Article

Enhancing First-Grade Children's Mathematical Development with Peer-Assisted Learning Strategies

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Abstract

The purpose of this study was to examine the effects of a dyadic peer-mediated treatment, Peer-Assisted Learning Strategies (PALS), on first-grade children's mathematics development. Within schools, 20 classrooms were assigned randomly to PALS or no-PALS groups. Teachers implemented PALS three times each week for 16 weeks. Treatment fidelity was measured with direct observation; teachers completed questionnaires about treatment effectiveness and feasibility; and 323 students were pre- and posttested. Effects were separated for low-, average-, and high-achievers, and effect sizes and the percentage of nonresponders for 18 students with disabilities were calculated. Results indicated that treatment implementation was strong; teachers judged PALS to be effective and generally feasible; and students with and without disabilities, at all points along the achievement continuum, benefited from PALS. Implications for research and practice are discussed.

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... Math PALS is composed of a set of peer-assisted activities and strategies designed to support the learning of mathematics, and it was designed as a supplement (not a substitute) for any mathematics curriculum. Math PALS was included as the treated control condition in the larger study for the following three reasons: first, the participating school district requested that the control treatment be additional mathematics instruction; second, we aimed to honor that request with an existing instructional program that was evidence-based research and had reported efficacy (Fuchs et al., 1995(Fuchs et al., , 2001(Fuchs et al., , 2002. Third, Math PALS utilizes a professional development (PD) protocol similar to that designed to support the intervention used in our treated control condition, which allowed us to offer the same intensity of PD to teachers of either participant group but focused on either reading or math. ...
... Prior research in mathematics instruction has demonstrated positive effects of peer-assisted learning for children in general, throughout the school years (e.g., Fuchs et al., 1995;Rohrbeck et al., 2003;Webb & Farivar, 1994), and for the Math PALS program specifically (Fuchs et al., 2001(Fuchs et al., , 2002 through a scope and sequence that accounts for the demands of progressive mathematical learning (Fuchs et al., 2002). These positive effects of Math PALS have been reported for students performing at different levels of mathematics achievement, including young elementary students with or without learning disabilities (e.g., Fuchs et al., 2001). ...
... Prior research in mathematics instruction has demonstrated positive effects of peer-assisted learning for children in general, throughout the school years (e.g., Fuchs et al., 1995;Rohrbeck et al., 2003;Webb & Farivar, 1994), and for the Math PALS program specifically (Fuchs et al., 2001(Fuchs et al., , 2002 through a scope and sequence that accounts for the demands of progressive mathematical learning (Fuchs et al., 2002). These positive effects of Math PALS have been reported for students performing at different levels of mathematics achievement, including young elementary students with or without learning disabilities (e.g., Fuchs et al., 2001). ...
Article
To investigate whether child × instruction effects contribute to mathematics gains in first grade, we conducted a cluster randomized controlled trial with 454 (205 treatment; 249 control) students in 28 classrooms. Classrooms were randomly assigned to implement Math Peer Assisted Learning Strategies (Math PALS) to supplement Saxon Math or Saxon Math alone. Teachers received professional development on either Math PALS (treatment) or individualized reading instruction (control). Intent-to-treat and treatment-on-the-treated results revealed no significant difference between the Math PALS and control groups in student mathematics gains. However, Math PALS effectiveness varied with initial math skills. Based on modeled results of the continuous fall math score, students who scored at the 75th percentile of the sample demonstrated significantly stronger mathematics outcomes compared with the treated control group; there was no significant treatment effect for students at the 50th percentile. For students with lower initial math skills (modeled at the 25th percentile of the sample), the effect of the treatment was negative. Students with lower initial mathematics skills made greater gains in the control group (Saxon Math alone) versus the Math PALS group.
... The 15-minute classwide fluency-building intervention included: (a) 3 min of guided practice with peer coaching and feedback for each member of the dyad, for a total of 6 min of peer coaching; (b) a 2-minute timed interval of independent practice; (c) immediate corrective feedback with a verbal explanation to one's math partner; (d) goal setting; and (e) a group contingency for improved class performance (VanDerHeyden, McLaughlin, Snyder, & Algina, 2012). The peer coaching portion of the intervention was similar to classwide peer tutoring (Greenwood, 1991) and peer-assisted learning strategies (Fuchs, Fuchs, Yazdian, & Powell, 2002), both of which have demonstrated moderate effects on math achievement through experimental studies (Slavin & Lake, 2008). Dyads were formed based on the beginning of year screening data such that higher-performing students were matched with lower-performing students and middle-performing students were matched with each other. ...
... To provide additional context for the results of this study, we estimated incremental cost-effectiveness ratios for two more math interventions: (1) Peer-Assisted Learning Strategies (Fuchs et al., 2002) and (2) Fraction Face-Off! (Fuchs et al., 2013). ...
... Peer-Assisted Learning Strategies was chosen for its similar structure to the classwide intervention examined in this study and broad evidence-base for improving literacy and math outcomes (Fuchs, Fuchs, Mathes, & Simmons, 1997;Fuchs, Fuchs, Phillips, Hamlett, & Karns, 1995;Mathes & Babyak, 2001;McMaster, Fuchs, Fuchs, & Compton, 2005;Sáenz, Fuchs, & Fuchs, 2005;Stein et al., 2008). Barrett and A.M. VanDerHeyden Journal of School Psychology xxx (xxxx) xxx The specific procedure and results described in Fuchs et al. (2002) were chosen because it is the only study that met the same level of rigor as the RCT described in this study (i.e., WWC evidence standards without reservations) and were the basis for the relative cost-effectiveness estimates. Fuchs et al. (2002) differed from the current study in that the intervention was implemented with first graders and targeted corresponding first grade math skills (e.g., quantity comparison). ...
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Given limited resources, schools are encouraged to consider not only what works, but also at what cost. Cost-effectiveness analysis offers a formal methodology to conceptualize and calculate the ratio of the costs to implement an intervention to its effects (i.e., incremental cost-effectiveness ratios). This study used the ingredients method to analyze secondary data from a randomized controlled trial (N = 537 fourth- and fifth-grade students) to calculate the cost-effectiveness of a classwide math intervention, and provides an overview of cost-effectiveness analysis for readers unfamiliar with the formal methodology. For fourth-graders, the incremental cost-effectiveness ratio was $169.07, indicating it cost $169.07 per student for a 1 standard deviation increase in scaled scores on the state assessment. For fifth-graders, there was no statistically significant effect on the state assessment, but there were improvements in curriculum-based measurement (CBM) scores with incremental cost-effectiveness ratios ranging from $65.08 to $469.12, depending on the type of CBM probe and implementation context. Additionally, using number-needed-to-treat (i.e., the number of participants who must be provided with the intervention to prevent one failure on the state assessment), the cost was $126.90 to prevent failure on the state assessment for one fourth-grade student receiving special education services or for one student who scored below the 25th percentile on the prior year's state assessment. Implications and directions for future research are discussed.
... A lack of fluency in basic computations can lead to mathematics difficulties that can persist across the lifespan (Nelson et al. 2013). Addressing these deficits early provides a greater chance for success, before the school mathematical curriculum increases in scope and difficulty (Fuchs et al. 2002). ...
... The use of SAFMEDS as a method of instruction for math facts could potentially have impacted on the lack of academic gains demonstrated by the tutor group. The benefits observed for tutors in the previous research is often attributed to the process of constructing explanations for tutees on the material being taught, requiring the tutor to elaborate and generate connections between the current material and previously learned information (Fuchs et al. 2002). For example, in an intervention involving teaching of algebra, tutors combine their knowledge of basic math facts with the algebraic equations they are helping their tutees to learn. ...
Article
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The current study employed a randomized controlled trial to evaluate the use of peer tutoring and fluency-based instruction to increase mathematics fluency with addition and subtraction computation skills. Forty-one elementary school students between the ages of eight and 12 years participated in the 8-week study using cross-age peer tutoring, Say All Fast Minute Every Day Shuffled, frequency building, and the morningside math facts curriculum (Johnson in Morningside mathematics fluency: math facts (vol 1–6; curriculum program), Morningside Press, Seattle, 2008). Pre- and post-test measures of mathematics fluency and calculation were conducted with all participants. A measure of social skills and competing problem behaviors was also conducted at pre- and post-testing to evaluate any additional effects of the peer tutoring model. The results demonstrated a statistically significant difference between groups on measures of mathematics fluency, with the experimental group demonstrating significantly higher scores than the control group at post-testing. There were no significant differences between groups on measures of social skills and competing problem behaviors or calculation. The findings indicate that cross-age peer tutoring and fluency-based instruction resulted in positive outcomes for tutees in the mathematics domain, specifically mathematics fluency.
... Programs that incorporate peer interactions can improve math-related school readiness skills in kindergarten in areas such as number identification, number concepts, number relations, math vocabulary, and arithmetic (Fuchs, Fuchs, & Karns, 2001;Gardner, Rudman, Karlsen, & Merwin, 1987). Improvements have also been found on performance on standardized tests of math achievement of children from kindergarten through second grade on skills such as advanced arithmetic problems and computation (Fuchs et al., 2001;Fuchs, Yazdian, & Powell, 2002;Slavin & Karweit, 1985). ...
... During 30-minute sessions using materials and manipulatives, pairs would focus on different mathematical concepts, such as recognizing numerals, ordering and comparing numerals on a number line, and arithmetic. Students who participated in the PALS programs scored higher on portions of standardized tests that aligned with the materials covered during the interactions compared to children who did not participate in the program (Fuchs et al., 2002). ...
Chapter
The Handbook of Social Influences in School Contexts draws from a growing body of research on how and why various aspects of social relationships and contexts contribute to children’s social and academic functioning within school settings. Comprised of the latest studies in developmental and educational psychology, this comprehensive volume is perfect for researchers and students of Educational Psychology. Beginning with the theoretical perspectives that guide research on social influences, this book presents foundational research before moving on to chapters on peer influence and teacher influence. Next, the book addresses ways in which the school context can influence school-related outcomes (including peer and teacher-student relationships) with specific attention to research in motivation and cognition. Within the chapters authors not only present current research but also explore best-practices, drawing in examples from the classroom. With chapters from leading experts in the field, The Handbook of Social Influences in School Contexts provides the first complete resource on this topic.
... PALS is based on basic instructional principles such as dyadic and class-wide peer tutoring, which is usually implemented three times per week for a 16-week period. It has been shown that PALS is effective in increasing basic maths skills of primary schools students, both those with and without a learning disability (Fuchs, Fuchs, Yazdian, & Powell, 2002). ...
... The results of this study are promising, however, we acknowledge that our sample size was relatively small when compared to studies exploring other maths intervention programmes such as PALS, Numeracy Recovery Scheme and Catch up Numeracy (e.g., Dowker & Sigley, 2010;Fuchs et al., 2002). Therefore, further research is needed to assess if the results found in our study can be replicated with a larger sample. ...
Article
The use of SAFMEDS cards, which stands for “Say All Fast Minute Every Day Shuffled” has been widely reported in the literature as an effective fluency-building tool. Most studies have focused on students with a learning disability or those classed as at risk of failing academically. In addition, most of the research has implemented SAFMEDS one-to-one or in small groups. We investigated the use of SAFMEDS in a high school setting, targeting basic maths skills across the whole class. Forty-eight students aged 11–12 years participated in the study over a 4-week period. Our results showed that using SAFMEDS to compliment students’ maths lessons can further increase basic maths skills when compared to standard maths classes alone. We also found that the gains were maintained at a 1 month follow-up. An application quiz showed that students could also transfer the information they had learned to real-world maths problems.
... Researchers have studied the effects of various aspects of RTI, including Tier 1 (Al Otaiba et al., 2011;Clarke et al., 2011;Coyne, Kame'enui, Simmons, & Harn, 2004;Fuchs, Fuchs, & Hollenbeck, 2007), Tier 2 (Bryant, Bryant, Gersten, Scammacca, & Chavez, 2008;Fuchs, Fuchs, Yazdian, & Powell, 2002;Kerins, Trotter, & Schoenbrodt, 2010;Vaughn, Denton, & Fletcher, 2010), Tier 3 (Compton, Gilbert, Jenkins, & Fuchs & Vaughn, 2012;Denton et al., 2013;Powers & Mandal, 2011;Vaughn et al., 2010), and CBM (Christ, Zopluoglu, Monaghen, & Van Norman, 2013;Deno et al., 2008;Reschly et al., 2009;Stecker et al., 2005). More recently, researchers have investigated the effects of RTI in its entirety on student achievement. ...
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Response to intervention (RTI) emerged from the 2004 reauthorization of the Individuals with Disabilities Education Act, but the roots of RTI are found embedded within the history of the field of learning disabilities (LD) as well as other sources of influence. In what follows, we provide a brief history of LD and highlight the connection between the controversies of LD and the emergence of RTI. We offer discussion on the evolution of RTI through current practice, along with implications and cautions regarding future practice so that school personnel might gain a better understanding of RTI.
... A few studies were identified that conducted wholeclass instruction, typically Tier 1 instruction with younger students. For example, whole-class intervention programs, such as Number Worlds (Griffin et al., 1994) and Peer Assisted Learning Strategies (Fuchs, Fuchs, & Karns, 2001;Fuchs, Fuchs, Yazdian, & Powell, 2002), provide effective practices for teaching numeracy skills to low-achieving students. ...
... In much the same way as discussion, the literature on peer tutoring highlights the expansive benefits student-to-student interaction can have on academic outcomes in social studies classrooms. While the bulk of the work in the area of peer tutoring has centered on English Language Arts (Fuchs, Fuchs, & Burish, 2000) and the development of basic math skills (Fuchs, Fuchs, Yazdian, & Powell, 2002), several studies show the benefits of peer tutoring in history classrooms. For example, Mastropieri and colleagues (Mastropieri, Scruggs, Spencer, & Fontana, 2003) found that matching higher and lower performing readers from a range of ethnic backgrounds (21% Asian/Pacific Islander, 12% Hispanic, and 9% African American) into dyads in a high school world history class, teaching a summarization strategy, and collaborative practice resulted in higher outcomes on content knowledge tests than their same-aged peers who were exposed to a more traditional form of instruction. ...
Chapter
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This chapter provides an overview of programs of intervention research that have provided frameworks for effective instruction in history. It reviews studies that have made a particular impact on academically diverse learners including students with disabilities, and ethnically diverse learners. To start, the chapter highlights select studies that focused on content enhancement strategies including graphic organizers, mnemonic tools, and text structure instruction. It then examines work in the area of historical discussion, peer tutoring, and extending opportunities for heterogeneous student-to-student and small group interaction. The chapter synthesizes several studies that employ twenty-first-century learning tools such as the Virtual History Museum, project-based learning, and innovative methods to engage a diverse population of learners. The chapter also reviews some select studies that explore teaching discipline-specific cognitive strategies through a cognitive apprenticeship model. Finally, it offers suggestions for how this work fits into the larger framework for historical learning and implications for the field.
... Similarly, the SSS program compels the student to use outlines and note cards to organize information, techniques associated with best practice study strategies (Marzano et al., 2001). Another SSS study skill device is to encourage each student and teacher to share personal strategies in a format similar to that described in the peer assisted learning literature (e.g., Fuchs, Fuchs, Yazdian, & Powell, 2002). Finally, each study strategy is revisited six times by the student to counterbalance any assumed bias that students might have relative to their capacity to remember information (Kornell & Bjork, 2009). ...
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An overview of the Student Success Skills (SSS) program is offered, including descriptions of the curricular structure, extant research support related to SSS effectiveness for academic achievement and improved school behaviors, and a theory of change for student development. Recent research has demonstrated the value of the SSS program as it connects to student academic achievement and related learning outcomes. To demonstrate how these findings can be generalized as a theory of change in myriad educational circumstances, specific SSS curricular skills and strategies are explicated, including those that are cognitive, attitudinal, self-regulatory, behavioral, and social.
... Today, small group learning is considered a favored teaching strategy among both primary and secondary school teachers and is widely used from pre-school through to post-secondary (Johnson and Johnson 2002). When employed correctly, the benefits of small group learning include development of critical thinking skills, promotion of interpersonal relationships, consideration of alternative perspectives, and practice justifying viewpoints (Blumenfeld et al. 1996;Fuchs et al. 2002). Further, implementation of small group learning activities is viewed as a cornerstone of inclusive classrooms, as when properly implemented has been demonstrated to increase motivation and peer acceptance for learners of all abilities (Belland et al. 2009). ...
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Existing research on small group learning and high-achieving students has been divided, with some stating that this technique is detrimental to high-achievers, while others tout the benefits. The current study aimed to assess whether academic achievement is associated with affects students’ perspectives on small group learning. Forty-seven children between the ages of six and 12 participated in the study by answering questions pertaining to group learning. Students’ academic achievement was assessed via their report card grades. A binomial logistic regression failed to find that academic achievement was predictive of the likelihood that students preferred working alone, however, a second binomial logistic regression discovered that higher achieving students were more likely to report that they learn better individually as opposed to in groups. This elucidates the results of previous studies, by suggesting that perhaps it is not that high-achievers do not enjoy group work, but rather, they feel more confident in their individual abilities.
... The first step in many tiered support systems is identifying a classwide need, something that occurs when the median score of the universal screener for a given classroom falls below the seasonal benchmark for proficiency. For example, if an MAP score at or below the 40th percentile suggests that an individual needs intervention, (Fuchs, Fuchs, & Karns, 2001;Fuchs, Fuchs, Yazdian, & Powell, 2002). ...
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This article is about a school‐district‐initiated partnership with university faculty and their effort to implement a mathematics multi‐tiered system of support (MTSS). In addition to reporting research about MTSS implementation, we describe how this district translated research into practice. We also share the perceptions of key stakeholders about implementing mathematics MTSS in their district. We found that stakeholders identified time and human capacity as barriers to implementation, while the primary facilitator to implementation was identified as the acquisition of concrete strategies and tools supporting instruction. These stakeholder perceptions have implications for other districts with limited resources attempting to implement mathematics MTSS in their buildings through professional development and coaching.
... Typically, the teacher takes the role of an expert; however, more capable peers can also take on that role, albeit not always knowingly. For example, Fuchs, Fuchs, Yazdian, and Powell (2002) examined the effect of peer collaboration on math learning. In the study, 10 first-grade classes were assigned either to a teacher-led instructional group or to a treatment where students were assigned to peer groups by math achievement scores. ...
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In this study, we present an educational board game designed to promote both mathematics and Chinese language learning. We use text‐mining techniques to analyze dialog by 40 students, in six groups playing a board game in a dual language immersion context. Our findings provide evidence to support past claims and arguments that play and specifically play within board games can provide a learning environment in which students can experiment with concepts and language without fear of failure. In our study, we not only found that learners were willing and excited to use their L2 skills within the context of the game but also that the board game promoted peer learning, which subsequently provided support for both math and language development. In addition to providing motivating experiences, to what extent can the use of collaborative board games help dual language immersion educators to integrate subject content and target language instruction in a language‐rich, meaningful, and engaging way? Video_Abstract_and_Discussion
... One of our biggest challenge is to convince school administrators to see the value of a Math Circle that does not offer a traditional tutoring program. Our plan is to evaluate our program by collecting more data to show that Math Circle programs provide better learning opportunities [2,3,5]. ...
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In this article, we summarize our personal journey to establish a successful Math Circle in a community that is not very familiar with such mathematics enrichment programs. We share the story of how our Math Circle began three years ago, as well as the lessons we learned and our organizational challenges and successes. Additionally , we outline three primary perspectives: the founder perspective, the student volunteer perspective, and the faculty volunteer perspective .
... Rosebrock et al., 2010), fehlt es an Originalarbeiten, die ebenfalls Outcomes auf sozialer Ebene im Grundschulbereich berichten. Gleiches gilt für Studien mit Kindern mit externalisierenden Verhaltensproblemen. Zur Förderung mathematischer Basiskompetenzen mithilfe des PALS-Programms (Fuchs, Fuchs, Yazdian & Powell, 2002) ...
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Der Beitrag beleuchtet tutorielle Leseverfahren mit Grundschulkindern mit externalisierenden Verhaltensproblemen und deren Wirkungen auf fachliche und soziale Indikatoren. Über eine systematische Literaturrecherche wurden insgesamt 25 Studien ermittelt, die entweder a) mit Kindern mit Verhaltensproblemen durchgeführt wurden oder b) Effekte im Bereich sozialer Kompetenzen oder sozialer Beziehungen der Kinder untereinander berichten. Methodisch-didaktische Differenzen und Gemeinsamkeiten zwischen den einzelnen Verfahren werden dargestellt. Nennenswerte Adaptionen im Hinblick auf die teilnehmende Klientel (wie bspw. zusätzliche Unterstützungsangebote für Kinder mit Verhaltensproblemen etc.) konnten dabei insgesamt nicht festgestellt werden. Basierend auf den Rechercheergebnissen beinhaltet der Artikel zudem konzeptionelle Überlegungen sowie Perspektiven für Forschungsvorhaben vor allem für den deutschen Sprachraum.
... The implementation of math interventions in schools could provide continuous support for students with mathematics learning disability. Past studies have shown that mathematical interventions can reduce skills gaps and prevent deficits that may occur in the future (Clements & Sarama, 2007;Fuchs et al., 2002;Sophian, 2004). The success of mathematics interventions for students with learning disabilities has been extensively demonstrated through various means and recommendations (Geary, 2013;Gersten et al., 2005Gersten et al., , 2009Jaspers et al., 2017;Kroesbergen & Luit, 2003;Lemons et al., 2015;Suhaimin & Mohamed, 2017). ...
... Only one study of a supplementary intervention leveled the playing field by reducing the treatment group's regular math instructional program by the amount of time students were exposed to the supplementary treatment. 57 Agodini et al. compared the effectiveness of four curricula. 58 At the second-grade level, Saxon Math had a dosage time of about 6.9 hours and comparison groups had times of about 5.5 hours, a 25 percent advantage for Saxon Math. ...
Article
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A Study of the Usefulness of RCTs in the What Works Clearinghouse: The paper is a careful analysis of the useful of 27 mathematics RCT studies that resided in the WWC in 2016. We find twelve serious threats to the usefulness of the RCTs, with at least one threat residing in all fo the 27 RCT studies.
... A number of studies suggest that strategy instruction in word problem solving can be an effective approach in helping learners improve their word problem-solving accuracy (e.g., Baker, Gersten, & Lee, 2002). Instructional strategies that researchers have found effective for improving word problem-solving accuracy include (a) direct and explicit strategy instruction that teaches conceptual understanding of a word problem (e.g., math concepts and principles; Fuchs, Fuchs, Finelli, Courey, & Hamlett, 2004;Griffin & Jitendra, 2008;Jitendra, DiPipi, & Perron-Jones, 2002;Jitendra, Griffin, Deatline-Buchman, & Sczesniak, 2007;Swanson, 2 The Journal of Special Education XX(X) Hoskyn, & Lee, 1999;Xin & Jitendra, 1999;Xin, Jitendra, & Deatline-Buchman, 2005), (b) strategy training that helps to develop visual spatial skills (e.g., Van Garderen & Montague, 2003), (c) instructional feedback (e.g., Fuchs, Seethaler, et al., 2008), and (d) using peer-assisted collaborative learning strategies during instruction (e.g., Fuchs, Fuchs, Yazdin, & Powell, 2002). ...
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English language learners (ELLs) struggle with solving word problems for a number of reasons beyond math procedures or calculation challenges. As a result, ELLs may not only need math support but also reading and linguistic support. The purpose of this study was to assess the effectiveness of a math comprehension strategy called Dynamic Strategic Math (DSM) on word problem solving for Latino ELLs. The strategy provides performance-contingent feedback based on the student’s reading and language comprehension level. A multiple baseline design was used to assess 6 second-grade Latino ELLs at risk for math failure/math disability. As compared with the baseline phase, DSM increased word problem solving for all the participants. All students’ level of performance was maintained during follow-up sessions. The results suggest the intervention facilitated math problem–solving performance.
... According to Gooding (2009), learners who have difficulty reading English as the language of learning and teaching (LoLT) usually have trouble solving MWPs. Fuchs and Fuchs (2002) added that learners who struggle with reading skills find word problems challenging to execute, usually performing worse than learners experiencing only mathematics difficulties, or learners experiencing neither reading nor mathematics difficulties. On the other hand, Salihu, Aro and Räsänen (2018) noted that reading difficulties exacerbate rather than cause mathematics difficulties. ...
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Understanding the challenges pertaining to the teaching and learning of mathematics word problems is important in order to formulate effective strategies that will address the challenges. The qualitative case study reported in this article describes the teachers' and the learners' experiences regarding mathematics word problems. Data were collected through focus group discussions and reflection sessions, through the use of the free attitude interview technique used to initiate the conversations. Thematic analysis was used to analyse data. Analysis of data revealed challenges related to lack of English proficiency, limited knowledge of mathematical vocabulary, the effects of "out of context" meanings and lack of understanding mathematical language and structure to be the sources of difficulty for teaching and learning mathematics word problems. Findings of the study suggest the need for challenges to be understood in context in order for meaningful possible solutions to be formulated. Thus the learners' experiences should be regarded as important guidelines for informing better teaching of mathematics word problems.
... Clear instructional activities are planned in advance by the teacher and based on material that has been taught; Procedures and routines for working in pairs are taught by the teacher in advance of peer work; Members of pairs may differ in ability levels (reading, math, or English proficiency) Peers work together approximately for a stipulated time period [8]. Peer tutoring has not only been effective in reading [9][10] but has been found effective in the area of mathematics too both in primary school children as low as in grade 1 and in secondary students [11][12]. ...
... While peer and cross-age tutoring has a long history in the public school system, the evidence base for this model is far more limited. Programs such as Reading Buddies and Peer Assisted Learning Strategies that incorporate elements of peer tutoring have been used in schools for decades and have been found to be effective (Fuchs et al., 2002;McMaster et al., 2005;Stein et al., 2008;What Works Clearinghouse, 2012, 2013. Evidence from larger meta-analyses reporting results specifically for peer tutoring programs show meaningful effects on student achievement (Dietrichson et al., 2017;Slavin et al., 2009). ...
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In this thought experiment, we explore how to make access to individualized instruction and academic mentoring more equitable by taking tutoring to scale as a permanent feature of the U.S. public education system. We first synthesize the tutoring and mentoring literature and characterize the landscape of existing tutoring programs. We then outline a blueprint for integrating federally funded and locally delivered tutoring into the school day. High school students would serve as tutors/mentors in elementary schools via an elective class, college students in middle schools via federal work-study, and 2- and 4-year college graduates in high schools via AmeriCorps. We envision an incremental, demand-driven expansion process with priority given to high-needs schools. Our blueprint highlights a range of design tradeoffs, implementation challenges, and program costs. We estimate that targeted approaches to scaling school-wide tutoring nationally, such as focusing on K–8 Title I schools, would cost between $5 and $16 billion annually.
... Here, we review interventions that have targeted distinct math difficulties as well as general cognitive deficits in MD. Previous behavioral research has shown that interventions using speeded retrieval of number combinations together with conceptual number knowledge can significantly improve math skills in elementary school children (Christensen and Gerber, 1990;Okolo, 1992;Fuchs, Fuchs et al. 2002;Fuchs, Fuchs et al. 2004;Fuchs, Fuchs, Hamlet et al., 2006;Fuchs, Fuchs, Compton et al., 2006;Fuchs, Fuchs, Compton et al. 2007;Fuchs, Fuchs and Luther, 2007). Specifically, extensive research by Fuchs and colleagues have shown that interventions that directly target specific areas of math, such as the memorization of arithmetic facts Powell, Fuchs et al., 2009), conceptual understanding of arithmetic procedures , and word problem-solving (Fuchs, Fuchs et al. 2004), can significantly improve numerical skills in children with MD. ...
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The purpose of this chapter is to describe effective mathematics instructional programs delivered in general education settings by elementary classroom and middle school mathematics teachers. Following a discussion of critical mathematical concepts and skills and the role of instructional practices in enhancing learning for all students and in preventing mathematics difficulties before they become intractable, instructional design features that promote the mathematical development of struggling students are highlighted. This chapter also describes the nature and results of specific mathematics instructional programs in elementary and middle schools to understand the instructional conditions that need to be in place to promote mathematics success. Finally, study limitations and recommendations for future research are discussed.
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Thesis
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For the preparation of this thesis, two studies in German comprehensive schools were conducted. Fifth grade students in regular classroom settings were trained using reciprocal teaching methods (Palincsar & Brown, 1984). The aim of this research project was to prove the possible implementation of reading programmes based on reciprocal teaching procedures in regular classroom settings. An additional aim was to explore how the effects of interventions vary when programme elements are blanked out or added. Furthermore the data was reanalyzed to gain information about the predictive power of the variables reading time, reading fluency, vocabulary and reading strategies in a path model of reading comprehension and also about the way these variables are integrated in such a model. The major focus of the first study was on the effects of instructing various combinations of reading strategies. In the study 380 students of 15 classes were trained using modified reciprocal teaching methods. For the second study the aim was to prove the additional effects of the programme when elements of cooperative learning were integrated into the intervention. Sample size of study 2 was 228 students of 10 classes. Results of the two studies confirm that reciprocal teaching is a promising approach to foster the reading comprehension of German fifth grade comprehensive school students in the short and medium term. The present work shows, that the positive effects of reciprocal teaching can also be achieved in regular classroom settings. Additionally variations of the method can cause increased effects on the reading comprehension of students. The reported path model of reading comprehension verifies the importance of reading strategies for reading literacy and shows that a specific order in the application of reading strategies on texts accounts for reading comprehension proficiency.
Article
The purpose of this study was to develop and explore the impact of a synchronous peer tutoring system, which integrated a structured peer tutoring strategy with technological advances, for students with learning disabilities (LD). The system provided a learning activity management module for teachers to administer peer tutoring activities, and included various math representation objects, communication tools, and reward schema for facilitating online peer learning activities. Four fourth-grade students with LD participated in this study in the online peer learning setting for two semesters. The results indicated that the proposed system was effective to enhance the mathematics learning of students with LD, especially the learning of conceptual and application math problems. Students with LD showed improvement in math fluency on conceptual problems. The findings also supported the effectiveness of the math objects provided by the synchronous peer tutoring system for facilitating communication among students and understanding of math concepts in the online activities. The results are discussed from the perspective of online peer learning research © International Forum of Educational Technology & Society (IFETS).
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Available for download at http://nirn.fpg.unc.edu/resources/implementation-research-synthesis-literature
Thesis
Eng verknüpft mit der Effektivität von Bildungsprozessen stellt die Modellierung und Messung professioneller Lehrkompetenzen ein zentrales Forschungsinteresse der empirischen Lehrerbildungs- und Unterrichtsforschung dar. Unangefochtenes kennzeichnendes Merkmal von Kompetenzen ist deren Ausrichtung auf die erfolgreiche Bewältigung von Anforderungen in spezifischen Situationen. Dem Begriff der Kompetenz schwingt damit die Perspektive einer realized ability mit. Aus forschungspragmatischen Gründen wird dieser mehr oder minder explizite Handlungsbezug jedoch oft vernachlässigt. Einschlägige Studien zur Kompetenzmessung definieren Kompetenzen deshalb als kontextbezogene kognitive Leistungsdispositionen, die sich funktional auf Situationen und Anforderungen in bestimmten Domänen beziehen. Versteht man Kompetenz jedoch tatsächlich als Handlungskompetenz, greifen Erhebungsmethoden in Form von Selbstauskünften wie Wissenstests, Selbsteinschätzungen oder Interviews zu kurz. Es fehlt die Perspektive des tatsächlichen Handlungsvollzugs. Zwar unterstellt man diesen Messergebnissen quasi Stellvertreter und Garant für die entsprechende Handlung zu sein, ob die getesteten Personen in der realen Situation jedoch tatsächlich so handeln und sich als kompetent erweisen, muss bei diesen Messverfahren in letzter Konsequenz ungeklärt bleiben. An dieser Diskrepanz setzt das vorliegende Forschungsprojekt an. Ziel ist es, die methodische Vorgehensweise bei der Kompetenzmessung eng an die theoretische Fundierung von Kompetenz als Handlungskompetenz zu binden. Die methodologische Grundannahme dabei ist: Wenn sich (Lehr)Personen als kompetent erweisen, dann müssen sie das in der konkreten, kontextuell gebundenen Handlungssituation tun; ihre Kompetenz wird in der Performanz beobachtbar. Kernanliegen der Studie ist die Entwicklung eines Instruments, das Kompetenz stellvertretend über die Performanz erfassen kann. Der Einsatz von Videoanalysen drängt sich damit auf. Die vorliegende Studie interessiert das kompetente Handeln von Lehrkräften angesichts der Heterogenität der Lerner. Professionellen Lehrpersonen gelingt es, auf unterschiedliche Ausgangslagen einzugehen und adaptive Lernsettings bereitzustellen. In der universitären Ausbildungsphase sollen dazu die ersten Teilkompetenzen erworben werden. Für den Modellierungsprozess adaptiver Lehrkompetenz wurde das Modell der Entwicklung professioneller Handlungskompetenz von BAUMERT und KUNTER (2006) im Rückgriff auf WEINERT (2001) herangezogen. Professionelles Lehrerhandeln entsteht demnach aus einem Zusammenspiel von Aspekten professioneller Wertvorstellungen und Überzeugungen, motivationaler Orientierungen, selbstregulativer Fähigkeiten und Professionswissen. Diese personimmanenten Dispositionen wurden auf die Situation adaptiven unterrichtlichen Handelns von Studierenden spezifiziert. Analog dazu wurden stellvertretend für jede Prädiktordimension Personmerkmale erhoben, die aus theoretischer Sicht Prognosen im Hinblick auf das beobachtbare Kompetenzlevel zulassen (z.B. Einstellungen zum Lehren und Lernen, Lehrerinteressen, Selbstwirksamkeitserwartungen, Belastungserleben, Professionswissen hinsichtlich individualisierenden Lehrens und Lernens). Ebenso wurde adaptive Lehrkompetenz auf zwei Niveaustufen zunächst theoretisch in Form einer Minimalstufe zu Beginn der Ausbildung und einer Maximalstufe als hypothetisches Professionalitätsmaximum modelliert. Ausgehend von den theoretischen Vorarbeiten zur Minimalstufe wurde ein niedrig inferentes Beobachtungsschema entwickelt, das die Erhebung der Performanz adaptiver Lehrkompetenz bei Studierenden ermöglicht. Insgesamt wurden 50 Unterrichtsvideos kodiert und entsprechend die adaptive Lehrkompetenz der Probanden identifiziert. Vor diesem Hintergrund wurden die einzelnen Prädiktordimensionen hinsichtlich ihrer prognostischen Qualität überprüft. Die Ergebnisse weisen darauf hin, dass es weniger die als relativ stabil geltenden Dispositionen sind, die ein hohes Maß an adaptiver Lehrkompetenz ausmachen, als das relativ leicht veränderbare Merkmal des im Studium erworbenen Wissens.
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En l’àmbit internacional, s’utilitzen diverses estratègies i pràctiques escolars d’agrupament dels estudiants per atendre la diversitat i fer front a les dificultats que s’hi associen. Sembla observar-se un consens segons el qual la reducció de la ràtio entre professor i alumne, implícita en les estratègies d’agrupament, facilita la tasca docent i l’atenció a la diversitat. Hi ha, tanmateix, diferents aproximacions sobre com i segons quins criteris cal agrupar els estudiants. Aquestes aproximacions tenen implicacions diverses en termes d’organització escolar i poden oferir diferents resultats en termes d’aprenentatge. La diversitat es pot gestionar, per exemple, a través de “formes de diferenciació”, que inclouen els agrupaments per nivells entre les classes (ability tracking o streaming) i els agrupaments per nivells dins de les classes (intra-classroom ability grouping o setting), que en el cas català s’aproparien als anomenats “agrupaments flexibles”. Aquestes estratègies busquen la creació d’espais homogenis per facilitar la tasca docent mitjançant un ensenyament centrat en uns objectius i uns continguts més alineats amb les aptituds dels estudiants. D’altra banda, també es duen a terme agrupaments que segueixen criteris d’heterogeneïtat, principalment segons l’habilitat, les aptituds i altres característiques observables dels estudiants. En aquests casos, la diversitat sovint esdevé una de les condicions de l’organització i del funcionament dels grups d’aprenentatge. Estratègies com ara l’aprenentatge cooperatiu parteixen de l’heterogeneïtat interna dels grups per dur a terme estratègies que es beneficiïn de la diversitat de perfils i habilitats de l’alumnat (interdependència positiva, ajuda mútua entre els estudiants, peer effects, etc.).
Article
Reform in educational policy and federal legislation has placed an emphasis on data collection pertaining to student outcomes in the academic setting. In response, school systems have shifted to multi-tiered frameworks that utilize varying levels of support through the implementation of evidence-based interventions. Data-based decision making determined by student success within these interventions is, at best, inconclusive without the collection of treatment integrity data. However, present evidence-based methods of improving treatment integrity are reactive and also require time and staffing demands that may not be feasible in the school setting. The present research aimed to investigate Computer-Guided Implementation Planning as an effective and more feasible option to consider when supporting implementer levels of treatment integrity. Teachers were asked to implement the academic intervention Cover, Copy, and Compare with nominated students having difficulty with mathematics fluency. Following the completion of Computer-Guided Implementation Planning, teachers consistently demonstrated substantially improved levels of implementation adherence and moderately improved levels of implementation quality. They also found Computer-Guided Implementation Planning to be socially valid. Improved levels of treatment integrity were found to align with improved levels of fluency for the majority of students who participated. Implications and future directions related to the present findings are discussed below.
Article
The purpose of this article is to synthesize the extant research on peer-mediated interventions (PMIs) with English language learners (ELLs) in kindergarten through Grade 12. Fourteen studies that were published in peer-reviewed journals from 1983 to 2013 were examined in terms of study characteristics, the effects on academic outcomes, study quality, and overall effectiveness. Structured, heterogeneous grouping was used in the 10 peer pairing and 4 collaborative/cooperative grouping PMIs with ELLs. Eight of the 14 studies included high methodological quality. Overall, PMIs with ELLs are associated with medium to large effects on measures of phonemic awareness, vocabulary, and comprehension when compared to teacher-mediated comparison conditions. More research on PMIs with ELLs in high school and across core content areas, particularly mathematics, is warranted. Implications and future research for PMIs with ELLs are discussed.
Chapter
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This chapter reviews studies in three broad categories of peer tutoring employed with students with disabilities and tested by researchers: class-wide peer tutoring (CWPT), reciprocal peer tutoring (RPT) including peer-assisted learning strategies (PALS), and nonreciprocal peer tutoring (NRPT). The primary objective of the current systematic review is to examine the extent to which peer tutoring interventions have resulted in increases in student academic achievement for diverse students with disabilities. The chapter also reviews and discusses the following study features: type of intervention (i.e., CWPT, PALS, RPT, and NRPT); participants and diversity; settings for intervention (i.e., general or special education classes); academic subject areas; research designs; and academic outcomes. It describes each type of tutoring, followed by a summary of some studies and the distinguishing features of those studies, i.e., participants and diversity, settings, academic subjects, research designs, and outcomes.
Chapter
This chapter draws on teacher effectiveness research (TER) and elaborates on factors associated with teacher effectiveness to make suggestions for professional development. The first part provides a critical review of TER in which the major findings of this field are studied. In the second part, taking into account the limitations of TER, the dynamic model of educational effectiveness is presented. The rationale and major assumptions of this model are outlined. Effectiveness factors operating at the teacher level and their measurement dimensions are presented, and the concept of grouping of factors is introduced. In the third part, the authors provide a summary of national and international studies that were conducted to test the validity of the dynamic model at the teacher level. This part is also concerned with empirical studies that revealed relationships among factors operating at the teacher level which helped the authors define specific stages of effective teaching. In the last part, implications for TER and research on teacher professional development are drawn.
Article
In 2010, the Institute of Education Sciences commissioned a much-needed national evaluation of response to intervention (RTI). The evaluators defined their task very narrowly, asking “Does the use of universal screening, including a cut-point for designating students for more intensive Tier 2 and Tier 3 interventions, increase children’s performance on a comprehensive reading measure?” Their regression-discontinuity analysis showed that first-grade children designated for (but not necessarily receiving) more intensive intervention in the 146 study schools performed significantly worse than children not designated for it. There were no reliable differences between designated and nondesignated students in Grades 2 or 3. The provocativeness of these findings notwithstanding, the evaluation’s focus and design weakens its importance. RTI implementation data were also collected in the 146 study schools. These data suggest many of them were not conducting RTI in a manner supported by research and policy. Such findings and others’ evaluations of RTI advance the idea that simpler frameworks may encourage more educators to implement RTI’s most important components with fidelity.
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The study attempts to investigate the concept of peer tutoring and its impact on learning. Peer tutoring can be applied among the students of the same age group or students from different age groups. The students learn from each other in an organized way through the process. It is a well-organized and beneficial learning experience in which one-student acts as the tutor or teacher and the other one serves as the tutee or learner. Peer tutoring creates an opportunity for the students to utilize their knowledge and experience in a meaningful way. In this process the tutors reinforce their own learning through reviewing and reformulating their knowledge. On the other hand, the learner or tutee gets one on one attention. Peer tutoring enables both tutor and tutee to gain self-confidence, the tutor by observing self-competence in his or her capability to help someone and the tutee by gaining positive reinforcement from the peers. Therefore, peer tutoring has a very positive impact on the process of learning.
Article
A meta-analysis of findings from 50 independent studies of peer tutoring programs in Mathematics at multiple educational stages showed that 88% of these programs have positive effects on the academic performance of the participants (Hedge's g = 0.333). Some of the variables to be taken into account when developing a peer tutoring experience were analyzed. Results showed that variables such as the ages of the participants, roles, skills of the tutees (disabled or at academic risk vs non-disabled and not at academic risk), length of the sessions and frequency were not significant moderators of the academic achievement. Variables such as educational stage, design of the study, duration of the program, level of knowledge of the tutors, time of the day (school time vs out of school time) and sample size turned out to be significant moderators. Results are discussed and proposals for future research are suggested.
Article
The authors examined the social practices and outcomes of 23 immigrant and 16 nonimmigrant preschoolers in English only preschool classrooms. In both classrooms, the majority of the children (nearly two thirds) were immigrant, English language learners. The children's social attempts, social strategies, speech functions, and degree of social success were observed and comparisons were made between nonimmigrant and immigrant peers. There were similarities between groups in their social engagement and social construction strategies; there were differences in social roles, social language functions, and types of social construction strategies. There also were significant differences in the social success of the two groups. Immigrant children experienced rejection of their social bids more than their preschool peers did. Immigrant children also were less likely to be leaders and seemed positioned in a lower social status among their peers did. These results are discussed along with implications for educational practices.
Book
This book presents an extensive review of research on effective interventions for students with social, emotional and behavioural difficulties.
Article
The purpose of this meta-analysis was to examine the effectiveness of early numeracy interventions for young students, including students with disabilities or those at risk for math difficulty (MD). This study evaluated preschool, kindergarten, and 1st-grade interventions on early numeracy content, instructional features, and methodological components that improved students’ math achievement. A total of 34 studies met inclusion criteria for this meta-analysis, with 52 treatment groups. The average weighted effect size for numeracy interventions with two outliers removed was moderate ( g = 0.64), and the 95% confidence interval did not include zero [0.52, 0.76]. Results of the final metaregression model predicted larger treatment effects for interventions that included counting with 1-to-1 correspondence and were 8 weeks or shorter in duration. The results of the metaregression also showed that, on average, interventions were more effective for students with lower levels of risk for MD according to screening criteria compared to typically achieving students; interventions were less effective for students with higher levels of risk for MD according to screening criteria and risk according to low socioeconomic status compared to typically achieving students. Directions for future research and implications for educators implementing early numeracy interventions are discussed.
Article
Strong foundational skills in mathematical problem solving, acquired in early childhood, are critical not only for success in the science, technology, engineering, and mathematical (STEM) fields but also for quantitative reasoning in everyday life. The acquisition of mathematical skills relies on protracted interactive specialization of functional brain networks across development. Using a systems neuroscience approach, this review synthesizes emerging perspectives on neurodevelopmental pathways of mathematical learning, highlighting the functional brain architecture that supports these processes and sources of heterogeneity in mathematical skill acquisition. We identify the core neural building blocks of numerical cognition, anchored in the posterior parietal and ventral temporal-occipital cortices, and describe how memory and cognitive control systems, anchored in the medial temporal lobe and prefrontal cortex, help scaffold mathematical skill development. We highlight how interactive specialization of functional circuits influences mathematical learning across different stages of development. Functional and structural brain integrity and plasticity associated with math learning can be examined using an individual differences approach to better understand sources of heterogeneity in learning, including cognitive, affective, motivational, and sociocultural factors. Our review emphasizes the dynamic role of neurodevelopmental processes in mathematical learning and cognitive development more generally.
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Background Low levels of numeracy and literacy skills are associated with a range of negative outcomes later in life, such as reduced earnings and health. Obtaining information about effective interventions for children with or at risk of academic difficulties is therefore important. Objectives The main objective was to assess the effectiveness of interventions targeting students with or at risk of academic difficulties in kindergarten to Grade 6. Search Methods We searched electronic databases from 1980 to July 2018. We searched multiple international electronic databases (in total 15), seven national repositories, and performed a search of the grey literature using governmental sites, academic clearinghouses and repositories for reports and working papers, and trial registries (10 sources). We hand searched recent volumes of six journals and contacted international experts. Lastly, we used included studies and 23 previously published reviews for citation tracking. Selection Criteria Studies had to meet the following criteria to be included: • Population: The population eligible for the review included students attending regular schools in kindergarten to Grade 6, who were having academic difficulties, or were at risk of such difficulties. • Intervention: We included interventions that sought to improve academic skills, were conducted in schools during the regular school year, and were targeted (selected or indicated). • Comparison: Included studies used an intervention‐control group design or a comparison group design. We included randomised controlled trials (RCT); quasi‐randomised controlled trials (QRCT); and quasi‐experimental studies (QES). • Outcomes: Included studies used standardised tests in reading or mathematics. • Setting: Studies carried out in regular schools in an OECD country were included. Data Collection and Analysis Descriptive and numerical characteristics of included studies were coded by members of the review team. A review author independently checked coding. We used an extended version of the Cochrane Risk of Bias tool to assess risk of bias. We used random‐effects meta‐analysis and robust‐variance estimation procedures to synthesise effect sizes. We conducted separate meta‐analyses for tests performed within three months of the end of interventions (short‐term effects) and longer follow‐up periods. For short‐term effects, we performed subgroup and moderator analyses focused on instructional methods and content domains. We assessed sensitivity of the results to effect size measurement, outliers, clustered assignment of treatment, risk of bias, missing moderator information, control group progression, and publication bias. Results We found in total 24,414 potentially relevant records, screened 4247 of them in full text, and included 607 studies that met the inclusion criteria. We included 205 studies of a wide range of intervention types in at least one meta‐analysis (202 intervention‐control studies and 3 comparison designs). The reasons for excluding studies from the analysis were that they had too high risk of bias (257), compared two alternative interventions (104 studies), lacked necessary information (24 studies), or used overlapping samples (17 studies). The total number of student observations in the analysed studies was 226,745. There were 93% RCTs among the 327 interventions we included in the meta‐analysis of intervention‐control contrasts and 86% were from the United States. The target group consisted of, on average, 45% girls, 65% minority students, and 69% low‐income students. The mean Grade was 2.4. Most studies included in the meta‐analysis had a moderate to high risk of bias. The overall average effect sizes (ES) for short‐term and follow‐up outcomes were positive and statistically significant (ES = 0.30, 95% confidence interval [CI] = [0.25, 0.34] and ES = 0.27, 95% CI = [0.17, 0.36]), respectively). The effect sizes correspond to around one third to one half of the achievement gap between fourth Grade students with high and low socioeconomic status in the United States and to a 58% chance that a randomly selected score of an intervention group student is greater than the score of a randomly selected control group student. All measures indicated substantial heterogeneity across short‐term effect sizes. Follow‐up outcomes pertain almost exclusively to studies examining small‐group instruction by adults and effects on reading measures. The follow‐up effect sizes were considerably less heterogeneous than the short‐term effect sizes, although there was still statistically significant heterogeneity. Two instructional methods, peer‐assisted instruction and small‐group instruction by adults, had large and statistically significant average effect sizes that were robust across specifications in the subgroup analysis of short‐term effects (ES around 0.35–0.45). In meta‐regressions that adjusted for methods, content domains, and other study characteristics, they had significantly larger effect sizes than computer‐assisted instruction, coaching of personnel, incentives, and progress monitoring. Peer‐assisted instruction also had significantly larger effect sizes than medium‐group instruction. Besides peer‐assisted instruction and small‐group instruction, no other methods were consistently significant across the analyses that tried to isolate the association between a specific method and effect sizes. However, most analyses showed statistically significant heterogeneity also within categories of instructional methods. We found little evidence that effect sizes were larger in some content domains than others. Fractions had significantly higher associations with effect sizes than all other math domains, but there were only six studies of interventions targeting fractions. We found no evidence of adverse effects in the sense that no method or domain had robustly negative associations with effect sizes. The meta‐regressions revealed few other significant moderators. Interventions in higher Grades tend to have somewhat lower effect sizes, whereas there were no significant differences between QES and RCTs, general tests and tests of subdomains, and math tests and reading tests. Authors’ Conclusions Our results indicate that interventions targeting students with or at risk of academic difficulties from kindergarten to Grade 6 have on average positive and statistically significant short‐term and follow‐up effects on standardised tests in reading and mathematics. Peer‐assisted instruction and small‐group instruction are likely to be effective components of such interventions. We believe the relatively large effect sizes together with the substantial unexplained heterogeneity imply that schools can reduce the achievement gap between students with or at risk of academic difficulties and not‐at‐risk students by implementing targeted interventions, and that more research into the design of effective interventions is needed.
Article
Despite encouraging findings that show that interventions can improve students’ math understanding, achievement gaps in math often persist or even widen for students who struggle. Practitioners play a significant role in closing these achievement gaps because they have the responsibility to select or design interventions. Practitioners may wish to consider factors that influence intervention effectiveness. This study evaluated numeracy interventions and explored how features of the studies and interventions may have influenced reported effects. Exploratory analyses revealed smaller effects when only distal measures were considered (g = 0.35; SE = 0.05), or when studies reported including more than 30 percent of participants as English learners (g = 0.44; SE = 0.12). Results also indicated variable effects across the same intervention programs. Implications for practitioners related to selecting interventions are discussed.
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Word problems for English language learners (ELLs) at risk for math disabilities are challenging in terms of the constant need to develop precise math language and comprehension knowledge. As a result of this, ELLs may not only need math support but also reading and linguistic support. The purpose of this study was to assess the effectiveness of a word problem–solving strategy called Estratégica Dinámica de Matemáticas (EDM). This strategy was designed to provide math support in the native language based on students' math comprehension levels. A changing criterion multiple baseline design was used to instruct six second-grade Latino ELLs at risk for math disability. As compared with the baseline phase, EDM increased word problem solving for all participants. All students' level of performance were maintained and generalized during follow-up sessions. This study has implications for a native language intervention that focuses on strategy training to facilitate word problem–solving performance.
Article
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This study identified student behaviors that best predicted mathematics learning in peer-directed small groups among students who needed help. Two behaviors were hypothesized to predict achievement: receiving explanations instead of only the right answer and subsequently carrying out constructive activity (solving or explaining how to solve problems using concepts stated or implied in the explanations received). Six classes of 7th graders participated in 2 sequential instructional units. Students in 4 classes worked in heterogeneous small groups throughout a 3-wk unit on operations with decimal numbers (Unit 1); students in all 6 classes worked in groups throughout a 4-wk unit on operations with fractions (Unit 2). Analyses of the transcripts of tape recordings of students' verbal interaction confirmed the hypotheses. Level of constructive activity was the strongest predictor of achievement. The level of help that students received predicted level of constructive activity but did not predict achievement directly. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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The purpose of the present study was to examine the effectiveness and feasibility of phonological awareness training, with and without a beginning decoding component. 33 teachers in 8 urban schools were assigned randomly within their schools to 3 groups: control, phonological awareness training, and phonological awareness training with beginning decoding instruction and practice. Following training, teachers in the 2 treatment groups conducted the treatments for about 20 wks. In each teacher's class, pre- and posttreatment data were collected on 12–14 children ( N = 404); 312 children were tested again the following fall. At the end of kindergarten, the 2 treatment groups performed comparably and outperformed controls on the phonological awareness measures. On alphabetic (reading and spelling) tasks, however, the group participating in phonological awareness training with beginning decoding instruction did better than the other 2 groups. In the fall of the next year, many of these between-group differences remained but were less impressive. Implications are discussed for bridging research and practice. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
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The child's attempts to overcome sociocognitive conflict, under certain specific cognitive and social conditions, can lead to a restructuring of the child's thinking on a supraordinate level.
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The past fifteen years have shown a resurgence of interest in small-group, peer-directed learning in the classroom. This article reviews and analyzes the research linking task-related verbal interaction to learning in small groups in mathematics classrooms, as well as factors that have been shown to predict peer interaction in mathematics groups, and discusses strategies for shaping group interaction. Critical features of group interaction include the level of elaboration of help given and received and the responsiveness of help to the needs of students. Important predictors of group interaction included student ability, gender and personality, and group composition on ability and gender. Possible strategies for promoting effective small-group interaction include using certain group compositions, altering the reward structure, providing training in desirable verbal behavior, and structuring the group activity to require students to give explanations to each other.
Article
77 7th and 8th graders in mathematics classrooms learned a 2-wk unit on exponents and scientific notation in mixed- or uniform-ability groups. Group interaction was tape recorded. Three categories of interaction were related to achievement (ACH): Receiving no explanation for a question or error (receiving no response or receiving only the correct answer) was negatively related to ACH; giving and receiving explanations were positively related to ACH; and ACH and interaction in the group were related to group composition, sex, ability, and personality. Medium-ability Ss in uniform-ability groups showed higher ACH and received more explanations than medium-ability Ss in mixed-ability groups. Males showed higher ACH than females. There was a curvilinear relationship between ability and ACH in mixed groups: Highs performed best, and mediums and lows showed similar ACH. High-ability Ss gave more explanations than low-ability Ss. Introverts outperformed extroverts, but extroverts received more explanations. (45 ref) (PsycINFO Database Record (c) 2006 APA, all rights reserved).
Article
Students (N = 101) in 3 classrooms in grades 3-5 were taught math concepts in cooperative learning groups of 5-6 students for a 3-week unit. The 3 teachers involved received 9 2-hour training sessions on using cooperative learning during the 5 months prior to the study. Pre- and posttests of achievement were administered. Helping behaviors were taught to students for 3 weeks before the math unit and continued to be reinforced during the ensuing 3 weeks. Each student team was videotaped for 30 minutes over the 3-week period while it was engaged in math teamwork. The helping behaviors of each student were coded into 8 categories. Results showed that ''giving explanations,'' ''receiving explanations,'' as well as ''giving and receiving other help'' positively correlated with achievement gains. There was a negative correlation between ''receiving no help after requesting it'' and achievement. These results held for both boys and girls in all 3 grades. High achievers gave more explanations and other help than middle or low achievers. Low achievers asked for and received explanations and other help more often.
Article
The purpose of this study was to examine high-achieving students' interactions and performances on complex mathematics tasks as a function of homogeneous versus heterogeneous pairings. Participants were third and fourth graders who had been trained in, and had routinely practiced, constructive peer-tutoring interactions and had experience working individually on performance assessments. We videotaped 10 high achievers working with a high-achieving and with a low-achieving classmate on performance assessments. Results indicated that homogeneous dyads operated more collaboratively, generated greater cognitive conflict and resolution, and produced better quality work. Implications are discussed in terms of optimizing grouping arrangements during collaborative learning activities and preparing students to work productively together on complex tasks.
Article
The purpose of this classroom-based experiment was to explore methods for helping students generate conceptual mathematical explanations during peer-mediated learning activities. Participants were 40 general education classrooms in grades 2, 3, and 4, which were assigned randomly to 3 treatments: peer-mediated instruction (PMI) with training in how to offer and receive elaborated help (PMI-Elaborated); PMI with training in elaborated help and in methods for providing conceptual mathematical explanations (PMI-Elaborated+Conceptual); and contrast (i.e., no PMI). Teachers implemented PMI treatments for 18 weeks with their naturally constituted mathematics classes. From each of the 40 classes, we pre- and posttested the mathematics achievement of 4 students who represented 4 points on the achievement continuum. We also coded student interactions from tutoring generalization sessions videotaped 10 weeks after all training had been completed. Analyses revealed that PMI-Elaborated+Conceptual tutors asked more participatory, procedural questions and provided more conceptual explanations. Moreover, the achievement of PMI-Elaborated+Conceptual students was higher than that of PMI-Elaborated students, which in turn surpassed that of the contrast group. Findings are discussed in terms of teachers' use of collaborative learning methods.
Article
The purpose of this study was to examine the effects of a dyadic peer-mediated treatment on kindergarten children's mathematics development. Within schools, 20 classrooms were assigned randomly to experimental or control groups. Experimental teachers implemented the peer-mediated treatment twice weekly for 15 weeks. We measured the fidelity of treatment implementation, and teachers completed questionnaires about treatment effectiveness and feasibility. Within classrooms, we pre- and post-tested 168 students (84 per condition) who had been classified into achievement groups based on pretest scores; effects were separated for students identified for or referred to special education and for nondisabled low-, middle-, and high-achieving classmates. Results indicated that treatment implementation was strong for most, but not all, teachers; teachers judged the treatment to be effective and feasible for implementation on their own; and students with and without disabilities, at all points along the achievement continuum, benefited from the treatment. Implications for research and practice are discussed.
Article
This article examines the inclusive schools movement and compares it to that of the REI. After contrasting the movements’ respective advocates, goals, tactics, and understanding of and links to general education, we argue that the field's rhetoric has become increasingly strident and its perspective increasingly insular and disassociated from general education's concerns. We offer a pessimistic prediction about the current movement's success in forging a productive alliance with general education.
The goal of many recent intervention studies has been to examine the conditions that must be in place for all children to acquire adequate reading skills. Although the ultimate goal of reading instruction is to help children acquire the skills necessary to comprehend text, an important subgoal for early reading instruction is to teach children to identify words accurately on the printed page. Five recent studies of methods to prevent reading difficulties were examined in light of the goal that every child should acquire adequate word reading skills during early elementary school. It was estimated that our best current methods, if applied broadly, would leave anywhere from 2% to 6% of children with inadequate word reading skills in the first and second grades. Several broad characteristics of these "treatment resisters" are identified, and the implications of these findings for future research are discussed.
Article
Examined the arithmetic computation performance of samples of 229 normally achieving students (SNAs) and 101 students with learning disabilities (SLDs) in the age range of 9–14. A multicomponent battery consisting of separate tests for each of the 4 operations on whole numbers was administered by classroom teachers over a period of 4 days. Not only do the SLDs generally perform at lower levels than the SNAs, their progress from one age to another is extremely limited. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
the question of the effectiveness of early intervention or compensatory education for infants and children from socially disadvantaged families has been investigated in many ways by many social scientists over the past 25 years this chapter will summarize what is known about the efficacy of early education by carefully analyzing several exemplary intervention studies frequently developed for preschool-aged children and/or their families, early education programs have attempted to modify the course of early development to better prepare socially disadvantaged, at-risk children for public school we will summarize the programmatic features and intellectual results (outcome in terms of IQ) from exemplary educational experiments, and then discuss what we have learned and the implications of those results (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
Examined the effects of classwide peer-assisted learning strategies (PALS) in mathematics incorporating the use of curriculum-based measurement on the acquisition and transfer learning of low- and average-achieving 2nd–4th graders, and those with an identified learning disability. Ss were randomly assigned to treatments with and without PALS on a mathematics operations curriculum, and pretested and posttested for mathematics operations and concepts/applications. ANOVA indicated superior mathematics growth for Ss in the PALS condition. Patterns in the data, however, suggested the need for additional research on low-achieving and learning disabled Ss' transfer from the operations tutoring content to the broader mathematics curriculum and on the effects of PALS on conceptual and applications portions of the mathematics curriculum. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
Tested 3rd graders on 4 conservation-of-area tasks. Ss were then classified as conservers, nonconservers, or transitional conservers. 14 pairs of Ss were selected, each containing a conserver and a nonconserver. These Ss were told of the difference in their thinking on 2 of the pretest tasks, and asked to settle on 1 answer between them for each of the tasks. Posttesting on all 4 tasks used in the pretest was conducted 1 mo. later. 10 conservers and 13 nonconservers were given no peer interaction experience but were posttested. It was predicted that conservers would prevail over nonconservers during the interaction. This prediction was confirmed. All nonconservers who yielded to conservers continued to conserve on the posttests. Only 1 control S deviated from his pretest position on the posttest. Several explanations of the findings are discussed. (19 ref.) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
89 1st graders and 25 2nd graders were given information about conservation tasks that conflicted with their prior nonconservation judgments. Ss in a social interaction situation had higher conservation posttest scores than Ss who were given conflicting information in role-playing, imitation, and control conditions. The spontaneous generation of conservation assertions that occurred in the social interaction condition was related to significantly higher posttest scores. Results suggest that even incorrect information that conflicts with a prior but equally erroneous belief can stimulate cognitive growth. (10 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
We conducted a longitudinal investigation of differences in classroom ecological arrangements and student behaviors (processes) on low-SES and high-SES elementary students' growth in academic achievement (products). An experimental, low-SES group received Classwide Peer Tutoring implemented by their teachers during each grade from first through fourth, while a low-SES control group and a high-SES comparison group received teacher-designed instruction. Results indicated that the experimental group and the comparison group, with distinctly different ecological arrangements and significantly higher levels of academic engagement, produced significantly greater product gains than did the control group. The implications of these findings are discussed. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
This paper examines the effects of quantitative literacy on the likelihood of employment among young adults in the United States. The data set used is the 1985 Young Adult Literacy Assessment Survey. This survey of persons 21 to 25 years old makes available scores achieved by individuals sampled on a test measuring proficiency in the application of arithmetic skills to practical problems encountered every day. We use these scores as one of a set of variables in a probit model explaining the probability of a person being fully employed. It is found that quantitative literacy skills are a major factor raising the likelihood of full-time employment. Furthermore, low quantitative literacy appears to be critical in explaining the lower probability of employment of young Black Americans relative to Whites.
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Typescript. Thesis (M.S.)--University of Wisconsin--Madison, 1980. Includes bibliographical references (leaves 142-145).
Article
This longitudinal study investigated the effects of time spent in academic instruction and time engaged on elementary students' academic achievement gains. Three groups were compared over grades as follows: (a) an at-risk experimental group of low-socioeconomic status (SES) students for whom teachers implemented classwide peer tutoring (CWPT) beginning with the second semester of first grade continuing through Grade 3; (b) an equivalent at-risk control group; and (c) a non-risk comparison group of students of average- to high-SES. In both the control and comparison groups, teachers employed conventional instructional practices over Grades 1 through 3. Results indicated significant group differences in the time spent in academic instruction, engagement, and gains on the subtests of the Metropolitan Achievement Test that favored the experimental and comparison groups over the control group. Implications include the effectiveness of CWPT for at-risk students and the continuing vulnerability of at-risk students whose daily instructional programs provide less instructional time and foster lower levels of active academic engagement.
Article
This study examines the mathematical performance of 220 children from 8 years through 17 years of age diagnosed as having learning disabilities. Student records were searched for data indicating performance on standardized test instruments relating to mathematics. Data for the Woodcock-Johnson Psycho-Educational Achievement Battery math subtests and for the IQ scores from the Wechsler Intelligence Scale for Children-Revised were obtained. Comparisons were made among children at different ages and among specific age clusters. Primary attention was directed toward calculations and applications of math concepts and principles. Developmental patterns across the ages studied were discovered. Implications for long-term comprehensive programming are presented.
Peer interaction and learning: Can two wrongs make a right?
  • M Glachan
  • P Light
Wrapping up: Using peer commentaries to enhance models of mathematics teaching and learning
  • S Griffin
  • R Case
International achievement differences: An assessment of a new perspective
  • L C Stedman
Acquisition and transfer effects of classwide peer-assisted learning strategies in mathematics for students with varying learning histories
  • L S Fuchs
  • D Fuchs
  • N B Phillips
  • C L Hamlett
  • K Karns
An examination of explicit and constructivist reading practices. Paper presented at the University of Minnesota's second conference on reading comprehension in honor of Guy Bond
  • J Dole
Stanford 7 Plus (Primary 1)
  • E F Gardner
  • H C Rudman
  • B Karlsen
  • J C Merwin
The effects of knowledge and task on students' peer-directed questions in modified cooperative learning groups
  • L M Paradis
  • S Peverly