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Computer-based curriculum-based measurement (CBM) is a relatively common practice, but surprisingly few studies have examined the reliability of computer-based CBM. This study sought to examine the reliability of CBM administered via paper/pencil versus the computer. Twenty-one of 25 students in two third-grade classes (N = 21) participated in two generalizability studies. The primary facet of interest, format of assessment, was examined for two measures, a fact operation (fact family measure) and a more complex operation (multidigit addition). Researchers administered four alternate forms of each measure under both computer and paper/pencil conditions. Results indicated ideal reliability of measurement within all conditions and results were consistent across assessment formats for the fact operation. However, assessment format explained a large proportion of variance for the more complex skill (multidigit addition). Results indicate a need to consider the reliability of transitioning assessment from paper/pencil to computer-based response on a measure-by-measure basis. [ABSTRACT FROM AUTHOR]

The relative advantages and disadvantages of sum scores and estimated factor scores are issues of concern for substantive research in psychology. Recently, while championing estimated factor scores over sum scores, McNeish offered a trenchant rejoinder to an article by Widaman and Revelle, which had critiqued an earlier paper by McNeish and Wolf. In the recent contribution, McNeish misrepresented a number of claims by Widaman and Revelle, rendering moot his criticisms of Widaman and Revelle. Notably, McNeish chose to avoid confronting a key strength of sum scores stressed by Widaman and Revelle—the greater comparability of results across studies if sum scores are used. Instead, McNeish pivoted to present a host of simulation studies to identify relative strengths of estimated factor scores. Here, we review our prior claims and, in the process, deflect purported criticisms by McNeish. We discuss briefly issues related to simulated data and empirical data that provide evidence of strengths of each type of score. In doing so, we identified a second strength of sum scores: superior cross-validation of results across independent samples of empirical data, at least for samples of moderate size. We close with consideration of four general issues concerning sum scores and estimated factor scores that highlight the contrasts between positions offered by McNeish and by us, issues of importance when pursuing applied research in our field. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to explain and describe the use of presuppositional interviews as means of the researcher being able to expose their own, often unknown, assumptions about the phenomena of interest. Within this, we provide a philosophical and practical account for the development and use of a presuppositional interview from an insider perspective to expose insights which influence researcher reflexivity and directly impact on the research process. Author A's hermeneutic phenomenological study seeks to gain insights into the lived experience of children learning mathematics in outdoor environments, such as forests and woodland. The paper describes how the reflexive method of presuppositional interviewing helped him to understand more about his research position and find a clearing in his 'Being in the Wood.' A template for a presupposition interview schedule is presented. [ABSTRACT FROM AUTHOR]

This special issue brings selected papers from an international conference which brought a group of approximately 30 Science Technology and Society and Popularization of Science experts from nine South Asian and Southeast Asian countries (Bangladesh, India, Indonesia, Malaysia, Nepal, Pakistan, Singapore, Sri Lanka, and Thailand), plus the United States. They discussed how best to enhance public awareness about the role of women in Science, Technology, Engineering, and Mathematics (STEM). These papers show how to develop strategies for increasing the participation of women in STEM, both as STEM professionals and as informed and engaged, lifelong participants in a STEM-rich world. [ABSTRACT FROM AUTHOR]

Peer review has never been a uniform practice but is now more diverse than ever. Despite a vast literature, little is known of how different disciplines organize peer review. This paper draws on ninety-five qualitative interviews with editors and publishers and several hundred written reports to analyze the organization of peer review in pure mathematics. This article focuses on the practice of "quick opinions" at top journals in mathematics: asking (senior) experts about a paper's importance, and only after positive evaluation sending the paper for a full review (which most importantly means checking the paper's correctness). Quick opinions constitute a form of "importance only" peer review and are thus the opposite of the "soundness only" approach at mega-journals such as PLOS ONE. Quick opinions emerged in response to increasing submissions and the fact that checking correctness in mathematics is particularly time-consuming. Quick opinions are informal and are often only addressed to editors. They trade on, indeed reinforce, a journal hierarchy, where journal names are often used as a "members' measurement system" to characterize importance. Finally, quick opinions highlight that a key function of the peer-reviewed journal today, apart from validation and filtration, is "designation"—giving authors items on their CV. [ABSTRACT FROM AUTHOR]

The importance of computational thinking (CT) as a 21st-century skill for future generations has been a key consideration in the reforms of many national and regional educational systems. Much attention has been paid to integrating CT into the traditional subject classrooms. This paper describes a scoping review of learning tools for integrating CT and mathematics in current empirical studies published from 2015 to 2021. The review showed that most of the studies implemented CT-intensive Math-connected integration. Five major types of CT tools had been identified, i.e., digital tangibles, apps and games, programming languages, formative or summative assessments, and other technological tools. In many instances, the tools also provide functions of assessment of CT skills. The most assessed CT competencies were including algorithms and algorithmic thinking, abstraction, testing and debugging, loops, and sequences. Geometry and Measurement was the most assessed mathematics topic. Our scoping review is beneficial in the investigation of the literature on CT and mathematics education, as well as guides those who are interested in developing curriculum, programs, or assessments that involve the integration of CT and mathematics. [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]

Introduction: This study examines the spatial abilities of middle school students with visual impairments (i.e., blindness and low vision) in the context of spatial visualization. The study also aims to examine the strategies used by such students in solving questions requiring spatial ability. Methods: Participants comprised eight students with visual impairments attending the 8th grade of a school in Ankara, Turkey, which teaches students with visual impairments. The data collection tool is composed of eight questions under the guidance of the definition for spatial visualization. Question types belonging to the spatial visualization subcomponent were organized in four topics: 2D rotation, 3D rotation, paper folding, and cube folding. Results: It was observed that students with visual impairments used mental rotation and key feature strategies for 2D rotation questions. They used the key feature strategy for 3D rotation questions and the mental manipulation strategy for cube folding and paper folding questions. Discussion: In this study, it was identified that strategies used by students with visual impairments show similarities with spatial strategies defined in the literature as used by students without visual impairments. Of all the other types of questions, the most successful question of students with visual impairments is the paper folding question. Implications for practitioners: The results of this article can help teachers become aware of the kind of difficulties that students with visual impairments encounter when they try to solve questions that require spatial ability. [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]

Written answers to open-ended questions can have a higher long-term effect on learning than multiple-choice questions. However, it is critical that teachers immediately review the answers, and ask to redo those that are incoherent. This can be a difficult task and can be time-consuming for teachers. A possible solution is to automate the detection of incoherent answers. One option is to automate the review with Large Language Models (LLM). They have a powerful discursive ability that can be used to explain decisions. In this paper, we analyze the responses of fourth graders in mathematics using three LLMs: GPT-3, BLOOM, and YOU. We used them with zero, one, two, three and four shots. We compared their performance with the results of various classifiers trained with Machine Learning (ML). We found that LLMs perform worse than MLs in detecting incoherent answers. The difficulty seems to reside in recursive questions that contain both questions and answers, and in responses from students with typical fourth-grader misspellings. Upon closer examination, we have found that the ChatGPT model faces the same challenges. [ABSTRACT FROM AUTHOR]

Mathematics training is a challenge for students with visual impairments (VI). However, there are few protocols to assess math skills for them, especially the content related to counting and measurement. The objective of this article was to develop and test the applicability of a protocol to assess math skills in counting and measuring for children and adolescents with VI. The work was organized into two studies. The first dealt with the development of a protocol for assessing pre-arithmetic skills and knowledge and the second study assessed its applicability. In the first study, the protocol was developed from the few papers found on a literature review. In the second study, the protocol was applied to 12 participants with VI aged 5 and 16 years. The results showed that 8 of the 12 participants had performance ranging from 83% to 100% of correct responses in the protocol application, both for counting and measuring skills. The protocol applicability and difference in participants' performance are discussed. The study concludes that the protocol can be used as a tool to assess math knowledge for children at the end of Early Childhood Education or at the beginning of Elementary School, with or without VI. [ABSTRACT FROM AUTHOR]

Improvements in the quantification and visual analysis of data, plotted across non-standardized graphs, are possible with the equations introduced in this paper. Equation 1 (an expression of graphic scale variability) forms part of the foundation for Equation 2 (an expansion on the traditional calculation of the tangent inverse of a line's algebraic slope). These equations provide clarification regarding aspects of "slope" and graphic scaling that have previously confused mathematicians. The apparent lack of correspondence between geometric slope (the angle of inclination) and algebraic slope (the m in y = mx + b) on "non-homogeneous" graphs (graphs where the scale values/distances on the y -axis are not the same as on the x- axis) is identified and directly resolved. This is important because nearly all behavior analytic graphs are "non-homogeneous" and problems with consistent visual inspection of such graphs have yet to be fully resolved. This paper shows how the precise geometric slope for any trend line on any non-homogeneous graph can quickly be determined—potentially improving the quantification and visual analysis of treatment effects in terms of the amount/magnitude of change in slope/variability. The equations herein may also be used to mathematically control for variability inherent in a graph's idiosyncratic construction, and thus facilitate valid comparison of data plotted on various non-standard graphs constructed with very different axes scales—both within and across single case design research studies. The implications for future research and the potential for improving effect size measures and meta-analyses in single-subject research are discussed. [ABSTRACT FROM AUTHOR]

Background: Play is an important part of the childhood. The learning potential of playing and creating non-digital games, like tabletop games, however, has not been fully explored. Aim: The study discussed in this paper identified a range of activities through which learners redesigned a mathematics-oriented tabletop game to develop their ideas and competencies in an integrated STEM (science, technology, engineering, and mathematics) class. Method: Third and fourth graders worked as teams to make changes on Triominos over a period of six weeks. Considering what could be changed from the original game, each group provided a different design for Triominos to accommodate the changes introduced. We gathered data through weekly observations of two classes (about 45 learners, ranging from age eight to ten) in a west-Canada school. In this paper, we present the works of three groups of three teammates. Results: We found that any change made by learners not only influenced mechanics, dynamics, and aesthetics of the game but also helped engage learners, encourage unconventional ideas, promote learning, and solve problems. Based on our findings, we suggest redesigning games facilitated learners deepen their understanding of mathematical concepts as part of a designed game system in STEM classes. [ABSTRACT FROM AUTHOR]

Shadow education helps students become academically competitive. Currently, little is known about whether shadow education can effectively fulfill either remedial or enrichment purposes in China. Using the nationally representative data from the China Education Panel Survey (CEPS) collected in 2013 and 2014, this paper explored the opportunity gap in shadow education and its impact on Chinese eighth-grade students' mathematics and English reading performance. This study further examined how this effect differs by students' prior performance and school ranks by hierarchical linear modeling (HLM). The results show that affluent socioeconomic resources and parental pressure predicted larger chances of students using shadow education. On average, supplementary tutoring had a positive effect on academic achievement. After re-estimating the effect by groups, this study found that students disadvantaged by prior knowledge and quality of schooling benefited more from supplementary tutoring. The findings suggest that the expansion of shadow education may contribute to social reproduction within the current education system. [ABSTRACT FROM AUTHOR]

Although STEM is an essential feature of 21st-century education and learning, there is a lack of awareness about it in Pakistan, especially at the K-12 and tertiary levels. Recently many initiatives have been launched across Pakistan to create more interest in STEM education. In order to assist in raising the level of STEM awareness in Pakistan, this study sought to examine the current state of research and identify recent contributions and gaps in the literature. A systematic literature review was conducted using 22 research papers from five renowned databases. Results produced limited research in this area, with the majority being descriptive and only four being interventional studies. Regrettably, no research explored the engineering component of STEM education. Trends indicate that STEM education research has experienced a downward trend in Pakistan. The observed decline may have occurred due to a lack of understanding among Pakistani researchers regarding the importance of STEM education. Additionally, we identified the current gaps in research on STEM education and subsequently provided recommendations for future research. [ABSTRACT FROM AUTHOR]

In this paper we explore the hypothesis that constrained uses of imagination are crucial to economic modeling. We propose a theoretical framework to develop this thesis through a number of specific hypotheses that we test and refine through six new, representative case studies. Our ultimate goal is to develop a philosophical account that is practice oriented and informed by empirical evidence. To do this, we deploy an abductive reasoning strategy. We start from a robust set of hypotheses and leave space for the generation of further hypotheses and theoretical claims based on the qualitative analysis of new empirical data. [ABSTRACT FROM AUTHOR]

Automated scoring of free drawings or images as responses has yet to be used in large-scale assessments of student achievement. In this study, we propose artificial neural networks to classify these types of graphical responses from a TIMSS 2019 item. We are comparing classification accuracy of convolutional and feed-forward approaches. Our results show that convolutional neural networks (CNNs) outperform feed-forward neural networks in both loss and accuracy. The CNN models classified up to 97.53% of the image responses into the appropriate scoring category, which is comparable to, if not more accurate, than typical human raters. These findings were further strengthened by the observation that the most accurate CNN models correctly classified some image responses that had been incorrectly scored by the human raters. As an additional innovation, we outline a method to select human-rated responses for the training sample based on an application of the expected response function derived from item response theory. This paper argues that CNN-based automated scoring of image responses is a highly accurate procedure that could potentially replace the workload and cost of second human raters for international large-scale assessments (ILSAs), while improving the validity and comparability of scoring complex constructed-response items. [ABSTRACT FROM AUTHOR]

Grounded in 'expectancy-value' theory, this paper reports on the psychometric properties of an instrument intended to measure students' motivation in mathematics. The participants were 2045 third-, fourth- and fifth-grade students from Estonia, Finland, Norway, Portugal, Serbia and Sweden. The Expectancy-Value Scale (EVS) was found to be suitable for early grades of primary education in measuring competence self-perceptions and subjective task values relative to the mathematics field. The results indicate a good model fit aligned with the expectancy-value theory. The EVS dimensions showed good reliability, and scalar invariance was established. However, findings also indicated high correlations between some of the EVS dimensions, which is well documented for students at this age. The findings are discussed relative to the 'expectancy-value' theory framework and students' age. [ABSTRACT FROM AUTHOR]

With over two decades of research showing a close association between working memory (WM) and maths performance, WM training has been suggested as one way to supplement conventional remedial instructions. Although initial findings were promising, recent reviews have found that training typically resulted in WM improvement but no transfer to maths performance. This paper focused on the utility of WM training for maths performance. In addition to a brief review of relevant works, I described my own efforts and insights gained from three iterations of an intervention that produced mixed findings. One of the main questions addressed in this paper was the reasons for robust findings of near but not far transfer. Some of the older studies were beset by poor methodological designs. However, the finding that more recent, better executed studies also found a similar lack of far transfer is troubling. I examined whether the use of WM training for improving maths performance is simply misguided. I also examined the possibility that the extant approaches to intervention may be approaching the problem from the wrong perspective. [ABSTRACT FROM AUTHOR]

This study investigated the effectiveness of four Digitalized Interactive Components (DICs) designed based on cognitive principles to accommodate individual differences among students with learning difficulties in geometry during computer-based assessments. The four DICs were annotations (allowing students to make notes on the screen), pop-up glossary (providing definitions of math terms upon clicking), signaling (displaying corresponding visual information upon clicking verbal information), and rotation (allowing students to rotate shapes). Sixteen high school students with mathematics difficulties participated in the study and were tested with and without the principled DICs. The findings indicate that the principled DICs statistically significantly improved students' accuracy on the majority of tested problems and increased the average duration engaged in solving geometry problems. Analysis of video data revealed that the pop-up glossary was the most frequently used DIC, followed by signaling, while annotation was the least used. [ABSTRACT FROM AUTHOR]

One perceived advantage of computer-based testing is that accessibility tools can be embedded within the testing format, allowing students with disabilities to use them when necessary to remove unique barriers within testing. However, an important assumption is that students activate and use the tools when needed. Initial data from large-scale computer-based testing suggest many students with disabilities are not using them; information is needed to understand why. Both computer skills and motivation are likely necessary for students to use accessibility tools; therefore, we explored whether prior computer use, math motivation, and test motivation predicted accessibility tool use on a national math test. We further explored the relationship between accessibility tool use and test performance. Accessibility tool use was relatively infrequent. Test motivation was weakly associated with text-to-speech use. Use of eliminate choice and scratchwork tools were weakly associated with performance. When combined with related empirical work, findings suggest a potential need to improve student test motivation and corresponding use of accessibility tools to improve validity of low-stakes test scores. However, given the weak relationships identified between tool use and performance, evidence-based math interventions are anticipated to be more helpful for improving math performance than mere promotion of accessibility tool use. [ABSTRACT FROM AUTHOR]

The quality of diagnostic profiles and probability assignment depends on the validity of the proposed attributes and Q-matrix. The rule-space method (RSM), one of diagnostic classification models, provides the quality indices of diagnostic profiles, such as the classification rate and the squared Mahalanobis distance. The study aims to further validate the attributes and Q-matrix that represent construct validity of mathematics tests as well as diagnostic profiles by applying differential item functioning (DIF) analysis along with a different grouping technique. The grouping technique is based on the Q-matrix and diagnostic profiles (i.e., attribute mastery patterns and probabilities) from the RSM. For the validity evidence, it is expected to exhibit DIF for all test items in this study. The results indicated that approximately 90% of items were identified as DIF items that all favored the mastery groups. This suggests that the proposed attributes and Q-matrix with RSM work well to map Taiwanese students into appropriate attribute mastery patterns and to assign appropriate attribute mastery probabilities to them. This study also provides evidence that a DIF approach with the new grouping technique is a viable method for the validation research. More discussion and suggestions are presented in the paper. [ABSTRACT FROM AUTHOR]

In this article, the focus is on the entangled relations between digital technology, art activities, mathematics, literacy and children in Swedish preschool ateliers. As part of an ethnographic study, the researcher follows how children use digital technologies and non-digital materials (such as shells, pens, paper, wood, bubble wrap and light) to create and make the visual and aesthetic aspects of the technology seen. In the analysis of the children's play-based and art-oriented activities in the atelier, the subjects of literacy and mathematics become visible. The analytical approach includes the use of sociocultural theory and multimodal theory, and looking at mathematics in accordance with the six organising principles described by Alan Bishop. The results show that the children's activities with digital technology and non-digital artefacts appear to activate, expand and transform their understanding and use of literacy and mathematics. [ABSTRACT FROM AUTHOR]

In a large-scale quantitative study that adopted a learning analytics approach, we searched for associations between students' activity in a game-based online mathematics learning environment and their mathematics achievements on a national standardized test. Students were active in the environment throughout the school year, and particularly during an online National Mathematics Olympiad (N = 239 schools). Overall, our findings point to a positive association between online game-based activity during the Olympiad and mathematics test scores. This association remained even after controlling for socioeconomic factors, which are known to contribute to academic achievements. The paper discusses these findings and suggests evidence for causality, in particular cognitive, meta-cognitive, and affective effects of the online activity that may have positively affected test scores. [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]

Background & aims: In recent years, there has been an increased interest in analyzing the mathematical performance of students with learning difficulties in order to provide them with teaching methods adapted to their needs. In particular, the importance of studying the type of informal strategy that students use when solving problems has been highlighted. Observing how these strategies emerge and develop in children with learning difficulties is crucial, as it allows us to understand how they develop a subsequent understanding of arithmetic operations. In this paper we study the effect of explicit instruction in addition strategies, focusing on the minimum addend strategy, and analyze the difficulties that arise during this process. Methods: An adapted multiple-probe design across students with a microgenetic approach was employed to assess the effectiveness of the teaching instruction and the acquisition of the minimum addend strategy while solving addition word problems. The participants were three primary-school children (two boys and one girl) with learning difficulties, one of them diagnosed with autism spectrum disorder. The instruction on the minimum addend strategy was sequenced into levels of abstraction based on the addends represented with and without manipulatives. Results: The results show that the three participants were able to acquire the minimum addend strategy and transfer it to two-step problems. They all showed difficulties during the instructional process, with quantity comparison difficulties predominating. The instruction provided to address these and other difficulties is detailed for each participant. Conclusions: The teaching of the minimum addend strategy has proven effective, and all three students acquired it throughout the instruction. The results concerning the student diagnosed with autism spectrum disorder are especially interesting given the lack of studies that focus on the strategies employed by students with this disorder to solve arithmetic problems. In this sense, the use of the microgenetic approach was especially useful to observe the type of spontaneous strategies used by this participant, and how they varied in response to the instruction. Implications: Each study participant faced different difficulties and needed different periods of time to assimilate the new strategy. Conclusions are drawn for educators to help children with learning difficulties advance to more sophisticated strategies, so they can acquire these and subsequent mathematical concepts. [ABSTRACT FROM AUTHOR]

In this paper, we explore the challenges experienced by a group of Primary 5 to 6 (age 12–14) students as they engaged in a series of problem-solving tasks through block-based programming. The challenges were analysed according to a taxonomy focusing on the presence of computational thinking (CT) elements in mathematics contexts: preparing problems, programming, create computational abstractions, as well as troubleshooting and debugging. Our results suggested that the challenges experienced by students were compounded by both having to learn the CT-based environment as well as to apply mathematical concepts and problem solving in that environment. Possible explanations for the observed challenges stemming from differences between CT and mathematical thinking are discussed in detail, along with suggestions towards improving the effectiveness of integrating CT into mathematics learning. This study provides evidence-based directions towards enriching mathematics education with computation. [ABSTRACT FROM AUTHOR]

In the Amazonian literature, the scarcity of numerical terms and lack of interest in counting, which characterize diverse indigenous peoples in the region, are usually associated with linguistic issues or cultural limitations. My purpose in this paper is to take a different approach and relate the enumeration processes of one of these peoples, the Wari', to their conception of beings as intrinsically transformative, which affects the determination of quantities and the stability of sets. [ABSTRACT FROM AUTHOR]

With increased technology use in mathematics classrooms, as well as the increased prevalence of online instruction, digital calculators and online games are two types of digital tools that support students with learning disabilities (LD) in elementary and middle school mathematics. Teachers need to understand the advantages and limitations of different options and factors that help determine which tool may be most beneficial to support the goals of the mathematics lesson as well as the individual needs of students with LD. When used appropriately and efficiently, digital mathematics tools, such as calculators and online games, can increase students' conceptual understanding of mathematics content as well as their confidence and engagement in the mathematics classroom. This column presents a variety of virtual calculators and online math games, why they are effective, how they can be implemented, as well as a short scenario depicting one way the tool can be used in the classroom. [ABSTRACT FROM AUTHOR]

The article reports on intervention research on what works to improve the outcomes of students with learning disabilities or learning difficulties, opportunity gaps and achievement gaps for culturally and linguistically diverse (CLD) students with learning disabilities or learning difficulties. Topics include experience inequities in both access and achievement outcomes; and Inequities in education access and outcomes for CLD students with learning disabilities or learning difficulties.

Background: The field of mathematics education has made progress toward generating a set of instructional practices that could support improvements in the learning opportunities made available to groups of students who historically have been underserved and marginalized. Studies that contribute to this growing body of work are often conducted in learning environments that are framed as "successful." As a researcher who is concerned with issues of equity and who acknowledges the importance of closely attending to the quality of the mathematical activity in which students are being asked to engage, my stance on "successful learning environments" pulls from both Gutiérrez's descriptions of what characterizes classrooms as aiming for equity and the emphasis on the importance of conceptually oriented goals for student learning that is outlined in documents like the Standards. Though as a field we are growing in our knowledge of practices that support these successful learning environments, this knowledge has not yet been reflected in many of the observational tools, rubrics, and protocols used to study these environments. In addition, there is a growing need to develop empirically grounded ways of attending to the extent to which the practices that are being outlined in research literature actually contribute to the "success" of these learning environments. Purpose: The purpose of this article is to explore one way of meeting this growing need by describing the complex work of developing a set of classroom observation rubrics (the Equity and Access Rubrics for Mathematics Instruction, EAR-MI) designed to support efforts in identifying and observing critical features of classrooms characterized as having potential for "success." In developing the rubrics, I took as my starting place findings from an analysis that compared a set of classrooms that were characterized as demonstrating aspects of successful learning environments and a set of classrooms that were not characterized as successful. This paper not only describes the process of developing the rubrics, but also outlines some of the qualitative differences that distinguished more and less effective examples of the practices the rubrics are designed to capture. Research Design: In designing the rubrics, I engaged in multiple cycles of qualitative analyses of video data collected from a large-scale study. Specifically, I iteratively designed, tested, and revised the developing rubrics while consistently collaborating with, consulting with, and receiving feedback from different experts in the field of education. Conclusions: Although I fully acknowledge and recognize that there are several tensions and limitations of this work, I argue that developing rubrics like the EAR-MI is still worthwhile. One reason that I give for continuing these types of efforts is that it contributes to the work of breaking down forms of practice into components and identifying key aspects of specific practices that are critical for supporting student learning in ways that make potentially productive routines of action visible to and learnable by others, which may ultimately contribute to the development of more successful learning environments. I also argue that rubrics like the EAR-MI have the potential to support researchers in developing stronger evidence of the effectiveness of practices that prior research has identified as critical for marginalized students and in more accurately and concretely identifying and describing learning environments as having potential for "success." [ABSTRACT FROM AUTHOR]

This paper reports research into the relationship between personal and contextual variables and gendered differences in students' attainment in mathematics that take account of 'place' at different levels of intra-national locality (i.e. regional and macro-geographical levels, within the same country). A multilevel analysis performed on secondary data collected in Italy, where on average boys outperform girls in mathematics, showed that gender differences at local levels are complex and nuanced and not always consistent with the national picture. Moreover, gender differences in mathematics are associated with socio-cultural and economic factors that vary by region. We argue that educational research focusing on national and international level findings (such as for example PISA) should explore the association between gender differences in mathematics and sub-national socio-cultural and economic contexts in order to adequately inform policy and practice. Finally, we suggest that European researchers of inequality may need to attend to regionality and localities of place, and that the principle of subsidiarity could imply that policy and practice be devolved to the levels that research proves to be relevant. [ABSTRACT FROM AUTHOR]

Students' talent and potential cannot be served until they are recognized by schools or caregivers. While the field of gifted education has had success in identifying many students with talents in reading and mathematics, those with spatial talents are often overlooked. This article reviews how we might identify spatial talent using traditional tests as well as observations during planned activities. Identifying spatial talent is an area in need of further research and assessment development. [ABSTRACT FROM AUTHOR]

A robust finding in cognitive psychology is that training children's spatial abilities is an effective route to improving mathematics performance. Despite this finding, there is limited representation of spatial reasoning in school curricula. To bridge this gap between research and practice, we created the Spatial Reasoning Toolkit (SRT; Gifford et al., 2022). In Study 1, we provide quantitative data of practitioner knowledge of spatial reasoning (N = 94) and their intended use of the SRT (N = 74). One year after the toolkit was launched, we compare these samples to a sample of SRT users (N = 59). In Study 2, we present case studies from three different school settings of users of the SRT. Results demonstrate that practitioners judged the SRT to be very useful. As intended, practitioners used it mainly for professional learning and for planning, but confidence in their ability to define spatial reasoning was mixed. Three diverse case studies demonstrate flexibility in application of the SRT resources, exemplifying that every child is unique and might not conform to the 'typical' trajectory. Practitioner time was presented as a barrier; this limitation was somewhat overcome by presenting multiple resource types, but nevertheless highlighted the need to maximize accessibility when translating research to practice. [ABSTRACT FROM AUTHOR]

Children with mathematical difficulties need to spend more time than typically achieving children on solving even simple equations. Since these tasks already require a larger share of their cognitive resources, additional demands imposed by the need to switch between tasks may lead to a greater decline of performance in children with mathematical difficulties. We explored differential task switch costs with respect to switching between addition versus subtraction with a tablet-based arithmetic verification task and additional standardized tests in German elementary school children in Grades 1 to 4. Two independent studies were conducted. In Study 1, we assessed the validity of a newly constructed tablet-based arithmetic verification task in a controlled classroom-setting (n = 165). Then, effects of switching between different types of arithmetic operations on accuracy and response latency were analyzed through generalized linear mixed models in an online-based testing (Study 2; n = 3,409). Children with mathematical difficulties needed more time and worked less accurately overall. They also exhibited a stronger performance decline when working in a task-switching condition, when working on subtraction (vs. addition) items and in operations with two-digit (vs. one-digit) operations. These results underline the value of process data in the context of assessing mathematical difficulties. [ABSTRACT FROM AUTHOR]

In order to make appropriate educational recommendations, psychologists must understand how cognitive test scores influence specific academic outcomes for students of different ability levels. We used data from the WISC-V and WIAT-III (N = 181) to examine which WISC-V Index scores predicted children's specific and broad academic skills and if cognitive-achievement relations varied by general intelligence. Verbal abilities predicted most academic skills for children of all ability levels, whereas processing speed, working memory, visual processing, and fluid reasoning abilities differentially predicted specific academic skills. Processing speed and working memory demonstrated significant interaction effects with full-scale IQ when predicting youth's essay writing. Findings suggest generalized intelligence may influence the predictive validity of certain cognitive tests, and replication studies in larger samples are encouraged. [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]

Basic numerical abilities such as number line estimation have been observed repeatedly to be associated with mathematical achievement. Recently, it was argued that the association between basic numerical abilities and mathematical achievement is fully mediated by visuospatial abilities. However, arithmetical abilities have not yet been considered as influencing this association, even though solution strategies in number line estimation as well as mathematical achievement often involve arithmetical procedures. Therefore, we investigated the mediating role of arithmetical and visuospatial abilities on the association between number line estimation and mathematical achievement in a sample of n = 599 German elementary school students. The results indicated that arithmetical abilities as well as visuospatial abilities mediated the association between number line estimation and mathematical achievement. However, neither visuospatial nor arithmetical abilities fully mediated the association between number line estimation and mathematical achievement when considered in isolation. This substantiates the relevance of the intertwined development of visuospatial and arithmetical abilities as well as basic numerical abilities such as number line estimation (i.e., the combination of domain-specific numerical and domain-general abilities) driving mathematical achievement. [ABSTRACT FROM AUTHOR]

Introduction: When the United States adopted Nemeth Code within Unified English Braille (UEB) Contexts and UEB Math/Science in 2016, students who were using braille had to learn a new code for science, technology, engineering, and mathematics (STEM). In late 2016, Bell and Silverman surveyed students about their initial experiences transitioning to a new braille code. However, to date there has not been additional research that includes students' perspectives regarding the long-term effect of the transition to a new braille code on their ability to learn. The purpose of this study was to learn about students' experiences in transitioning to a new braille code, whether students receive STEM braille materials in a timely manner, the technology students use in STEM, and what advice students have for teachers of students with visual impairments. Methods: In the spring of 2021, 11 middle and high school students who use braille for STEM classes participated in one of three focus groups. The data were analyzed using open-coding methods. Results: All participants had initially learned the Nemeth Braille Code for Mathematics and Science Notation and subsequently transitioned to one of the new braille codes. Students typically characterized learning a new braille code as easy. Most of the students had experienced delays in receiving braille materials, which sometimes negatively affected their ability to learn. Students reported using a variety of mainstream and assistive technologies. Discussion: Students should have consistent access to high-quality STEM materials in a timely manner in the braille code that they prefer. The students in this study articulated their preferences and were willing to advocate for themselves to overcome learning challenges in their STEM courses. Implications for Practitioners: Teachers of students with visual impairments can partner with general education STEM teachers and administrators to resolve persistent issues. Teachers can encourage students to voice their preferences and assist students in developing strategies before challenges arise. [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]

With complex, visual concepts prevailing in science and mathematics curricula, these subjects are often inaccessible to students with visual impairments (VI), leading to their underrepresentation in science, technology, engineering and mathematics (STEM) careers. While researchers have identified strategies that can facilitate students with VI's learning within special schools, less is known about how students with VI access science and mathematics within a mainstream context, even though this is where the majority are educated. This seems important to address given the additional barrier students with VI face within mainstream schools, including negative attitudes from mainstream teachers. Consequently, the current study was conducted to explore how students with VI's access to and learning of science and mathematics can be improved within the mainstream context. Two interviews were conducted with qualified teachers of children and young people with vision impairment (QTVIs), revealing the importance of classroom adaptations, such as hands-on experience and increased lesson time, to facilitate students with VI's learning of science and mathematics. These findings are discussed in relation to policy and practice, suggesting mainstream teachers should be trained to make small but effective adaptations in their teaching, and that students with VI are given the opportunity to learn skills needed to become independent learners. [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]

Computational thinking (CT) has received much attention in mathematics education in recent years, and researchers have begun to experiment with the integration of CT into mathematics education to promote students' CT and mathematical thinking (MT) development. However, there is a lack of empirical evidence and new theoretical perspectives on the mechanisms of interaction between CT and MT. To address this research gap, this study analyses the participants' thinking processes in solving programming-based mathematical problems from a flexibility perspective, focusing on the interplay between computational and mathematical thinking, that is, how CT and MT work together to influence and determine the problem-solver's choice of solution strategy. Using data collected from a large design-based study, we summarise two types of flexibility and six subtypes of flexibility demonstrated by participants in the programming-based mathematical problem-solving process using thematic analysis. These different types of flexibility provide researchers and mathematics educators with new theoretical perspectives to examine the interplay of CT and MT. Findings will also contribute toward student learning characteristics in programming-based mathematical problem-solving to sketch the big picture of how CT and MT emerge in complementary or mismatching ways. [ABSTRACT FROM AUTHOR]

In our educational institution, despite significant progress in educational achievements, there is a prevalent issue of mathematics lessons focusing on rote memorization and superficial understanding, leading to learner dissatisfaction. This study presents a research project conducted by a group of five individuals, including myself as a teacher researcher and four other teachers. The project aimed to address this issue by employing a participatory action research approach. Through innovative planning, teaching, and evaluation methods, the research group successfully demonstrated how making mathematics more relevant and meaningful can increase student engagement and agency. The collaborative nature of the group fostered self-awareness among the teacher researchers regarding social justice issues within their mathematics classrooms. The research project highlighted the potential of mathematics as a powerful tool for developing students' understanding of social justice issues and establishing meaningful connections between these issues and mathematical concepts. Importantly, the project emphasized the significance of student agency, showcasing how collaborative and problem-solving approaches to teaching, coupled with student autonomy in selecting issues to explore and mathematical procedures to apply, can contribute to the development of student agency. [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]

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 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]

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]

The purpose of this study was to develop a framework for 3D subject-specific computational models capable of simulating velopharyngeal biomechanics for anatomic changes that occur following pharyngoplasty and to gain insight into biomechanical factors that may lead to different speech/surgical outcomes. Patient-specific models for two, matched participants with differing speech/surgical outcomes were developed: one with a successful pharyngoplasty outcome and one with a failed pharyngoplasty outcome. Surgical scenarios were simulated to model pharyngoplasty location, identify LVP muscle biomechanics, and identify an optimal pharyngoplasty location for each participant. These simulations illustrate the potential for optimizing pharyngoplasties based on patient-specific geometry. [ABSTRACT FROM AUTHOR]