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This study's purpose was to examine the effects of the concrete-representational-abstract integrated (CRA-I) sequence on the performance of students who struggled with rational number concepts. Three students in southeastern U.S. fifth grade class participated in the study. The CRA-I intervention was grounded in the principles of explicit instruction and showed rational number concepts related to fractions and decimals using fraction blocks, number lines, base 10 blocks, and coins. Students learned about unit fractions, fraction magnitude, fraction equivalence, addition of fractions with unlike denominators, equivalent decimals, and notation of fractions as decimals. The researchers used a multiple probe across behaviors design and demonstrated a functional relation between CRA-I and three behaviors: decreased fraction estimation error, accuracy in adding fractions with unlike denominators, and accuracy writing fractions as decimals. [ABSTRACT FROM AUTHOR]

Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated instructional sequence featuring concrete, representational, and abstract stages of learning. In contrast, research on representational sequences featuring virtual manipulatives is less robust. Thus, this study evaluated an instructional strategy with virtual manipulatives, static representational drawings, and abstract algorithms to teach multiplication to three U.S. elementary students with mathematics difficulty. A functional relation was established via a single-subject multiple probe design between the treatment and students' accuracy performance. Baseline-corrected Tau estimates confirmed a medium effect size for all three students, while student performance on measures assessing the number of errors committed and the duration of sessions also returned favorable findings. [ABSTRACT FROM AUTHOR]

Presently, in Malta, syllabi are being replaced by learning outcomes. For ages 3–7, the outcomes are framed holistically (e.g. identity, communication, etc.), and it is recommended that children learn mathematics informally through play and projects. For ages 8–11, learning outcomes are subject-based, and new mathematics textbooks are being phased in. I discuss the importance of a smooth transition between informal and structured approaches to learning mathematics. I draw on Anna Sfard's 4-element definition of discourse, linking the theory with my research classroom data. I argue that a discourse perspective can provide a basis for ensuring continuity across Grade levels. [ABSTRACT FROM AUTHOR]

Educators are required to use evidence-based practices to support student development of academic skills. Results from single-case experimental designs are well suited for this purpose and may be more flexible for applied use than group-based designs. However, educators also require information about which interventions work for whom and under what conditions. Although previous reviews of single-case experimental designs exist, most focused on design characteristics related to internal validity. The purpose of this U.S. study was to determine the participant characteristics within multiple-baseline and multiple-probe across participant designs targeting academic skills. Representation of various demographic subgroups differ between studies targeting different academic skill areas (mathematics, reading, and writing). However, reporting was often inconsistent, with a substantial proportion of records omitting information about participants' race/ethnicity, economic status, and English learner status. This finding was divergent from best practice recommendations. Implications for future research are discussed within the context of the study's limitations. [ABSTRACT FROM AUTHOR]

The present study empirically investigates how school-based bullying victimization affects students' learning outcomes, taking into consideration international and gender perspectives. The main objective of the present research is to provide a better understanding of the consequences of bullying victimization in the learning process of adolescents. We estimate a statistical function that empirically establishes the relationship between the students' outcomes in mathematics, reading, and science (output) and a wide set of explanatory variables (educational factors), one of which is that of being bullied. The present study uses a large sample of 612,004 students between 15 and 16 years old, attending 21,903 schools in 79 countries. The data come from the 2018 round of the Programme for International Student Assessment. The results indicate that bullying victimization is associated with decreases in academic achievement in mathematics, reading, and science. In addition, no relevant differences by gender are observed in reading and science but, other factors being equal, bullied males score less than bullied females in mathematics. [ABSTRACT FROM AUTHOR]

This article introduces and describes the studies that are part of the thematic special series aimed at exploring research questions for improving learning outcomes for students with learning disabilities (SLD) in science and mathematics. Special educators have the requisite knowledge and skills to meaningfully include these students in studies that focus on important disciplinary understandings; yet, to date, relatively few special educators develop and validate interventions for students with high incidence disabilities to learn about science or mathematical practices. Given the fact that most SLD receive instruction in the general education classroom, where there are reforms that call for increased rigor in instruction and meaningful problem-solving for all students, it is imperative that SLD receive effective supports for deep content learning. We hope the current articles spark readers' interests in adding to this emerging body of research and invite others to build on the ideas shared in the special series. [ABSTRACT FROM AUTHOR]

The current study investigated the effectiveness of an intensive writing intervention focusing on mathematical reasoning through written expression. A group pretest–intervention–posttest comparison experimental design was used to implement a 12-lesson intervention, delivered through a combination of Google Classroom and in-person classroom teacher support, to fifth-grade students with specific learning disabilities (n = 19). Although underpowered, our results indicated the intensive writing intervention led to all students in the intervention group (n = 11) significantly outperforming the students in the control group (n = 8) on subtraction and division word problems requiring an explanation of their solution in written form. Additionally, student treatment interviews revealed the strategy was both enjoyable and helpful in solving and explaining their word problem solutions and the teacher provided insight into potential additional scaffolds to support the most intensive students. Lessons learned and implications for research and practice are presented. [ABSTRACT FROM AUTHOR]

The purpose of this study was to examine the effects of a number line intervention with supported self-explanation on student understanding of fraction magnitude and quality of explanation. Participants were three U.S. middle school students with significant behavior problems. Participants were given eight lessons containing explicit instruction for fraction number line placement and self-explanation. A multiple-probe design was used to evaluate the effects of the intervention. Visual analysis and Tau- U showed the intervention was very effective for improving student placement of fractions on the number line and increasing the quality of student explanations for their answers. Discussion of results and implications for future research and practitioners are included. [ABSTRACT FROM AUTHOR]

Preschool students' mastery of early numeracy skills is important, so they enter kindergarten with the necessary prerequisite skills, which are predictive of achievement in later elementary grades. The purpose of this study was to examine the effects of a concrete-representational-abstract (CRA) instructional package on the foundational early numeracy skills of three preschool students. A multiple baseline across participants design was employed. Treatment sessions were 15 to 20 minutes long and held twice a week. The primary outcome variable was a measure of match quantity, and the generalization outcome variable was a measure of number sequencing. Results indicate that CRA was effective for increasing the match quantity fluency skills of two of three participants; however, the effects did not generalize to number sequencing. [ABSTRACT FROM AUTHOR]

The purpose of this study was to investigate the effects of the concrete-representational-abstract–integrated (CRA-I) sequence on students with learning disabilities' performance when learning fraction and decimal concepts. Three elementary-level students in Grades 4 and 6 participated in a single-case multiple probe across behaviors study. The intervention involved explicit use of fraction blocks, coins, base ten blocks, number lines, pictures, and abstract symbols to teach unit fractions, fraction and decimal equivalence, addition of fractions with unlike denominators, and writing fractions as decimals. The researchers demonstrated a functional relation between CRA-I and three different behaviors related to fraction concepts: decreased error in estimating fraction magnitude, addition of unlike fractions, and writing fractions as decimals. The findings show promise in the use of CRA-I for teaching fraction concepts to students with learning disabilities. [ABSTRACT FROM AUTHOR]

Students with autism spectrum disorder frequently face challenges when learning mathematical concepts. For example, they may have difficulties solving mathematical word problems, in particular Cartesian product problems. This research is a case study with a multiple probe design in which the participants were three Spanish students diagnosed with autism spectrum disorder. A conceptual model-based problem-solving approach adapted to the characteristics of the participants was used to teach them how to solve Cartesian product word problems introduced sequentially in the instruction (first multiplication, then division, and finally both operations). The results show a functional relationship between the intervention and the students' performance. The three participants generalized their learning to two-operation Cartesian product problems (an addition and a multiplication). Moreover, two of them retained what they learned 6 weeks after completing the instruction. The implications for teaching this and other mathematical content to students with autism are discussed. [ABSTRACT FROM AUTHOR]

Research suggests the need to assess both positive and negative forms of student engagement. The purpose of this study was to pilot disaffection items with the Student Engagement Instrument (SEI) with a sample of middle school students from a rural area in the Southeastern U.S. This study explored the factor structure of the piloted items alongside the SEI, measurement invariance, and associations between student engagement and disaffection with educational outcomes such as mathematics and reading test scores, discipline referrals, and absences. Results hold implications for our theoretical understanding of engagement, suggesting that engagement and disaffection dimensions are theoretically and psychometrically distinct. [ABSTRACT FROM AUTHOR]

This study explored whether initial skill moderated outcomes of Promoting Algebra Readiness, a Tier 2 sixth-grade mathematics intervention targeting conceptual and procedural knowledge of fractions. The study analyzed data from a quasi-experimental pilot study in which at-risk students (N = 198) from Oregon middle schools were assigned to the treatment or control condition at the school level. Proximal and distal measures of math proficiency were collected in the fall (pretest) and spring (post-test). Analyses examined initial student achievement as a moderator of mathematics outcomes. Results indicated that intervention outcomes were not moderated by initial skill. Implications for tiered mathematics instruction and future mathematics intervention research are discussed. [ABSTRACT FROM AUTHOR]

Executive function (EF) training has shown promise for remedying general EF deficiencies faced by students with mathematics difficulty (MD) and for improving their performance. However, latest research also suggests that the instant and sustained effects of EF training remain inconsistent. In this study, 32 Chinese students with MD, age 7 to 10 years, were recruited and randomly divided into two groups: the training group (n = 16, 25 training sessions) and the control group (n = 16). Both groups took a pretest, a posttest, and a follow-up test (after 6 months) on EF, fluid intelligence, and mathematics skills. In the posttest, the training group's performance significantly improved in 2-back, number shifting, letter shifting, calculation fluency, and mathematics problem-solving tasks, but not in Stroop, Flanker, 1-back, numerical operations, and colored progressive matrices tasks. In the follow-up test after 6 months, the effects of training only on the 2-back and letter shifting tasks were sustained. The effect on the numerical operations task appeared; however, the effects on number shifting, calculation fluency, and mathematics problem-solving tasks disappeared. The results of this study show that EF training has instant effects of improving EF and mathematics skills of students with MD, and 6-month sustained effects on some of the improved skills. However, for fluid intelligence, the effects may be very limited. [ABSTRACT FROM AUTHOR]

The effects of whole number computation interventions among school students with learning disabilities in Grades K to 5 were examined using a multilevel meta-analysis. Applying a correlated and hierarchical effect model of robust variance estimation, we examined the intervention effects among 15 peer-reviewed articles and dissertations (two group-design and 13 single-case design studies) published between 1989 and 2021. Whole number computation interventions demonstrated a statistically significant and large effect on whole number computation outcomes ( g ¯ = 3.74). The type of mathematical operations, type of whole number computation measures, and the number of instructional components did not significantly affect the magnitude of the effect size estimate. However, the results showed slightly larger average effect sizes for the addition problem, the accuracy measure, and the additional number of instructional components by one. The limitations and implications for the practice of the meta-analysis are discussed, and future research directions are proposed. [ABSTRACT FROM AUTHOR]

In this paper, we present a detailed action plan under continuous quality improvement (CQI) exercise of outcomes based education framework related to Mathematics concerns highlighted by the Electrical Engineering (EE) Department. Failing and low performed student learning outcomes (SOs) and course learning outcomes (COs) in range of core EE courses were observed to be linked with weak Mathematics basis of students. This feedback was achieved through an automated CQI system in EvalTools under Faculty Class Assessment Report (FCAR) tab, where each instructor is required to make reflections about failing as well as low performed SOs and COs. Feedback was reviewed comprehensively, and mathematical concepts which significantly affect the performance of students in the core EE courses were derived. Moreover, a high level of Mathematics pre-requisite covering required mathematical concepts is identified for the range of core EE courses. Consequently, well-defined tasks were assigned to continuously evaluate and monitor improvement in required Mathematics concepts to ensure SOs and COs achieved in core EE courses. Results are given to exhibit the effectiveness of continuous improvement management system (CIMS). [ABSTRACT FROM AUTHOR]

Understanding rational numbers is critical for secondary mathematics achievement. However, students with mathematics difficulties (MD) struggle with rational number topics, including fractions, decimals, and percentages. The purpose of this systematic review was to describe the instructional foci of rational number interventions, determine the overall effect size, and explore potential moderators. Forty-three studies were included and 150 effect sizes were meta-analyzed using robust variance estimation. The majority of studies focused on teaching fraction magnitude and arithmetic. An overall effect size of g = 1.02 [0.80, 1.25] was found for rational number interventions favoring treatment conditions over business as usual control. Proximal measures contributed to higher effect sizes than distal measures. Limitations included a high number of fraction interventions contributing to the overall effect size and a large amount of heterogeneity among study effect sizes. [ABSTRACT FROM AUTHOR]

One of the most persistent areas of difficulty in mathematics for children with learning disabilities (LDs) and difficulties is fractions. We report the development and initial testing of an intervention designed to increase access to and advancement in conceptual understanding. Our asset-based theory of change—a tested and confirmed learning trajectory of fraction concepts of students with LDs grounded in student-centered instruction—served as the basis for our multistage scientific design process. We report on foundational (i.e., a theory of change, establishment and refinement of learning trajectories, and core instructional components) and evaluative (pilot data on student outcomes) components of the intervention. The results of the study reveal positive effects of the program's fidelity and potential to improve student outcomes in school settings. The positive outcomes support continued exploration and expansion of a new framework for supplemental intervention grounded in trajectories of student learning. [ABSTRACT FROM AUTHOR]

Math achievement in U.S. high schools is a consistent predictor of educational attainment. While emphasis on raising math achievement continues, school-level interventions often come at the expense of other subjects. Arts courses are particularly at risk of being cut, especially in schools serving lower socioeconomic status youth. Evidence suggests, however, that arts coursework is beneficial to many educational outcomes. We use data on 20,590 adolescents from the High School Longitudinal Study of 2009 to answer two research questions: (1) Does student accumulation of fine arts courses across different topic areas relate positively to math test scores in high school? (2) Does school SES differentiate this potential association? Results indicate that youth attending higher-SES schools take more art courses and taking music courses is related to higher math test scores. However, this benefit only seems to only apply to more socially advantaged student bodies. Results reveal a site of additional educational advantage for already privileged youth. [ABSTRACT FROM AUTHOR]

In intervention studies, high rates of implementation fidelity are important markers of a study's success; however, the definition of implementation fidelity is both complex and dynamic. In this synthesis, we examined the dimensions of implementation fidelity measured and reported in 99 studies in which researchers utilized a mathematics intervention for elementary students (i.e., Grades 1–5). We examined implementation fidelity following recommendations made by Dane and Schneider (1998), O'Donnell (2008), and DeFouw et al. (2009) to capture a comprehensive representation of the implementation fidelity data collected and reported within mathematics intervention studies. We organized our conceptualization of implementation fidelity into four overarching categories and nine dimensions within those categories: intervention design (i.e., theories of change and logistics), fidelity of implementor (i.e., adherence, quality of delivery, dosage, and implementor knowledge or experience), student engagement, and treatment analysis (i.e., treatment differentiation and analysis of implementation fidelity). Overall, findings indicate many author teams reported adherence data and dosage data, but significantly fewer studies reported quality of delivery data, student engagement data, or treatment differentiation data. In addition, author teams were more likely to report at least one form of logistics, such as implementor support, than theories of change. Implications for research and practice are discussed. [ABSTRACT FROM AUTHOR]

Fraction competence is essential for learning algebra and pursuing careers in science, technology, engineering, and mathematics. However, many children have difficulty using fractions, especially those struggling with mathematics. In this study, we examined the effect of a Tier 2 multicomponent fraction intervention for fifth graders, using a multiple-probe design across groups. The intervention included multiple instructional components: (a) explicit instruction; (b) multiple representations; (c) addressing misconceptions; (d) flexibility, reversibility, and generalizations; and (e) self-graphing. The intervention addressed fraction concepts and skills that need to be taught at Grade Levels 3 to 5 based on the Common Core State Standards for Mathematics content standards. The researcher provided the intervention in an intervention classroom at a U.S. charter school three times a week. The total session length ranged from 885 to 906 min across the groups. The results of this study indicated a functional relation between the fraction intervention, and all six students' percentages of correct answers obtained using fraction probes. The results from the fidelity of intervention and assessment and social validity during the intervention were also reported. Limitations and suggestions for future research and implications for practices are discussed. [ABSTRACT FROM AUTHOR]

Students with exceptionalities who do not make adequate progress with core instruction in mathematics require more intensive research-based interventions such as explicit instruction or video modeling to address instructional needs. This study examined the effects of combining point-of-view video modeling, explicit instruction, and augmented reality to teach mathematics to students with disabilities. The researchers employed a multiple baseline across skills, single-subject research design to evaluate the effects of the intervention on student performance across four mathematics skills. Two eighth grade students identified as having a disability impacting mathematics, one with autism spectrum disorder and one with a specific learning disability, participated in the study. Visual analysis determined a functional relationship between the dependent and independent variables. Tau-U result for the intervention phase was 1.0 across all four skills for each participant. Participants demonstrated high levels of maintenance, and with one exception, students were able to apply the skills to word problems without additional training. Limitations and implications for future research and practice are discussed. [ABSTRACT FROM AUTHOR]

This pilot study examined the promise of a Tier 2 Grade 6 intervention program for students at risk for difficulties in mathematics. The study utilized a quasi-experimental design. The final sample included 112 students in treatment (Promoting Algebra Readiness) and 86 students in control (standard district practice) conditions. The Promoting Algebra Readiness program consisted of 93 lessons across four strands focused on key concepts and applications of fractions. Measures of mathematics achievement were collected at pretest and posttest. Feasibility and usability data indicated favorable impressions by users and strong levels of implementation fidelity. Gain scores of treatment students were significantly greater than those of control peers on two of four proximal measures of mathematics achievement. Positive nonsignificant effects were found on additional proximal and distal measures. Implications for educators delivering instruction for at-risk students in multitier service delivery models are discussed. [ABSTRACT FROM AUTHOR]

Background: Current efforts to promote reasoning, problem solving, and discussion are often framed as advancing equity, but scholarship suggests individual students' opportunities to learn can vary considerably in classrooms that attempt to take up these approaches to teaching mathematics. Noticing students' mathematical strengths and positioning their contributions as competent is among aspects of instruction associated with more equitable learning outcomes for students from marginalized groups, but research has yet to comprehensively examine the range and nuance of this aspect of teachers' practice in classrooms that feature broad distributions of participation. Purpose: The purpose of this study was to examine teachers' instructional practice with respect to assigning competence in two mathematics classrooms that demonstrated high levels of student participation. We investigated the kinds of situations in which teachers positioned students as competent, and the ways assigning competence opened opportunities to participate. Setting: Data were collected at a public elementary school in a culturally, linguistically, and economically diverse neighborhood in southern California. Participants: Participants included two teachers and 45 students from two third-grade classrooms. Teachers had participated in ongoing professional development focused on leveraging children's mathematical thinking in instruction. Research Design: We drew from qualitative methods for analyzing video to investigate classroom interactions from 12 mathematics lessons. Data sources included video recordings, transcripts, and student work. We used Studiocode software to parse each lesson into phases and episodes. Drawing from previous studies, we identified a subset of episodes in which teachers explicitly positioned a student's contribution as competent. An iterative process of coding and discussion was used to analyze patterns with respect to student participation, teacher support, and the unfolding of rights and obligations related to participating in mathematical activity. Findings: Analyses revealed different kinds of situations in which students participated in mathematically substantive ways (in terms of providing detailed explanations of their ideas or engaging with the details of a peer's idea) and teachers positioned their contributions as competent. These situations included highlighting, clarifying, and amplifying contributions; supporting the specificity of student contributions; recognizing emergent ideas; and validating unprompted attention to mathematical details. Assignments of competence emerged in ways that were integrated into teachers' ongoing efforts to surface and make explicit the details of their mathematical ideas, while also broadening the kinds of contributions students could make to joint mathematical work. Conclusions: Helping students to know what it could look and sound like to participate in the moment while recognizing a wide range of contributions as competent created openings for students who in many classrooms might be excluded or relegated to the periphery of conversations. Making competence explicit was a contingent, relational practice that required teachers to find specific ways of leveraging student strengths to support their participation. Recommendations for advancing mathematics teaching must attend to the nuances with which particular practices unfold to open or constrain individual students' opportunities to learn. [ABSTRACT FROM AUTHOR]

Native Americans are severely underrepresented in science, technology, engineering, and math (STEM). In this study, we examined the construal, salience, and relevance of the barriers that Native American college students believe could impact their STEM career preparation. An exploratory factor analysis of the Perceptions of Educational Barriers Scale conducted with 152 Native American college students yielded 8 perceived barrier factors: school expensive, lack of access, lack of preparation, not smart enough, not good at math/science, family responsibilities, discrimination, and lack of support. School expense was by far their greatest barrier, and for men, this barrier negatively predicted their STEM career self-efficacy, with self-efficacy positively predicting their STEM career outcome expectations. For women, lack of support positively predicted their STEM career self-efficacy, with self-efficacy positively predicting and discrimination negatively predicting their STEM career outcome expectations. Results are interpreted in light of social cognitive career theory. [ABSTRACT FROM AUTHOR]

This meta-analysis examined the ecological and population validity of intervention research for students with low mathematics achievement (SWLMA). Forty-four studies published between 2005 and 2019 that met the inclusionary criterion were included in this analysis. Our findings suggest, to improve the external validity and generalizability of research, more detailed descriptions of participants and the socio-cultural contexts of the intervention studies are warranted. [ABSTRACT FROM AUTHOR]

In this meta-analysis of single-case designs, the researchers investigated the effects of word-problem instruction for students with learning disabilities in Grades 1 through 12, as reported in 20 peer-reviewed articles published between 1975 and 2020. A two-level multilevel model with a robust variance estimation method was implemented to calculate the effect sizes. A significant overall effect of word-problem instruction for students with learning disabilities was found, and the results indicate that studies meeting all three quality indicators of implementation fidelity (i.e., adherence, dosage, and regularity) showed greater effects. The average weighted effect sizes of word-problem instruction varied depending on the content and practice standards of the Common Core State Standards for Mathematics. Limitations and future research directions are also discussed. [ABSTRACT FROM AUTHOR]

This meta-analysis assessed the effect of word-problem-solving interventions on the word-problem-solving accuracy of students identified as having a learning disability (LD) or at risk for an LD in kindergarten to the sixth grade. Eighteen randomized control group designed studies met the inclusion criteria. Overall, word-problem-solving interventions yielded a significant positive effect on the word-problem-solving accuracy of students in elementary grades with LD (effect size [ES] = 1.08). Instructional components that underlie effective studies were also identified. Results suggest that peer interaction and transfer instructions yielded large effects on treatment outcomes. Results also suggested that intensive interventions (50-min sessions, 34 total sessions) in Grade 3 regardless of instructional setting yielded the largest ESs. These findings support the need to develop and implement quality evidence-based instruction in classroom settings (Tier 1 instruction) prior to utilizing additional resources for more intensive and individualized intervention. [ABSTRACT FROM AUTHOR]

Learning to compute with fractions is a major challenge for many students and especially for students with disabilities (SWD). Phase 1 of this study employed a randomized pretest–posttest comparison design to test the effects of two versions of formative assessment combined with an instructional program called Fractions at Work. In one condition, teachers used technology-assisted prompts to assess student performance and remediate errors. In the comparison condition, teachers gave students the same items for assessing progress but used their own methods of reteaching. Results indicated no difference between the two methods. However, pretest-to-posttest gain scores were significantly higher on all three measures regardless of type of formative assessment, and students maintained much of what they had learned. Phase 2 examined issues related to instructional dosage. Students who received additional weeks of instruction scored significantly higher than students who went back to their business-as-usual curriculum. [ABSTRACT FROM AUTHOR]