Brown, & Newman, 1990; Good & Brophy, 2003; Marzano, 2007; Sousa, 2008; Stevenson & Stigler, 1992; Wood, Bruner, & Ross, 1976). Catapult Learning programs follow a threeday 60-minute lesson sequence that includes direct instruction and guided practice on Days 1 and 2, with independent practice and application on Day 3.

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Assessment: Effective instruction includes diagnostic assessment to determine students’ entrylevel skills, formative assessment to monitor student progress toward instructional goals, and summative assessment at the end of an instructional program to measure student learning gains (Black et al.,2003; 2004; Black & Wiliam, 1998; 2009; Bransford, Brown, & Cocking, 2000; Marzano, Gaddy, & Dean, 2002; McTighe & O’Connor, 2005; Shepard, 2005). All students enrolled in Catapult Learning AchieveReading and/or AchieveMath take a proprietary pre-assessment that is standardized, curriculum-based, criterion-referenced, and designed specifically for students who have not been successful in core instructional programs and are at risk of failing.

The pre-assessment identifies students’ reading and math skill deficits and determines an appropriate instructional level for each student. Pre-assessment results are used to generate individualized student learning plans aligned to AchieveReading and AchieveMath program objectives, as well as to national and state standards. This diagnostic/prescriptive process ensures that every student begins the intervention with the greatest potential for effective learning gains. Two additional forms of the standardized assessment, mid-point and end-of-program, measure individual student performance progress along the continuum of skills aligned with program instructional objectives.

In addition, at every third session of the instructional cycle, students complete formative assessment activities that are evaluated by their teacher using Catapult Learning’s Rubric for Evaluation of Student Progress. Performance scores are recorded on each student’s Lesson and Performance Tracking Tool (LPTT). Data from LPTTs are used to update Progress Reports for classroom teachers and parents.

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AchieveReading AchieveReading is an integrated language arts program that focuses on students’ oral and written language skills by engaging students in ongoing reading and writing activities.

The consumable Student Resource Book is an integral component of the program and includes four activity sheets per lesson; one to reinforce each lesson component (phonics/ word study, fluency, comprehension, and vocabulary).

Reading is not a single skill; it is an intricate interplay of five important abilities: phonemic awareness, phonics, fluency, vocabulary, and comprehension (National Reading Panel, 2000). Catapult Learning’s AchieveReading strengthens each of these competencies.

Phonemic awareness and phonics: Phonemic awareness is the ability to hear, replicate, and manipulate phonemes – the separate sounds in words that constitute the building blocks of language. Learning to read depends upon students’ ability to notice, identify, reproduce, and manipulate individual phonemes so that they can then represent these sounds by letters. In the English language 44 different phonemes can be combined in countless ways to form syllables, words, and sentences to convey meaning (Liberman, 1999; Moats, 1999; 2004).

Phoneme-awareness skills include working with words, syllables, onset-rimes, and phonemes. Many students develop phonemic awareness and phonics abilities to the point of automaticity during the early grades, but many others – maybe as many as 30% – need additional explicit instruction and practice, without which they can fall behind and be misdiagnosed as learning disabled.

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While phonemic awareness is the ability to hear and manipulate the sounds in language, phonics, in an alphabetic system like English, is the ability to represent the sounds with letters or combinations of letters (graphemes). This representational system by which the 26 alphabetic

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Each lesson plan incorporates guidelines for teachers to help them

letters of English, alone or in combination, represent the 44 phonemes of the English language, is known as the alphabetic principle.

Reading draws upon the same meaning-making processes used in speaking and listening, but additional automatic decoding processes

address both the common remedial needs of the group and the unique

are required to transform the graphemes on the page into words and ideas. Explicit instruction in phonics helps students develop the intricate neurological processes that connect written words to their

instructional needs of each student through

oral pronunciations so that students “hear” the written words in their minds as they see them; a necessary step to making meaning

differentiation activities.

of the ideas conveyed by the words (Bowerman & Levinson, 2001).

Learning the coding and decoding system of phonics is challenging, however, because the English language does not always afford a regular one-to-one correspondence between letters and phonemes.

Many sounds in the English language can be spelled in different ways (Blachman, 2000; Ehri, 1995; 1998; Ehri et al., 2001; Moats, 1999; Snow, Burns, & Griffin, 1998). For students who struggle, intensive, systematic, explicit intervention instruction – targeted at the specific phonemic awareness and phonics skills needed by the individual student and administered over a sufficient span of time so that the skills become internalized and automatic – has been proven effective in helping students to master these skills (Blachman et al., 2004; Harm, McCandliss, & Seidenberg, 2003; National Reading Panel, 2000; Moats, 1999; Scanlon et al., 2005; Snow, Burns, & Griffin, 1998; Tallal, 2000; Torgesen, 2002a; 2002b; Torgesen & Mathes, 1998).

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AchieveReading supports students’ phonemic awareness and phonics skills to the point of automaticity so that they can progress to fluency and comprehension. Using an onset/rime instructional approach, AchieveReading teachers work intensively with students on sound blending. Students are taught to convert letters to phonemes and to blend phonemes into words using word-analysis skills that are sequenced from simple to complex. The goal of AchieveReading phonics instruction is to teach students to decode unknown words quickly and accurately.

Fluency: Fluency is the ability to read words and strings of words quickly, accurately, and without conscious effort, freeing working memory to pay attention to the meaning of the words (Bruner, 1990; Collins, Brown, & Newman, 1990; Hirsch, 2003; Lyon, 1998; Moats, 1999; Snow, Burns, & Griffin, 1998; Tallal, 2000; Vellutino et al., 1996). Fluency, vocabulary, and content-domain knowledge are the most reliable predictors of reading comprehension (Hirsch, 2003; Fuchs et al., 2001; Pikulski & Chard, 2005).

AchieveReading integrates work on fluency into the each instructional session’s activities through reading passages developed explicitly for a focus on fluency at each instructional level. Students have an opportunity for repeated oral readings of these passages, with a focus on reading with increased speed, accuracy, and intonation. Activities include initial oral readings by the teacher for modeling of rate and expression; student-partner reading for increased opportunity for oral reading; and student oral reading for increased fluency.

Vocabulary: Vocabulary skill involves the ability to learn meanings of new words and to add those words to a growing repertoire of words that can be recognized and used.

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Vocabulary is the link between the word-level processes of phonics and fluency and the meaning-making process of comprehension.

Students actually possess four vocabulary lexicons: the words they use when speaking, the words they use when writing, the words they understand when listening, and the words they understand when reading (Chall, 1983; Chall & Jacobs, 2003; Lehr, Osborn, & Hiebert, 2004). Although when students enter school their individual oral vocabulary sizes vary depending upon factors like socioeconomic background and prior experience, a student who has learned to read efficiently by third grade will add 2,000 to 3,500 distinct new words to her vocabulary each year (Chen & Vellutino, 1997; Foorman & Torgesen, 2001; Hart & Risley, 2003; Hirsch, 2003; Lehr, Osborn, & Hiebert, 2004; Lyon, 1998; Moats, 1999; Nation & Snowling, 2004; National Reading Panel, 2000; Snow, Burns, & Griffin, 1998; Stahl, 2003).

Vocabulary development is part of each AchieveReading lesson and is directly taught by focusing on word knowledge, structural analysis, and context clues. The AchieveReading three-day lesson sequence introduces students to key vocabulary prior to their first reading of the text selection in order to build their conceptual knowledge to support the first reading of the text. Indirect vocabulary support is provided throughout the instructional sessions – during phonemic awareness and phonics instruction; during the reading of a wide variety of text selections (e.g., decodable text, fluency passages, comprehension text selections); and during comprehension instructional activities. Students are provided with both oral and written vocabulary support through the inclusion of rich oral discussion, a hierarchy of comprehension questions, and a Student Resource Book of written activities.

Comprehension: Competent readers actively monitor their understanding as they read, purposefully using cognitive strategies

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to make connections between the text, personal experience, real world examples, and other texts.

Phonologic automaticity and reading fluency are necessary but not sufficient conditions for reading comprehension because decoding printed words at the word level and making meaning of them at the language level involve two different sets of skills. Students need to spend extended time reading—and being read to—from texts about the same topic. By discussing the facts and the ideas in texts that cover the same topic, students gain what E. D. Hirsch (2003) calls “world knowledge,” an essential component of reading comprehension (Beers, 2003; Biancarosa & Snow, 2006; Pressley, 2000).

AchieveReading targets key comprehension skills and strategies such as accessing prior knowledge, identifying main idea and supporting details, sequencing, story grammar, text features, and author’s purpose across the instructional levels. These skills and strategies are directly taught through teacherguided lessons and are applied meaningfully in connected text. To further promote the development of comprehension skills, Catapult Learning teachers provide direct instruction in effective reading strategies (e.g., slow down when it gets hard, read it again) monitoring and encouraging students’ use of these strategies throughout the program.

Text selections in AchieveReading’s Student Anthologies are both narrative and expository, and include decodable text and literature-based selections. Text selections represent cultural and economic diversity, and vary by topic, focus, genre, style, and format.

Further, AchieveReading includes a variety of graphic organizers at each instructional level for various elements of reading (e.g., phonics instruction, vocabulary development, comprehension skill development).

Graphic organizers are presented at the group level in teacher-directed lessons. They are drafted by students, with teacher support, as paired or partner work during guided practice, and are completed by students as written work within their Student Resource Books as independent practice activities.

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Writing: When students have frequent, regular opportunities to write about what they read, the teacher can gain insight into their levels of reading comprehension (Brady & Moats, 1997; Moats, 1999; Snow, Burns, & Griffin, 1998). AchieveReading™ students are presented with a variety of writing opportunities during each lesson to support their reading skill acquisition.

Writing activities are based on students’ instructional levels and on the reading strand, and include: • Phonics/Word Study: Matching, True/False, Fill-ins, Selected Response; • Comprehension: Graphic Organizers, Short Answer, Extended Response; and • Vocabulary: Matching, Fill-ins, Short Answer, Extended Response.

Lesson Design: The AchieveReading program follows this three-day, 60-minute session scaffolded lesson design:

Comprehension Vocabulary

Day 2

Day 3

Skill introduction and

Guided practice with

Independent practice with

guided practice

application to text

application to text

Passage introduction

Passage reread for

Passage reread for increased

comprehension & fluency

speed, accuracy, and intonation

Skill introduction and

Text selection introduction and

Text selection reread for

guided practice

skill application

comprehension and skill extension

Content word introduction

Content words direct

Vocabulary extension activities

Fluency

PA, Phonics, Word Study

Day 1

instruction and guided practice

Lessons include strategies for differentiating instruction, explicit skill instruction, teacher questioning, built-in practice, opportunity for re-teaching, and development of students’ metacognitive skills. Each lesson plan incorporates guidelines for teachers to help them address both the common remedial needs of the group and the unique instructional needs of each student through differentiation activities.

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AchieveMath Like AchieveReading, the AchieveMath program guides students through carefully scaffolded sessions that include concept development, teacher modeling, guided practice, and opportunities for independent practice and application. A hierarchy of objectives within and across grade levels addresses all of the NCTM content standards. At each level of the program, AchieveMath’s scope and sequence covers: • Numbers and Operations; • Algebra; • Geometry; • Measurement; and • Data Analysis and Probability.

Each AchieveMath level begins with lessons addressing basic number concepts. Students begin with whole numbers and continue to develop their number sense with fractions, decimals, percents, and integers. Students are taught the meanings of the operations and their inverses and how they relate to one another.

Algebra skills are addressed on every level of the AchieveMath program. Lessons for lower grades teach students to recognize, generate and analyze repeating and growing patterns. Later, students learn to represent and analyze mathematical situations and structures using algebraic symbols. In the upper grades, students are taught to analyze qualitative and quantitative change in various contexts, use equations, and understand functions.

AchieveMath also addresses the NCTM process standards: problemsolving, reasoning and proof, connections and communication, and representation and productive disposition. Further, AchieveMath is aligned to many of the National Mathematics Advisory Panel

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The

AchieveMath program guides students through

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(NMAP) research-based recommendations including: emphasis on algebra, coherent, progressive and sequential instruction, focus on the importance of fractions, reasoning and estimation, teacher

carefully scaffolded

professional development, and formative assessments.

sessions that include

In a synthetic approach to these standards, AchieveMath instruction interweaves procedural fluency, conceptual understanding, and problem

concept development,

solving; purposefully building mathematics vocabulary and students’ ability

teacher modeling, guided

to represent mathematical ideas in linguistic and nonlinguistic ways.

practice, and opportunities

Procedural Fluency, Conceptual Understanding, and Problem Solving: Procedural fluency and conceptual understanding are not “either/or”

for independent practice and application.

elements of mathematical knowledge – they grow together. Conceptual understanding rests on a framework of facts. Memorizing facts and skills is necessary, but not entirely sufficient for building mathematical understanding. Memorization is most effective when the facts and skills are organized in ways that allow them to be retained and recalled quickly and automatically for use in solving a new problem, confronting a new situation, or finding where in the existing schema to add or fit new information. The more facts and skills students have appropriately organized in their long-term memory schemas, the better their conceptual understanding. It is this organization of facts into conceptual frameworks that facilitates the retrieval, application, and transfer of knowledge (Bransford, Brown, & Cocking, 2000; Hiebert et al, 1997; Hirsch, 2006).

Conceptual understanding allows procedures to be appropriately selected and used flexibly. If students are taught mostly algorithms and rules based on abstract symbols (syntactic procedures) without opportunity to use these procedures in flexible ways to solve diverse problems, constraints are placed on problem solving ability.

Problem solving entails the ability to determine what a problem is about and to form a mental picture of what the problem represents (semantic analysis). Syntactic procedures alone can generate correct performance

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on direct measures; i.e., on the tasks for which they were specifically taught. However, that correct performance does not transfer well to novel problems across time. Semantic analysis, on the other hand, does transfer because it enables students to form correct representations of new problems (Hiebert & Wearne, 1988).

Conceptual understanding involves knowing what to do, while procedural fluency requires knowing how to do it. Growth in conceptual understanding and procedural skill is a bidirectional process. Practice in using skills and procedures across a range of problems strengthens conceptual understanding, while conceptual understanding enables students to know which procedures to select for particular problems, opening the way for further practice with the procedures (Miller & Mercer, 1992; 1997; Sophian, 1997).

Explicit, systematic instruction in problem solving has been shown to benefit students of all ability levels. Teaching students both how to do it and when to do it, and offering precise, constructive feedback during guided and independent practice, scaffolds student learning – providing temporary supports that can eventually be removed as students gain automaticity with skills and a deeper understanding of concepts. Students learn conceptual understanding, procedural fluency, and problem solving most effectively when teachers scaffold their learning by: • reviewing and building on students’ previous learning; • working toward clear, explicit learning goals; • presenting new material in manageable steps that encourage active student participation; • modeling, explaining, and prompting; • teaching students how to prepare and solve problems systematically; • teaching and discussing cognitive and metacognitive strategies;

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• presenting multiple examples of a concept so that students can deduce underlying principles; • asking students to propose preliminary solutions and providing feedback as to the effectiveness of their thinking; • providing regular practice with ongoing feedback, guidance, and correction; • grounding students’ learning in real-world contexts and applications so that students connect new information to their lives outside of school; • providing social contexts and peer modeling for learning; and • accurately assessing student progress and modifying instruction accordingly.

A consistent instructional cycle that incorporates all of these elements enables students to organize, store, and retrieve new knowledge, while strengthening interconnections between the pieces of information in their mental “maps” so that the information will be available to them for recall, transfer, and future use. When students have opportunity to practice skills to the point of automaticity their working memory is freed for new tasks and they are able to see patterns, relationships, and discrepancies in problems that they would have missed without such practice (Anderson, Greeno, Reder, & Simon, 2000; Bransford, Brown, & Cocking, 2000; Collins, Brown, & Newman, 1989; Ellis & Worthington, 1994; Good & Brophy, 2003; Marzano, Gaddy, & Dean, 2000; Means & Knapp, 1991; Pressley, et al, 1995; Rosenshine, 2002; Rosenshine & Meister, 1995; Stevenson & Stigler, 1992; Wenglinsky, 2002, 2004).

Problem-solving strategies and activities are core components of each AchieveMath lesson (e.g., use or make a table, look for a pattern, work backwards, make a picture or design, use physical manipulatives).

Explicit, systematic instruction in problem solving has been shown to benefit students of all ability levels. Teaching students both how to do it and when to do it, and offering precise, constructive feedback during guided and independent practice, scaffolds student learning

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Students develop reasoning skills through activities that require logical and critical thinking and make connections between skills that are grouped by concept and organized in a hierarchical order of difficulty. Students are asked to demonstrate these skills in response to questions such as: “How did you solve this problem?”; “What are some different ways we could solve this problem?”; “Does this answer seem reasonable?”; “Why or why not?”

Mathematical Vocabulary: Language plays a significant role in mathematics. Therefore, direct instruction of key mathematics vocabulary is a critical element in raising student. Striving readers, English language learners, and students who have language or developmental challenges all require additional support in developing academic vocabulary. Because students approach a lesson or problem with much, little, or incorrect prior knowledge of the topic or terminology at hand, effective teachers use questions, cues, and advance organizers to discern what and how much their students already know, and whether they have misconceptions (Marzano, Gaddy, & Dean, 2000).

Group discussions allow students to externalize and discuss thought processes that they may not have consciously considered if they were working alone and become familiar and adept at communicating in the “mathematical register” – the specialized vocabulary of mathematics. By describing problem solving processes, students can practice vocabulary, syntax, semantics, and discourse features related specifically to learning mathematics.

A variety of approaches and strategies have been proven useful for explicitly teaching word meanings in order to help students gain a deep understanding of abstract concepts. Research-confirmed methods for vocabulary instruction include: • u sing students’ sociocultural and linguistic experiences to make mathematical connections between natural language and mathematics-specific language; • presenting students with explanations and definitions of target words;

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• using objects; • providing demonstrations; • using facial expressions, gestures, and dramatizations; • using graphic organizers; • asking students to determine definitions from context; • asking students to produce their own definitions and then giving them feedback; • asking students to generate nonlinguistic representations of new terms or phrases; • asking students to compare and contrast new information with other knowledge and processes, identifying similarities and differences; • asking students to create their own metaphors and analogies; • clarifying and elaborating on key concepts and vocabulary by explaining in the student’s native language; • presenting fewer than seven new words at a time and having students work on these over the course of several lessons so that they learn the meanings at a deep level of understanding; • asking students to write and use the word in a variety of contexts; • helping students link the words to relevant, familiar experiences in their own lives; • writing key terms or phrases on the board, providing students a resource to use in their own speech; • using visual, kinesthetic, and auditory teaching approaches to explicitly move students from concrete to abstract understanding and performance and to give English learners a variety of ways to connect with the information being presented; • adjusting teacher speech to ensure student understanding – using controlled vocabulary, facing students, speaking slowly, enunciating clearly, pausing frequently, and paraphrasing or repeating difficult concepts;

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• asking students to provide reasons for their answers and explanations for their solutions; • focusing on student meaning, not grammar; • accepting and building on student responses – “revoicing” student statements using more technical terms in order to give students more linguistic input and more time to process complex material; • modeling academic language; • using students’ own terminology if it seems to capture meaning in a way that will be understood by other students; • encouraging students to express their ideas by responding with phrases like “tell me more about that” or “why do you think so?”

• using visuals, manipulatives, and concrete materials; • using hands-on learning activities that involve academic language; • checking frequently for understanding by eliciting requests for clarification and posing questions; and • rewriting word problems in simpler terms (Furner, Yahya, & Duffy, 2005; Gersten & Baker, 2000; Jarrett, 1999; Khisty & Chval, 2002; Marzano, Gaddy, & Dean, 2000; Moschkovich, 1999; Reed & Railsback, 2003; Short & Echevarria, 2004/2005).

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The ability to represent mathematical ideas in a variety of forms is especially vital to conceptual understanding, strategic competence, adaptive reasoning, and problem solving.

Utilizing these research-based strategies, AchieveMath supports development of the communication skills needed to speak, read, write, and listen effectively in the mathematics register. Central to each AchieveMath lesson is the direct teaching of mathematics vocabulary, which is introduced at the beginning of each lesson and reinforced throughout the lesson discussions and in subsequent lessons.

Multiple Representations of Mathematical Concepts: When students “see” or experience mathematical ideas through words, pictures, or concrete objects that represent the ideas in linguistic and nonlinguistic ways, they learn to translate between and among these multiple representations, resulting in deeper understanding and improved performance. Students typically move through three stages, from the simple to the complex, as they develop understanding of a mathematical concept (Bruner, 1966): • the enactive stage: Manipulating concrete materials; • the iconic stage: Working with pictures, graphs, diagrams, and charts; and • the symbolic stage: Expressing mathematical ideas through numerals, formulas, and theorems.

Further, mathematical understanding depends upon the quality of the connections students are able to build between: • formal and informal mathematical experience; • new information and prior knowledge; and • conceptual understanding and procedural skills.

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However, students do not automatically make these connections or transfer their informal or concrete mathematical understandings to formal, symbolic mathematics. They need to explicitly discuss these connections, argue why solutions are reasonable or unreasonable, and explain how they know what they know (Brenner et al, 1997; Hiebert & Carpenter, 1992; Lampert, 1986; Yetkin, 2003). Therefore, AchieveMath is designed according to the research that shows that students benefit from exploring new concepts through an interactive process with teachers and other students. This exploration includes creating non-standard representations which students can then connect to standard forms.

The ability to represent mathematical ideas in a variety of forms is especially vital to conceptual understanding, strategic competence, adaptive reasoning, and problem solving.

Thus, representations serve both as teaching tools and as the means by which AchieveMath students can think, explain, determine, and justify mathematical solutions (Boerst, 2005; Cifarelli, 1998; Cobb, Yackel, & Wood, 1992; Goldin, 2002; Kilpatrick, Swafford, & Findell, 2001; Marzano, Gaddy, & Dean, 2000; Pape & Tchoshanov, 2001).

AchieveMath incorporates multiple mathematical representations in every lesson. Physical manipulatives are used to introduce and model concepts and to support student learning (e.g., base ten blocks, unifix cubes, fraction tiles, geoboards, flashcards, rulers, graph paper, and dry-erase boards). Students use manipulatives throughout the learning process (during direct instruction, guided practice activities, and independent application activities) to communicate mathematical ideas.

Lesson Design: AchieveMath instruction follows this sequence:

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Brief Review and Practice

Teacher introduces interactive activities designed to review basic skills and previously taught concepts.

Math Vocabulary

Teacher introduces appropriate mathematical language and key terms for new lesson.

Concept Development

Teacher instructs and models using manipulatives and pictorials.

Guided Practice

Students demonstrate newly taught skill with guidance from teacher.

Independent Practice

Individually or in groups, students demonstrate what they have learned with little or no assistance.

Problem Solving

Students apply the newly learned skill to determine how to solve a problem.

Lesson Summary

Students articulate what they have learned during the lesson.

Daily Lesson Assessment

Teacher assesses what the students have learned and the skills that may need to be taught again.

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Catapult Learning teachers individualize and differentiate as needed within each lesson and skills are re-taught when necessary to ensure acquisition of conceptual understanding and procedural fluency for effective problem solving. Interactions between student and teacher within a small group setting allows for immediate feedback and additional opportunities to solve problems using multiple strategies.

Through this explicit, systematic, and intensive sequence, AchieveMath helps students build confidence in their mathematical abilities by targeting and strengthening the skills they need to successfully solve ever more difficult mathematical problems. AchieveMath students develop productive disposition toward mathematics – the ability to make sense of mathematics and to see it as a language of patterns and relationships that is useful and worthwhile.

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Summary Intensive academic interventions in the early grades and prior to high school can play a critical role in getting students back on track to school success and graduation before they have accumulated a cycle of academic failure. Research clearly demonstrates that instruction that results in lasting learning entails starting where students are in terms of knowledge and skill, intentionally sequencing appropriate student experiences to facilitate and support increasing knowledge and skill; and systematically checking for understanding all the way through the sequence. Catapult Learning AchieveReading and AchieveMath offer the systematic, explicit, and intensive Tier-2-level small-group interventions that research has shown will contribute to ameliorating the dropout dilemma.

Intensive academic interventions in the early grades and prior to high school can play a critical role in getting students back on track to school success and graduation before they have accumulated a cycle of academic failure.

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About the author Dr. Marcella L. Bullmaster-Day is an Associate Professor and the Associate Director of the Touro College Lander Center for Educational Research in New York City. She has worked as a teacher, principal, researcher, university professor, corporate executive, curriculum designer, and professional development consultant in urban educational contexts for over three decades.

Dr. Bullmaster-Day served as Executive Director of Curriculum for Kaplan K12 Learning Services and was Program Chair for Kaplan University’s Graduate School of Education where she developed the conceptual framework and innovative online courses for the University’s Masters Degree in Education. Dr. Bullmaster-Day holds a doctorate in Curriculum and Teaching from Columbia University Teachers College.

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