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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]

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]

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]

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]

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]

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 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]

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]

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]

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]

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]

Purpose: Department heads play a pivotal role in the functioning of departments in secondary schools. However, quantitative research about the role of departmental leadership for the development of professional learning communities (PLCs) in subject departments in secondary schools remains scarce. As PLCs are seen as promising contexts for teachers’ continuous professional development, it is highly relevant to study how department heads can facilitate PLC characteristics in their department. Research methodology: This study examines how two dimensions of departmental leadership (group- and development-oriented) relate to interpersonal PLC characteristics in departments. Survey data were collected from 248 experienced mathematics and French teachers in 62 departments in secondary schools in Flanders (Belgium). Two multilevel regression analyses were conducted with collective responsibility and reflective dialogue as dependent interpersonal PLC characteristics. We controlled for several demographic teacher variables and structural departmental variables. Findings: Our results nurture optimism about the potential of departmental leadership for interpersonal PLC characteristics. More specifically, teachers who perceive high group-oriented departmental leadership experience more collective responsibility in their department. Furthermore, teachers’ perceptions of both group-oriented and development-oriented departmental leadership are significantly related to the reported frequency of teachers’ reflective dialogues. Implications: This study suggests that department heads play a critical role in facilitating interpersonal PLC characteristics in departments. As a result, department heads need to be carefully selected and adequately supported. As this article is one of the first to offer a quantitative perspective on this matter, it offers an instrument for future studies and informs policy about departmental leadership practices. [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 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]

This paper aimed at investigating the impacts of some cultural, social and economic factors of the students' families on the students' education and attitude toward mathematics. This study has been carried out through the use of data envelopment analysis. Data envelopment analysis is a linear programming method that its main purpose is to compare and evaluate the efficiency of a number of similar decision-making units, and to compare and analyze them, which have different values of consumed inputs and produced outputs. In this study, the inputs are the various aspects of cultural, social and economic conditions (such as family income, physical and mental health condition of the family members, and parents' occupation) of the families of 300 sixth-grade elementary school students in district 4 of Tehran, and the outputs are the extent of achievement in the mathematics test and the interest of the students of the mentioned schools to the activities related to the mathematics course and moral discipline. After the completion of the investigations, the effective and ineffective units were identified and the results were completely interpreted. [ABSTRACT FROM AUTHOR]

Agreement studies are of paramount importance in various scientific domains. When several observers classify objects on categorical scales, agreement can be quantified through multirater kappa coefficients. In most statistical packages, the standard error of these coefficients is only available under the null hypothesis that the coefficient is equal to zero, preventing the construction of confidence intervals in the general case. The aim of this paper is triple. First, simple analytic formulae for the standard error of multirater kappa coefficients will be given in the general case. Second, these formulae will be extended to the case of multilevel data structures. The formulae are based on simple matrix algebra and are implemented in the R package "multiagree". Third, guidelines on the choice between the different mulitrater kappa coefficients will be provided. [ABSTRACT FROM AUTHOR]

While it is well established that the structure and organization of the education system affects youth transitions, less attention has been paid to the study of qualitative distinctions at the same level of education over time in the Irish context. Using data from the School Leavers' Survey over the period 1980-2006, this paper considers the hypothesis of effectively maintained inequality in the case of the Republic of Ireland. The data capture young people's transitions during three distinct and remarkable macro-economic fluctuations, and makes a particularly interesting test case for EMI. Over the cohorts under investigation, Ireland had changed from a recessionary economic climate and prolonged economic stagnation for much of the 1980s to a booming economy by the middle of the mid-2000s and one of the most dynamic economies in the world during the "Celtic Tiger" period. The patterns of social-class inequality over a 30-year paper reported in this article suggest that qualitative differences at the same level of inequality represent a persistent barrier to greater equality in the Irish context. Specifically, we find three notable patterns to support the hypothesis of EMI with regard to tracking decisions taken in the transition from lower secondary to upper secondary, subject-level differentiation in the upper secondary mathematics curriculum, and access to university higher education. [ABSTRACT FROM AUTHOR]

This paper written as a dialogue between two interlocutors, Julie and a Student, deals with Understanding and its role in the social sciences. The fictional dialogue takes place in Hannover, Germany, and the interlocutors are exchanging arguments about Verstehen and how it should be conceptualized in the philosophy of the social sciences. A range of different approaches is discussed and a naturalistic strategy emerges as a defensible alternative. [ABSTRACT FROM AUTHOR]

From ancient times, the traditional architectural practice 'Vastusastra' is rigidly followed and practised in many parts of the Indian sub-continent and has a unique position in Indian architecture. In Indian traditional domestic architecture, a hand calculator table and an index number system are used for finding the proportion and orientation of the building. The mathematical and logical background of this traditional practice, which is not known at present, is investigated in this paper. The study reveals that there is a strong and complex mathematical background behind this traditional architectural practice. [ABSTRACT FROM AUTHOR]

This article introduces the thematic special series on intersection of mathematics education and special education. This special series will include four research papers and one commentary. The four research papers rooted in a working group from the annual conferences of the International Group of the Psychology of Mathematics Education (PME) as well as its North American Chapter (PME-NA). [ABSTRACT FROM AUTHOR]

Students with mathematics difficulties and learning disabilities (LD) typically struggle with solving word problems. These students often lack knowledge about efficient, cognitive strategies to utilize when solving word problems. Cognitive strategy instruction has been shown to be effective in teaching struggling students how to solve word problems that employ specific word problem types. The cognitive strategy, Math Scene Investigator (MSI), is an example of a cognitive strategy for word problem solving. The MSI strategy described in this paper is suitable for primary-level students with mathematics difficulties and LD. Instructional steps are provided along with an example of an interactive lesson. [ABSTRACT FROM PUBLISHER]

Low temperature diesel combustion has been widely investigated over the last few years for reducing in-cylinder emissions of Direct Injection (DI) diesel engines without sacrificing efficiency and fuel consumption. The spatial distribution of the fuel within the combustion chamber and the air-fuel mixing quality are the key factors affecting temperature generation within the cylinder. Avoiding fuel rich areas within the cylinder can significantly reduce the local high temperatures resulting in low NOx formation. This paper investigates the effects of the combustion chamber geometry and spray angle on the air-fuel mixing and emissions formation of a DI diesel engine. A new quantitative factor measuring the air-fuel mixing quality has been adopted in order to analyze and compare air-fuel mixing quality for different piston geometries. The results have shown that pistons with a narrow entrance and a deep combustion re-entrant chamber benefit from increased air-fuel mixtures due to the significantly higher swirl generated within the cylinder. However, the improved air-fuel mixing does not consequently lead to a reduced NOx generation, which is highly affected by the combustion efficiency of the engine. [ABSTRACT FROM AUTHOR]

This paper presents a methodology to control construction task complexity and examined the relationships between construction performance and spatial and mathematical abilities in children. The study included three groups of children (N = 96); ages 7–8, 10–11, and 13–14 years. Each group constructed seven pre-specified objects. The study replicated and extended previous findings that indicated that the extent of component symmetry and variety, and the number of components for each object and available for selection, significantly predicted construction task difficulty. Results showed that this methodology is a valid and reliable technique for assessing and predicting construction play task difficulty. Furthermore, construction play performance predicted mathematical attainment independently of spatial ability. [ABSTRACT FROM AUTHOR]