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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]

The concept of identity has been used to interrogate a wide range of topics about children's learning in the content areas, including learning in literacy, math, and science. Despite this, there is a paucity of attention to how the construct of identities is conceptualized across content areas. This systematic integrative review aims to develop an empirically grounded view of how identities are conceptualized in childhood across content areas and to consider the feasibility of a shared conception of content area identities. To do this, the review examines 66 articles on content area identities in early childhood and childhood (birth through Grade 5). Findings show diverse theories are used to examine content area identities in children and at the same time significant consensus in the underlying assumptions about what content area identities are and how they develop. These findings suggest that researchers move away from the current siloed approach to content area identity research and toward a more connected field of study. [ABSTRACT FROM AUTHOR]

In this convergent mixed methods design study, single-subject and qualitative data were collected concurrently to provide an in-depth picture of the impact of a modified schema-based instructional intervention. The intervention was delivered using instructional trials embedded across general education math lessons and a modified concrete-semi-concrete-abstract instructional sequence. This study investigated the impact of the intervention on the word-problem-solving, strategy use, and concept acquisition of three students with extensive support needs. The paraprofessional-delivered intervention was implemented in elementary general education mathematics classrooms using embedded instruction and focused on teaching students to solve addition and subtraction word-problems. Single-subject data indicated that all three students learned to solve word-problems given concrete materials but needed more time to master the use of semi concrete supports. Qualitative data indicated that students used taught and untaught strategies to solve word-problems, and mastered addition word-problems before subtraction when they were taught simultaneously. Data were integrated in narrative format to explore how strategy use and concept acquisition related to student word-problem-solving performance. Limitations and implications for research are discussed. [ABSTRACT FROM AUTHOR]

This study assessed the effectiveness of a program aimed at improving the early numeracy skills of students with moderate intellectual disability. The persistence of the acquired skills and the program's impact on learning were monitored. Feedback from the students and their mothers was also gathered. Using a multiple-probe design across subjects, the results were visually presented through graphical analysis. Three male students aged 8–9 years participated. After obtaining high-reliability findings from reliability analyses, results showed the program effectively increased students' number skills with a high effect size. These skills persisted post-intervention, and both students and mothers expressed positive views of the intervention. [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]

This study extends prior research by manipulating both intervention and skill difficulty using a multiple baseline across participants design with changing phases in a virtual tutoring environment. Participants were four U.S. students from third and fifth grades for whom appropriate and challenging instructional targets were selected following diagnostic assessment using curriculum-based measurement. Instructional strategies were selected to align or misalign with those instructional targets. The multiple baseline design was used to determine the functional relationship between the instructional strategies (acquisition or fluency-building) with appropriate and challenging skills. Results suggested that indicated intervention strategies aligned with students' skill proficiency resulted in improvements but that contraindicated intervention strategies that were misaligned with students' skill proficiency did not. Furthermore, most students rated the contraindicated intervention strategies as less acceptable or reported higher levels of math anxiety. [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]

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]

Measurement concepts are an essential foundation for more advanced mathematical concepts. To address the challenges of students with autism spectrum disorder (ASD) in learning measurement concepts, this study investigated the effects of using a combination of explicit instruction and virtual manipulatives (VMs) to teach measurement concepts to students with ASD in China. Using a single-case multiple-probe across skills design, researchers examined whether the intervention could support the acquisition and maintenance of measurement concepts in students with ASD. Based on visual analysis, a functional relation was found between the independent variable (i.e., explicit instruction with VMs) and student performance on solving measurement concepts problems. Implications for practice and research are discussed. [ABSTRACT FROM AUTHOR]

Teachers set the tone for their classrooms, but what teacher beliefs shape students' sense of belonging? We investigate how teachers' mindsets—or their beliefs about learning and school—relate to adolescents' individual and collective reports of classroom belonging. Our pre-registered analyses include a multilevel design of how 1,200 US middle school students (ages 11–13; 50% female; 49% low income; 40% White, 30% Latinx, 13% Black, 9% Asian) and their teachers responded to surveys on educational mindsets. We find teachers' growth mindset and confidence in teaching positively relate to students' math class belonging—explaining between 30 and 40% of belonging among classes. Our data suggest a teacher's own sense of school belonging is unrelated to the belonging students feel in class, suggesting teachers' broad feelings of belonging may not influence students' specific classroom feelings of belonging as anticipated. These findings reinforce the notion that what teachers think and believe influence how students feel when in class. [ABSTRACT FROM AUTHOR]

Although women's representation in STEM fields and occupations has increased, science and math continue to be stereotyped as male domains. This paper links psychological and sociological explanations for gendered disparities in STEM by examining the relationship between the local "micro-situational" female learning environment and the gender gap in academic self-concept in math and science. We applied hybrid models to TIMSS 2015 data comprised of a pseudo-panel of repeated measures for individual student and peer achievement, academic self-concept, utility value, and interest-enjoyment value in math/science (at age 14). We analyzed data from three countries, including a subsample of students who were taught by the same teacher in both math and science, thus eliminating unobserved teacher heterogeneity. Results indicate that female peer climate in the classroom is important for understanding how girls' self-concept in math/science is formed, even though it was unrelated to the gender gap. [ABSTRACT FROM AUTHOR]

The mathematical abilities of children with autism spectrum condition have been understudied. Magnitude representation is a fundamental numerical ability that emerges early in development and is linked to children's learning of formal mathematics. It remains unclear about whether children with autism spectrum condition differ from their peers without autism spectrum condition in the precision of magnitude representations. This study recruited preschool-aged children with autism spectrum condition (N = 70; 64 boys, M age = 5.20 years) and without autism spectrum condition (N = 117; 63 boys, M age = 5.11 years), and tested their precision of magnitude representation with an approximate number comparison task (dot comparison). Children with autism spectrum condition exhibited the lower numerical comparison accuracy (i.e. the weaker magnitude representation) than their peers without autism spectrum condition, regardless of the congruency between numerosity and surface area of dots. Moreover, the lower numerical comparison accuracy was observed even controlling for multiple general cognitive abilities (working memory, inhibitory control, and nonverbal intelligence) and language abilities. In addition, the variability of the comparison accuracy was larger in children with autism spectrum condition than without autism spectrum condition. These findings suggest that children with autism spectrum condition are at risk of weaker magnitude representation from an early age, emphasizing the need for specialized mathematics education or interventions to support their learning. The mathematical abilities of children with autism spectrum condition have been understudied. Magnitude representation (e.g. presenting the number of a collection of objects) is a fundamental numerical ability presented since early infancy and is correlated with children's later learning of formal mathematics. It remains unclear about whether children with autism spectrum condition differ from their peers without autism spectrum condition in precision of magnitude representations. This study compared preschool children with and without autism spectrum condition in their precision of magnitude representation with an approximate number comparison task, in which children compared two sets of dots without counting and chose the set with more dots. Children with autism spectrum condition exhibited the lower numerical comparison accuracy (i.e. the weaker magnitude representation) than their peers without autism spectrum condition. This difference existed even when multiple general cognitive abilities (working memory, inhibitory control, and nonverbal intelligence) and language abilities were statistically controlled. Moreover, the individual difference of the numerical comparison accuracy was larger in children with autism spectrum condition than without autism spectrum condition. These findings suggest that children with autism spectrum condition are at risk of weaker magnitude representation from an early age, emphasizing the need for specialized mathematics education or interventions to support their learning. In addition, the large variance in the precision of their magnitude representation suggests that individualized mathematics interventions are needed for children with autism spectrum condition. [ABSTRACT FROM AUTHOR]

Black students' experiences in math and science courses in urban high schools were investigated. A critical race theoretical framing of qualitative data revealed teacher characteristics that encouraged and discouraged students. Teacher characteristics that encouraged students' interests included (1) shared racial/cultural background with students, (2) passion for students and subject matter, and (3) a caring and understanding approach to student engagement. Characteristics that discouraged student engagement included (1) lack of racial representation, (2) differential treatment of students based on race, (3) condescension and assumed incompetence, and (4) technology as a replacement for instruction. We offer recommendations to improve Black students' experience and increase interest in pursuing future STEM careers. [ABSTRACT FROM AUTHOR]

The purpose of this quantitative systematic literature review was to identify and describe published mathematics studies from 1980 to 2021 that incorporated a self-monitoring component (k = 22 studies; N = 1,787 students). We examined specific self-monitoring procedures, instructional contexts, implementation variables, and methodological quality. For inclusion, studies needed to (a) include self-monitoring (defined as students observing, evaluating, and/or recording their behaviors), (b) include co-occurring mathematics instruction, (c) include at least one mathematics outcome measure, (d) occur in a school setting, (e) include students in Grades K–12, and (f) utilize a single-case, experimental, or quasiexperimental design. Variables of interest were coded and methodological quality was assessed using What Works Clearinghouse standards. Our findings suggest that students with and without disabilities generally benefit from embedded self-monitoring procedures across mathematical content areas and tiers of instructional support. Future research should further unpack definitions of self-monitoring and related constructs. [ABSTRACT FROM AUTHOR]

The effectiveness of Tier 2 interventions may depend on the variability of student skills within an intervention group. We investigated the effect of pretest variability within intervention groups using data from a large-scale study of ROOTS, a Tier 2 kindergarten mathematics intervention. Our research questions were as follows: Does mathematics pretest variability within ROOTS groups predict student gains from the intervention, and is this relationship moderated by (a) intervention group size (two- vs. five-student groups), (b) quality of explicit instruction, or (c) group-level initial skill? We found that ROOTS groups with greater pretest variability on a closely aligned mathematics measure experienced smaller gains from the intervention. This association was more impactful in larger intervention groups (i.e., five-student groups compared with two-student groups) and in groups with higher quality of explicit instruction. We unpack these findings and conclude with recommendations for practice and future research. [ABSTRACT FROM AUTHOR]

How does a maths teacher rated as outstanding according to the 'DocenteMás' Performance Assessment System of Chile semiotically mediate her seventh-grade students' learning? With the goal of answering this question, this article used a qualitative, ethnographic case study method to describe the pedagogical strategies of the teacher and her students when covering the thematic unit on numbers and operations in primary school. The results show that the pedagogical strategies emerge from the communicative interaction in the classroom via a local and a global dynamic. With regard to the local dynamic, the pedagogical strategies discovered include exposition, experiential articulation and arithmetic understanding. In the global dynamic, pedagogical strategies of semiotic mediation like metaphors, question series and joint understanding of knowledge stood out. [ABSTRACT FROM AUTHOR]

Providing high-quality services to students with disabilities in rural settings can be challenging, as rural schools often lack resources both in and out of the classroom. One potential option to provide high-quality mathematics instruction to students with disabilities in rural areas is using virtual manipulatives and online instruction. In this study, a single-case research design was used to examine the progress of three high school students with intellectual and developmental disabilities (IDDs) as they used a virtual money manipulative within an online learning environment to solve making change problems. The researchers found a functional relation between the intervention package (i.e., a virtual money manipulative, modeling, system of least prompts) and the dependent variable of accuracy in solving making change problems across three students. In addition, all three students demonstrated an increase in independence during each session and maintained their accuracy and independence after the intervention concluded. [ABSTRACT FROM AUTHOR]

This study examined whether adolescent students' externalizing behavior and prosocial behavior affects their academic achievement (i.e., school grades and standardized test scores) in two major academic domains (i.e., mathematics and German) over and above well-established determinants of school achievement (i.e., prior achievement, intelligence, and domain-specific self-concepts). The study draws on longitudinal data from two independent samples of students (A/B) who were each followed from Grade 7 to Grade 9 (N A/B = 1143/1345). In each academic domain, structural equation models showed that externalizing behavior negatively predicted and prosocial behavior positively predicted academic achievement. When both behaviors were included simultaneously, prosocial behavior particularly predicted school grades in both domains, whereas externalizing behavior particularly predicted test scores in mathematics. Further analyses did not suggest differences between boys and girls in the effects of social behavior on academic achievement. Implications for future research and educational practice are discussed. [ABSTRACT FROM AUTHOR]

This article provides teachers with a toolkit for assessing students in the context of data-based individualization (DBI) in mathematics. Assessing students is a critical component of DBI because it provides teachers with information about what they may need to modify in their instructional programs. In this article, we provide teachers with step-by-step procedures for assessing students within the DBI process, including selecting an appropriate progress-monitoring tool, collecting baseline data, and analyzing graphed data to determine whether a student is making adequate progress. In addition, diagnostic assessment is discussed to help teachers target instructional priorities based on student needs. Providing a toolkit for assessment and supplementary resources should enable teachers to use DBI procedures more effectively and, ultimately, to boost students' mathematics achievement. [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]

Extreme response style (ERS), the tendency of participants to select extreme item categories regardless of the item content, has frequently been found to decrease the validity of Likert-type questionnaire results. For this reason, various item response theory (IRT) models have been proposed to model ERS and correct for it. Comparisons of these models are however rare in the literature, especially in the context of cross-cultural comparisons, where ERS is even more relevant due to cultural differences between groups. To remedy this issue, the current article examines two frequently used IRT models that can be estimated using standard software: a multidimensional nominal response model (MNRM) and a IRTree model. Studying conceptual differences between these models reveals that they differ substantially in their conceptualization of ERS. These differences result in different category probabilities between the models. To evaluate the impact of these differences in a multigroup context, a simulation study is conducted. Our results show that when the groups differ in their average ERS, the IRTree model and MNRM can drastically differ in their conclusions about the size and presence of differences in the substantive trait between these groups. An empirical example is given and implications for the future use of both models and the conceptualization of ERS are discussed. [ABSTRACT FROM AUTHOR]

Even before starting formal schooling, children show substantial variations in math skills suggesting that the home learning environment plays an important role in shaping young children's math skills. Here, I review interventions aimed at providing young children with opportunities to learn math at home to identify what types of parent-guided activities may be effective at improving young children's math. I also review interventions that may impact the frequencies and quality of the learning opportunities that parents provide to their children even if benefits for children's math outcomes were not found or have not been tested yet. While some studies show that parent-guided math activities can impact children's math skills, future work should carefully consider for whom interventions are most effective as both child and parent characteristics such as children's general cognitive skills or foundational number skills as well as parents' attitudes toward math may impact the effectiveness of the interventions. [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]

Fractions are challenging for both typically achieving children and adults. Although some prior research has focused on fraction difficulties of children with mathematics difficulties (MD), persistent difficulties encountered by adults with MD remain unknown. It is possible that these adults may be able to compensate for some deficits. In this study, we administered an un-timed, paper-based fraction achievement test to French adults with and without MD to compare their knowledge of fractions. Compared with controls, adults with MD performed worse in fraction number lines, fraction concepts, fraction arithmetic, and word problems. However, no difference in performance between the two groups was observed on symbolic representations. This suggests that adults with MD might be able to perform rote procedures such as transcoding from a verbal to a symbolic representation but are severely impaired for fraction number line, fraction concept, and fraction arithmetic. Exploratory error pattern analyses for fraction number line and fraction arithmetic further revealed mistakes similar to those observed in prior studies on children with MD, indicating core deficits in fraction understanding in individuals with MD. [ABSTRACT FROM AUTHOR]

This study, which used a multiple baseline across participants' design, examines the effectiveness of a modified schema-based instructional approach to improve the mathematical word problem solving performance of three students with mild intellectual disability, two of whom had an autism spectrum disorder. Following the intervention, the three students improved their performance when solving addition and subtraction change word problems; however, their performance was inconsistent on change word problems. The effects of the instruction were generalized to two-step addition and subtraction word problems for the three participants. Moreover, the results were generalized to an untrained setting and were maintained 8 weeks after the instruction. The implications of these findings for teaching problem-solving skills to students with intellectual disability are discussed. [ABSTRACT FROM AUTHOR]

Transcoding is the process of translating between spoken and written numbers, and it is correlated with other mathematical skills. In the present study, we investigated the link between French number writing of 49 students in the third grade (aged 7–9 years) and their language skills. Transcoding in French is of particular interest because the spoken number language system does not completely correspond to that of the written digits (e.g., quatre-vingt-dix [four-twenty-ten] and 90). We hypothesised that the complex linguistic structure of spoken numbers in French would be challenging for students who are learning to transcode. First and second French-language learners' accuracy and errors were recorded during a writing task of 3- to 7-digit numbers. Children also completed linguistic tests (e.g., receptive vocabulary, receptive syntax). Results showed that first- and second-language learners did not differ in their transcoding accuracy. Number size, decade complexity of stimulus number words in French (i.e., numbers containing a complex decade, operationalized as a number between soixante-dix, 70, and quatre-vingt-dix-neuf, 99), and receptive vocabulary predicted children's French transcoding skills. Students were more likely to produce errors (e.g., 68 or 6018 for 78) when they transcoded complex decade numbers compared with simple decade numbers. When an error was made on the complex decade portion of a number, it was likely a lexical error. In conclusion, third graders, both first- and second-language learners, found complex decade numbers challenging and their performance was related to their general vocabulary skills. [ABSTRACT FROM AUTHOR]

Students with disabilities experience differential levels of achievement in mathematics when compared with their nondisabled peers. Identifying and implementing evidence-based practices (EBPs) is essential to increase their mathematics achievement. However, an argument is re-emerging that calls into question the effectiveness of well-known EBPs, such as explicit/direct instruction. This argument is based on opinion and conjecture, rather than student outcome measures. In this commentary, we use research on explicit and direct instruction with mathematics to (a) highlight the confusion over theoretical implications, (b) call for researchers to reduce personal bias within research, and (c) emphasize the need for improving outcomes of students with disabilities that affect mathematics learning. [ABSTRACT FROM AUTHOR]

The purposes of this study included conducting a meta-analysis and reviewing the study reporting quality of math interventions implemented in informal learning environments (e.g., the home) by children's caregivers. This meta-analysis included 25 preschool to third-grade math interventions with 83 effect sizes that yielded a statistically significant summary effect (g = 0.26, 95% CI [0.07, 0.45) on children's math achievement. Significant moderators of the treatment effect included the intensity of caregiver training and type of outcome measure. There were larger average effects for interventions with caregiver training that included follow-up support and for outcomes that were comprehensive early numeracy measures. Studies met 58.0% of reporting quality indicators, and analyses revealed that quality of reporting has improved in recent years. The results of this study offer several recommendations for researchers and practitioners, particularly given the growing evidence base of math interventions conducted in informal learning environments. [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 present study examined whether learning disabilities (LD) in reading and/or math (i.e., reading disability [RD], math disability [MD], and RD+MD) co-occur with other diagnoses. The data comprised a clinical sample (n = 430) with LD identified in childhood and a sample of matched controls (n = 2,140). Their medical diagnoses (according to the International Classification of Diseases nosology) until adulthood (20–39 years) were analyzed. The co-occurrence of LD with neurodevelopmental disorders was considered a homotypic comorbidity, and co-occurrence with disorders or diseases from the other diagnostic categories (i.e., mental and behavioral disorders, diseases of the nervous system, injuries, other medical or physical diagnoses) was considered a heterotypic comorbidity. Both homotypic and heterotypic comorbidity were more common in the LD group. Co-occurring neurodevelopmental disorders were the most prominent comorbid disorders, but mental and behavioral disorders, diseases of the nervous system, and injuries were also pronounced in the LD group. Accumulation of diagnoses across the diagnostic categories was more common in the LD group. No differences were found among the RD, MD, and RD+MD subgroups. The findings are relevant from the theoretical perspective, as well as for clinical and educational practice, as they provide understanding regarding individual distress and guiding for the planning of support. [ABSTRACT FROM AUTHOR]

The number line is a powerful tool for supporting students' understanding of fraction magnitude. Fractions are a critical component of mathematics instruction in the elementary and intermediate grades. More specifically, understanding fraction magnitude is central to mathematical development. Yet, fractions are challenging for many students, particularly students with or at risk of learning disabilities (LD) in mathematics. This article shares (a) key recommendations when planning and implementing fraction number line instruction, (b) sample fraction number line activities for supporting students' understanding of fraction magnitude and overall mathematics achievement, and (c) strategies for helping students grasp the abstract number line representation. [ABSTRACT FROM AUTHOR]

Rational number proficiency is predictive of later mathematics achievement, especially for rigorous mathematics courses, such as Algebra I. Students with learning disabilities (LD) in mathematics struggle to make adequate progress on rational number concepts and skills that lay the foundation for successfully completing secondary mathematics courses. However, recent research has demonstrated that utilizing effective instructional design, such as the use of a number line with systematic and explicit instruction, can result in academic progress for students with LD in mathematics. This article presents teachers with a four-step teaching sequence utilizing the number line and effective strategies for teaching students with LD in mathematics to introduce fraction-to-decimal relationships in upper elementary, a prerequisite for middle school mathematics. [ABSTRACT FROM AUTHOR]

Building proficiency with fraction arithmetic poses a consistent challenge for students with learning difficulties or disabilities in mathematics. This article illustrates how teachers can use the number line model to support struggling learners in making sense of fraction arithmetic. Number lines are a powerful tool that can be used to help students represent and solve problems involving addition, subtraction, multiplication, and division with fractions while building conceptual understanding of the underlying operations. Evidence-based strategies for using number line models to teach fraction arithmetic concepts and skills are described and specific examples provided to illustrate how teachers can strategically integrate number line models with other mathematical representations to support the development of flexible understanding of fractions. [ABSTRACT FROM AUTHOR]

This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems. The authors draw from the existing research base to describe practices for incorporating number line representations to (a) support students' conceptual understanding of number and (b) teach addition and subtraction computational strategies. Specific examples are provided for teachers to integrate number line representations with other mathematical models to support the development of whole number understanding for students with LD in mathematics. [ABSTRACT FROM AUTHOR]

The number line has been proposed as a central construct used by students to solve a range of mathematics problems. Given the capacity of number lines to represent all real numbers and to be used in a variety of contexts, there have been calls to increase the use of number lines in mathematics instruction. However, due to the recency of these recommendations coupled with the myriad ways in which number lines can be used, little hands-on guidance has been provided how best to leverage number lines in mathematics instruction. This special series details five areas in which teachers can use number lines to support acquisition of critical mathematics concepts and skills. [ABSTRACT FROM AUTHOR]

Early mathematics skills are predictive of later achievement, but there is evidence teachers generally provide little mathematics instruction in preschool classrooms. We conducted this survey study to better understand teachers’ reported beliefs about their own mathematics skills, expectations, and practices for children with and without disabilities, and the impact of these reported beliefs and practices on the perceived effectiveness of their instruction. We found teachers had less confidence in their own mathematics skills than their mathematics teaching abilities and had differing expectations for children with and without disabilities. Their beliefs about their own mathematics abilities predicted their perceived effectiveness for typically developing children only, but their beliefs about their teaching abilities predicted their perceived effectiveness for children with and without disabilities. Implications include the need to better prepare and support teachers to teach mathematics to all children and collect data from varied sources on teachers’ practices. [ABSTRACT FROM AUTHOR]

This overview article introduces the Intervention in School and Clinic special series focused on implementing practices within an integrated multi-tiered system of support (I-MTSS) framework. The I-MTSS Research Network defines I-MTSS as “a comprehensive and equitable prevention framework for improving the outcomes of all students, including students with or at-risk for disabilities, through integrated academic and behavioral support.” In this special series, members of the I-MTSS Research Network Each descirbe a different component of I-MTSS: (a) integrating evidence-based practices in Tier 1, (b) integrating evidence-based practices in Tier 2, (c) integrating evidence-based practices in Tier 3, (d) providing professional development to support effective implementation, and (e) practical applications of I-MTSS in elementary settings. Across articles, demonstrate that integrating academic and behavior support within an I-MTSS framework can be feasible and effective with the right supports in place. [ABSTRACT FROM AUTHOR]

Objective: Developmental education provides postsecondary students requisite skills to take credit-bearing coursework. Yet, racial disparities exist in which students are most likely to be placed into developmental education. The present study investigates how multiple measures of students’ mathematics background ameliorate racial disparities in developmental math outcomes among U.S. community college students. Methods: The High School Longitudinal Study of 2009 was used to identify sample participants (n = 3,650) who attended a 2-year postsecondary institution (community college) within 3 years of high school graduation. A series of logistic regression models were employed with developmental math outcomes as dependent variables predicted by multiple measures of student’s math background and demographic covariates. Results: Compared to White students, Black and Hispanic students had poorer developmental math outcomes; however, inclusion of multiple measures of high school math experiences reduced racial disparities. Multiple measures significantly reduced developmental math enrollment by 13% for Black students and 15% for Hispanic students, improved developmental math passing rates for Black students by 25% and Hispanic students by 25%, and improved passing rates for the first college-credit bearing math course for Hispanic students by 73%. Conclusion: The present study highlights how multiple measures of students’ math background might be an important lever for more racially-equitable placement processes. For Black and Hispanic students, the most influential high school measures were high school math GPA, highest high school math course, and math motivation. More work is needed to fine-tune how multiple measures can be used to increase access and equitable outcomes for students. [ABSTRACT FROM AUTHOR]

Reading, mathematics and science are important subjects in the compulsory educational stage. Promoting students’ learning in these subjects has become a focus. Early reading achievement and reading interest may play a critical role. Using two waves of data collected from 2,722 Chinese students in Grade 4 and Grade 6, the study investigated the longitudinal within-domain relationship between reading achievement and reading interest, as well as their cross-domain effects on mathematics and science. The results of the structural equation model showed that reading achievement and reading interest were mutually reinforced over time. Except for the path from reading achievement to science interest, the two reading-related constructs in Grade 4 positively predicted achievement and interest in mathematics and science in Grade 6. The findings underline the significance for primary schools to cultivate proficient reading skills and positive reading attitudes in promoting students’ long-term learning in reading, mathematics and science. [ABSTRACT FROM AUTHOR]

Rate of change (i.e., slope) is a critical mathematics concept for success in everyday life, academics, and professional careers. Students with or at risk of learning disabilities struggle with solving rate-of-change problems, especially word problems. Interventions that incorporate representations and problem-solving strategies are effective for improving the word problem-solving performance of students with disabilities. This multiple-probe, multiple-baseline, single-case design study evaluated the effects of an intervention that included an integrated, concrete-representational-abstract teaching framework with an embedded problem-solving strategy (POD Check) on students’ rate-of-change word problem-solving performance. The intervention was delivered virtually via video conferencing technology. Four middle- and high-school students with or at risk of mathematics learning disabilities in the Intermountain West participated in the intervention. Results indicate evidence of a functional relation between the intervention and students’ word problem-solving performance, and effects were maintained 2–4 weeks after the intervention. The findings of this study provide implications for mathematics intervention research and practice for students with learning disabilities. [ABSTRACT FROM AUTHOR]

Additional research is needed to improve adult numeracy instruction, training for instructors, and our understanding of the feasibility and impact of innovations in these areas. The Adult Numeracy in the Digital Era (ANDE) project, funded by the Institute of Education Sciences (IES) at the U.S. Department of Education, seeks to develop and test an innovative, technology-enabled approach for improving adult numeracy and digital literacy instruction. We began this project guided by principles of user-centered design, specifically the principle of knowing the user’s wants and needs. We conducted a “field scan” of adult numeracy and digital literacy, by interviewing researchers, instructors, students; conducting classroom observations; and reviewing literature. We detail our key findings within two emergent themes: (1) extensive variability in learner backgrounds and readiness, instructors’ experiences, standards alignment, course structures, and classroom contexts; and (2) diversity of learner goals and the actions they and their instructors took as they worked together within the course and local policy contexts. We also identify three design principles to guide course development, suggesting that adult numeracy courses should be: aligned and relevant; interactive and participatory; and relationship-centered. These principles guided the design of our adult numeracy course, and we offer questions that current instructors can consider as they design their own adult numeracy lessons. [ABSTRACT FROM AUTHOR]

Mathematics plays a fundamental role in ecological research, yet its uses remain strikingly separate from advances in the environmental social sciences and humanities. In this paper, I work to address this impasse and outline the motivation and scope for an ‘ecological mathematics’, an approach to doing mathematics in environmental research which foregrounds relationship, embodiment and human difference. I begin by tracing the historical emergence of mathematics in ecology, noting how life processes have been conceptualised in a way which forces them to fit the ideals of mathematical models transplanted from the physical sciences. I then investigate the cultural factors shaping the evolution of mathematical thought, eliciting a malleability in how mathematical knowledge relates to the more-than-human world. This provides a place from which to rethink the role of abstraction in ecological thought, and develop mathematical methods grounded in ecological concepts. Drawing on ethnographic and perceptual accounts of space and time, I work with topological concepts from both mathematics and the social sciences to suggest a new correspondence between these subjects, elaborating a way of employing mathematical techniques which enliven, rather than deaden, the ecologies under study. The paper concludes with important philosophical clarifications to the approach of an ecological mathematics. [ABSTRACT FROM AUTHOR]

This article analyzes teachers’ perceptions and experiences using an educative curriculum designed to promote high levels of mathematical discourse. After participating in 2 days of professional learning, grade 3 teachers implemented a predifferentiated and enriched mathematics unit in their classroom. The curriculum was designed to be educative, meaning that teaching it served as professional learning. During implementation, researchers conducted an observation of each treatment teacher and after implementation was complete teachers participated in a post interview about their experiences. Findings from this qualitative study indicate that after teaching the curriculum teachers understood the value of oral discourse and how to implement it in their classroom and could identify student benefits from participating in this type of curriculum. This study illuminates promising practices that may support teachers in implementing research-based best practices. [ABSTRACT FROM AUTHOR]