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This case study demonstrates the application of an unsupervised topic modeling algorithm to 7,773 English-language articles published in the "Library Quarterly" from 1931 to 2015. The analysis of 85 years of the journal's output follows an exploratory data analysis framework to generate novel hypotheses about the history of LIS using topic modeling, a method for identifying clusters of co-occurring words within large collections of text. The paper closely examines two topics that suggest differences in gender representation in the journal to propose and support a new hypothesis regarding the historical inclusion of gendered objects of study in LIS literature.

The tidal forces generated by a black hole can be so powerful that they cause unlimited stretching, known as spaghettification. A detailed analysis of this phenomenon requires the use of Einstein's theory of general relativity. The aim of this paper is to offer an up-to-date and accessible analysis of spaghettification, in which the complex mathematics of Einstein's theory are replaced with the simpler and more intuitive concepts of Newtonian gravity. The article can serve as educational material for undergraduate modern physics or astronomy courses.

Calculus courses have been attracting the attention of mathematics education researchers over the last decades. Recent publications and special issues dedicated to calculus highlight the diverse roles of calculus courses in the pathways for STEM studies within and across educational levels, as well as issues related to the academic preparation of future STEM professionals, including mathematicians, non-mathematics professionals (NMPs) and teachers. In this paper, we review recent literature, mostly since 2015, to identify and characterize explicit references to such diverse roles of calculus courses. The review highlights an intrinsic tension between two institutional roles of calculus: "scaffolding" and "filtering." We find nuanced yet substantial variation in how the dual role of calculus is experienced and managed across different groups of students and stakeholders. With regard studies on calculus for mathematics students, recent studies attend to changes in the rules underpinning calculus notions and processes, and highlight the scaffolding potential of calculus courses towards abstraction and reasoning. In contrast, studies on calculus for NMPs report that such courses often promote filtering rather than scaffolding and question transferability and relevance of those courses for NMPs. Finally, studies challenge the perception that traditional tertiary calculus courses scaffold school teaching and underline the need for empirical research that would explain the nature of this scaffolding and how it can be realized in practice. We conclude that further empirical research, in particular theory development, is needed to address the diverse roles of calculus at the intersection of institutions, disciplines and communities.

The demand for engineering education and graduates is increasing daily because the current service and technological designs are unable to meet the needs of the society and the expected dramatic increase in the future. The emerging skill gap requires a shift in the type of expertise required of young professionals that will be needed to successfully lead organizations in the new economy. Researchers have identified various 'shapes' for the engineering professionals to make them relevant to the 21st century challenge, especially in the industry where their expertise is much needed. T-shaped professionals have skills that make them to be more preferred among others. The purpose of this paper is to present the need to upgrade engineering education curriculum to produce more T-shaped graduate engineers required in the changing industrial world. The potential benefits of T-shaped professionals to organizational performance are quite significant; hence, the demand for T-shaped professionals in knowledge-intensive, service-oriented economies is increasing. Unfortunately, the challenges associated with creating more T-shaped professionals are also significant. National regulatory bodies for engineering education in Nigeria are beginning to move towards integrated curriculum to break down discipline silos and produce T-shaped graduate engineers for the fast-changing industrial world. Service Science Management and Engineering (SSME) is an emerging discipline with over 250 programmes in 50 nations seeking to create more T-shaped professionals.

Understanding the intricate quantifier relations in the formal definitions of both convergence and continuity is highly relevant for students to use these definitions for mathematical reasoning. However, there has been limited research about how students relearn previous school mathematics for understanding multiply quantified statements. This issue was investigated in a case study in a 5-week teaching unit, located in a year-long transition course, in which students were engaged in defining and proving sequence convergence and local continuity. The paper reports on four substantial changes in the ways students relearn school mathematics for constructing quantified statements: (1) endorse predicate as formal property by replacing metaphors of epsilon strips with narratives about the objects [epsilon], N[subscript epsilon], and |a[subscript n] - a|; (2) acknowledge that statements have truth values; (3) recognize that multiply quantified statements are deductively ordered and that the order of its quantifications is relevant; and (4) assemble multiply quantified statements from partial statements that can be investigated separately. These four changes highlight how school mathematics enables student to semantically and pragmatically parse multiply quantified statements and how syntactic considerations emerge from such semantic and pragmatic foundations. Future research should further investigate how to design learning activities that facilitate students' syntactical engagement with quantified statements, for instance, in activities of using formal definitions of limits during proving.

Mathematical modelling has been included in many mathematics curricula worldwide, and China's curricula are no exception. The development of modelling competencies has recently been listed among the Chinese mathematics curriculum's six key objectives. However, the manner in which nationwide learning and teaching of modelling should be conducted presents a key challenge to China's schools, most of which are wholly lacking in experience of this practice. In this study we present a thematic analysis of the conceptions of four mathematicians, five mathematics educators and seven mathematics teachers, with regard to the learning and teaching of modelling. The results show that the participants' views of modelling can be categorised and linked to the following theoretical perspectives of modelling: applied, epistemological, educational, pedagogical and conceptual perspectives. Interestingly, the mathematicians and mathematics educators tended towards the atomistic approach to the learning and teaching of modelling, while the mathematics teachers placed greater emphasis on the holistic approach. The mathematicians and mathematics educators stressed student autonomy, while the teachers emphasised teacher demonstration. All participants considered group work to be an appropriate means of conducting modelling learning and teaching. Additionally, some teachers were concerned that modelling could not be incorporated into mathematical teaching and learning if it could not be included in high-stakes examinations. The paper concludes with a discussion on the rationale behind the existence of the various conceptions and the potential insights that may be drawn from these conceptions.

The teachers of mathematics education in China have gradually demonstrated the need for the systematic theory about mathematics education. However, the philosophy of mathematics education is biased towards the academic level, and there are few "readable materials" for direct application in practice. This paper prepares a curriculum system for the philosophy of mathematics education for normal students (the students of teaching universities). The purpose is to stimulate the discussion of the philosophy of mathematics education among the (future) mathematics teachers for practical guidance, to implant the necessary "genetic genes" for the benign development of mathematics education.

This paper serves two purposes. First, it offers an overview of the role of the Mathematical Markup Language (MathML) in representing mathematical notation on the Web, and its significance for accessibility. To orient the discussion, hypotheses are advanced regarding users' needs in connection with the accessibility of mathematical notation. Second, current developments in the evolution of MathML are reviewed, noting their consequences for accessibility, and commenting on prospects for future improvement in the concrete experiences of users of assistive technologies. Recommendations are advanced for further research and development activities, emphasizing the cognitive aspects of user interface design.

This paper explores a system that attempts to maximize high school students' sense of choice when selecting elective subjects. We propose that individual schools can tailor the combinations of subjects they offer in order to maximize the number of prospective students who can study their preferred subjects, potentially increasing enrolment numbers and academic outcomes while also reducing administrative overheads. We analyze the underlying computational problem encountered in this task and describe a suitable AI-based optimization algorithm that we have made available for free download. We also discuss some outcomes of using this method on a small number of case study schools.

This paper reports the results of three questionnaires applied to sixty-seven students preparing to become university-level mathematics teachers; the questionnaires were focused on knowing their conceptions and their mastery of the representations of functions in the development of power series. The theoretical and methodological background rests on the Mathematics Teacher's Specialised Knowledge (MTSK), specifically in the domain: Mathematical Knowledge (MK). As a result of the analysis of the responses to the questionnaires, it was identified that the notion of development of power series played an important role as a means of justification and that, from the three notions addressed (Taylor's Formula, limited development, development of power series), this was the most prevalent in the mind of the students. These results will be used as the starting point for the development of proposals that improve the teaching and learning of the subject of study.

This paper provides a current and thorough review of the literature on the use of video modeling for students with learning disabilities published over the last four and a half decades. Eight video modeling intervention studies were retrieved and grouped into four areas: (a) mathematics, (b) reading, (c) social studies, and (d) social behavior. Effect sizes were computed to estimate the effectiveness of the video modeling interventions included in this review. Overall, the findings showed moderate to very large effects on students' academic skills and social behaviors for seven of the eight studies.

In this paper, we describe our solution to predict student STEM career choices during the 2017 ASSISTments Datamining Competition. We built a machine learning system that automatically reformats the data set, generates new features and prunes redundant ones, and performs model and feature selection. We designed the system to automatically find a model that optimizes prediction performance, yet the final model is a simple logistic regression that allows researchers to discover important features and study their effects on STEM career choices. We also compared our method to other methods, which revealed that the key to good prediction is proper feature enrichment in the beginning stage of the data analysis, while feature selection in a later stage allows a simpler final model.

Collaborative problem solving (CPS) is an important 21st-century skill for academic and career success, and as a result, there is increased interest among businesses and educational institutions in the assessment and development of CPS skills. CPS skills are difficult to measure using traditional forms of assessment, and that difficulty has led to the use of computer environments that allow individuals to interact in complex situations and capture all actions throughout the process. In the current paper, we describe the design of a collaborative online mathematics task and explore student perceptions of the task and the extent to which the task elicits CPS skills. Results revealed areas of difficulty for students and showed that the task mostly elicited skills associated with the social dimension of CPS. We describe modifications to the task to provide better opportunities for students to display a broader range of CPS skills. An upcoming larger scale pilot study will explore whether the redesigned task can elicit the less observed CPS skills.

Visuospatial thinking is considered crucial for understanding of three-dimensional spatial concepts in STEM disciplines. Despite their importance, little is known about the underlying cognitive processing required to spatially reason and the varied strategies students may employ to solve visuospatial problems. This study seeks to identify and describe how and when students use imagistic or analytical reasoning when making pen-on-paper predictions about molecular geometry and if particular reasoning strategies are linked to greater accuracy of responses. Student reasoning was evidenced through penon-paper responses generated by high attaining, high school students (N = 10) studying Valence Shell Electron Pair Repulsion (VSEPR) Theory in their final year of chemistry. Through analysis and coding of students' open-ended paper-based responses to an introductory task, results revealed that students employed multiple reasoning strategies, including analytical heuristics and the spontaneous construction of external diagrammatic representations to predict molecular geometry. Importantly, it was observed that despite being instructed on the use of VSEPR theory to find analytical solutions, some students exhibited preference for alternative reasoning strategies drawing on prior knowledge and imagistic reasoning; showing greater accuracy with 3D diagrammatic representations than students who used the algorithmic method of instruction. This has implications for both research and practice as use of specific reasoning strategies are not readily promoted as a pedagogical approach nor are they given credit for in national examinations at school level.

The aim of the study reported in this paper was to explore and enhance experienced school mathematics teachers' knowledge of students'thinking, as it is manifested in practice. Data were collected from records of classroom observations, interviews with participating teachers, and weekly teacher-researcher meetings organized in the school. In this paper, we discuss the mathematical challenges faced by a primary school teacher as she attempts to unpack the structure of the division algorithm, while teaching in a Grade 4 classroom. Through this case study, we exemplify how a focus on mathematical knowledge for teaching 'in situ' helped in triggering a change in the teacher's well-formed knowledge and beliefs about the teaching and learning of the division algorithm, and related students' capabilities. We argue that in the context of educational reform, an analysis of knowledge demands placed on the teacher helps in understanding and supporting teachers' work.

The paper focuses on the parallels, which are rooted in the simultaneous development of mathematics and informatics. Both mathematics and informatics are based on problem-solving. However, the approaches to determining problems, solution techniques and interpretation of results are different. The paper shows different approaches of mathematics and informatics for solving a simple problem from the informatics competition. It was presented for students, who would be future informatics teachers, and it has become the beginning of the discovery of unexpected relationships and rules' chain, the source of successive tasks, and various methods of their solution. The paper brings the results of the constructivist teaching of students in the form of a fictional interview of mathematician and informatician. Fictional cooperation of a mathematician and an informatician in analysing and solving problems will allow for a detailed analysis and comparison of both fields, which will lead to determining both common and different elements.

The Computer Science Unplugged activities and project has been an influential STEM (Science, Technology, Engineering & Mathematics) initiative, providing enrichment and teaching activities supporting computational thinking. Many of its activities are suitable for children. One of the most popular Unplugged activities is "Kid Krypto", invented by Mike Fellows and Neal Koblitz. Kid Krypto demonstrates the mathematics underlying public-key cryptography without using advanced mathematics. The paper gives an example of a Kid Krypto-style encryption system that is based on disjoint cycles in a graph or network and which is accessible to a very young audience. Also described is the original Kid Krypto system which is based on a version of dominating set called perfect code. The paper urges research scientists to participate in mathematical sciences communication and outreach.

In the lead up to the 2016 election, fake news often "outperformed" actual news in users' social media feeds. This paper attempts to analyze the process in which fake news proliferates social networking sites and presents a method of understanding and articulating ways in which personalized feeds are shaped by algorithm-based user feedback. The algorithm systems are embedded programs that analyze past user data and search history in combination with other users' searches and history to calculate digital outcomes, anticipate possible recommendations, and present consumers with feeds that represent their own unique immersive media environments. Users may tend to believe misinformation or fake news regardless of their information echo-chamber, but rather as a result of algorithms tailoring cultural artifacts customized to the user in social media information and distribution systems. Social media platforms create user categories based on data collected through online behavior as well as data collected offline in "dataveillance" methods. Further complicating an understanding of information network analysis is the general "invisibility" of the algorithm in end-user interaction within social networking sites. When consuming digital media on various digital platforms, users often access media without interrogating how fake news is designed to find its way into user algorithms and social feeds. This paper analyzes how the algorithm itself should be considered an immersive media environment that permits users to consume unique media feeds that may affect civic actions.

The secondary-school mathematics curriculum is narrow in scope and technical in character; this is quite different from the nature of the discipline itself. As a result, it offers little inspiration to both students and teachers, and provides students with poor preparation for university mathematics courses and indeed for life. Over the past century, recently more than ever, there have been calls for change, for a curriculum that is true to the subject of mathematics as the creation and study of patterns and structures. While there are hopeful responses to this at the elementary level, there is almost nothing at the secondary level. Ironically, it is felt that in order to prepare students for university calculus, the secondary curriculum simply has to be what it is. This is a special case of a myth that needs to be destroyed.

The paper investigates how the order of numerical data in word problems on division of a whole into unequal parts affects achievement and reasoning of 14-16-year old pupils. The variable was altered in two word problems, in one of which also the context was changed (psychological variable) and in the latter "if-clause" is or is not used (linguistic variable). 182 pupils were involved in the experiment. The solutions were analysed quantitatively using Item Response Theory as well as qualitatively. The data suggest that pupils' success is affected by the order of numerical data in the statement in an unfamiliar context. The presence of "if-clause" in the statement was studied in a two-level problem. The order of numerical data played its role in case of formulations without "if". The results of the experiment are of interest for mathematics education as well as for construction of tests. The paper is an extended version of the paper by Novotná (2018).

Mathematics and science are important concepts that children's encounter in both daily and educational life. Early childhood is the time in which the first ideas of the mathematics and science developed. In this study, we investigated children's perceptions about mathematics and science through metaphors in terms of being able to provide rich information. This study was qualitative research in the form of phenomenological. Participants consisted of 88 children from five and six years old groups. As a data collection tool, we used a semi-structured interview form. As a result of the analysis, we found out that there were five positive and one negative category about mathematics. The category that was used most commonly about mathematics was "mathematics as a part of education". On the other hand, all of the metaphors about science were in the positive category. Metaphors about science were grouped under four categories. The category that included the highest number of metaphors was "science that involves phenomena and creatures in nature". In conclusion, children's metaphors about mathematics included elements such as "homework, line, and course", while the metaphors about science included elements such as "nature, curiosity, and research". [This article has been presented EJER Congress Antalya, Turkey, 2018.]

Education plays a major role in the development of the consciousness of the whole society. Education has been improved by analyzing educational data related to student academic performance. By using data mining techniques and algorithms on data from the educational environment, students' performances can be predicted. In this study, a novel Hybrid Ensemble Learning Algorithm (HELA) is proposed to predict the academic performance of students. The prediction results obtained from base classifiers namely Gradient Boosting, Extreme Gradient Boosting, Light Gradient Boosting Machine, and different combinations of these algorithms are given as input to the Super Learner algorithm. Hyper-parameters of base classifiers are optimized with a Random Search algorithm. Students' performances in Math and Portuguese classes are predicted by the proposed algorithm. In the experimental results, 96.6% and 91.2% accuracy values are obtained for the Mathematics course, and the Portuguese course, respectively. This paper is the first study, to our knowledge, to integrate the boosting and stacking-based ensemble learning algorithm for the prediction of students' academic performance that gives better predictive results with high efficiency.

In this paper, the construct of 'uncertainty' in professional mathematics is investigated in relation to mathematical creativity. Specific focus is on 'Big C' research mathematicians' conceptions of what uncertainty means and ways in which it influences their research. Based on the hypothesis that uncertainty is both a catalyst and a necessary condition for creativity, a qualitative research design was used to obtain and analyze data from a 4-year study involving 18 research mathematicians who were at the forefront of their research domains. Data analysis using analytic induction confirmed the hypothesis that uncertainty plays an important role as a catalyst of mathematical creativity. The emergent categories from qualitative analysis revealed a dialectic or tension between (1) logic versus heuristics (synthetic versus analytic), (2) learner-researcher and researcher-learner transition, (3) axiom tweaking versus constraints. The findings of the study indicate that textbooks, unexpected moments, risk taking, and a community of support play a crucial role and characterize the interplay of uncertainty with mathematical creativity. The schema for understanding the dialectics of uncertainty sheds new light on an hitherto unexplored aspect of mathematical creativity, namely, uncertainty, vital for the development of mathematicians as researchers in addition to the growth of their discipline.

Recently, machine learning (ML) has evolved and finds its application in higher education (HE) for various data analysis. Studies have shown that such an emerging field in educational technology provides meaningful insights into several dimensions of educational quality. An in-depth analysis of the application of ML could have a positive impact on the HE sector. However, there is a scarcity of a systematic review of HE literature to gain from the overarching trends and patterns discovered using ML. This paper conducts a systematic review and meta-analyses of research studies that have reported on the application of ML in HE. The differentiating factors of this study are primarily vested in the meta-analyses including a specific focus on student academic performance, at-risk, and attrition in HE. Our detailed investigation adopts an evidence-based framework called PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) for reporting the findings of our systematic review and meta-analyses of literature on the use of ML models, algorithms, evaluation metrics, and other criteria, including demographics for assessing student academic performance, at-risk and attrition in HE. After undergoing the PRISMA steps such as selection criteria and filtering, we arrive at a small-scale dataset of 89 relevant studies published from 2010 to 2020 for an in-depth analysis. The results show the outcomes of the quantitative analysis of the application of ML types, models, evaluation metrics, and other related demographics and provide quality insights of publication patterns and future trends towards predicting and monitoring student academic progress in HE.

In this paper, we examine mathematicians' views on the value of advanced mathematics for secondary mathematics teachers. The data comprise semi-structured interviews with 24 mathematicians from 10 universities. The findings indicate that the value of advanced mathematics courses for prospective secondary mathematics teachers lies in their potential to offer connections across mathematical domains, mathematical experience for the development of problem-solving abilities, and increased epistemological awareness of the subject. Additionally, mathematicians' examples that connect advanced and school mathematics are presented and discussed. While the mathematicians provided rich examples of such connections, we noted that such examples were relatively scarce and accordingly sought possible explanations in the discussion of the findings.

Patterns and generalization are one of the most fundamental aspects of mathematics, which makes recent decades, mathematical tasks which include patterns, whether they are numerical or graphical, are mostly used, for example researching generalization. The aim of this paper is to investigate how a special kind of task concerning well-known palindromes can diversify the process of generalization in three different age groups of students. More precisely, the paper includes the analysis of solutions of one task concerning counting of numbers of palindromes by middle school, high school and university students with the special attention for finding similarities and differences among advance of process of generalization and using methods of solving in researched groups. The researched groups chosen randomly from two distant part of Poland, were consisted of 44 middle school students, 102 high school students and 51 university students (including 42 pre-service teachers). All students solved the same task in limited time without any assistance of teachers. The research was carried out between 2013 and 2015.

Here, we systematically review research on teaching knowledge in the context of undergraduate STEM education, with particular attention to what this research reveals about knowledge that is important for evidence-based teaching. Evidence-based teaching can improve student outcomes in undergraduate STEM education. However, the enactment of promising evidence-based teaching strategies depends greatly on the instructor and potentially on the teaching knowledge they are able to deploy. The review includes an overview of prevalent teaching knowledge theory, including pedagogical content knowledge, mathematical knowledge for teaching, and pedagogical knowledge. We compare and contrast teaching knowledge theory and terminology across STEM disciplines in order to build bridges for researchers across disciplines. Our search for peer-reviewed investigations of teaching knowledge in undergraduate science, engineering and mathematics yielded 45 papers. We examined the theoretical frameworks used in each study and analyzed study approaches, comparing across disciplines. Importantly, we also synthesized findings from research conducted in the context of evidence-based teaching. Overall, teaching knowledge research is sparse and siloed by discipline, and we call for collaborative work and better bridge-building across STEM disciplines. Though disciplinary divergences are common in discipline-based education research, the effect is magnified in this research area because the theoretical frameworks are themselves siloed by discipline. Investigations of declarative knowledge were common, and we call for increased attention to knowledge used in the practice of teaching. Finally, there are not many studies examining teaching knowledge in the context of evidence-based teaching, but the existing work suggests that components of pedagogical content knowledge, pedagogical knowledge, and content knowledge influence the implementation of evidence-based teaching. We describe implications for future teaching knowledge research. We also call on those who develop and test evidence-based strategies and curriculum to consider, from the beginning, the teaching knowledge needed for effective implementation.

Given the vast experiences pre-service mathematics teachers (PSMTs) have with functions, one may assume that they have existing personal definitions and concept images. The purpose of this paper is to build an understanding of the variety of images that one might associate with a definition of function that includes 'for each input there is one output' and how these images are coordinated with the definition to determine whether an object is a function or not. Two cases are presented to describe PSMTs who were working from the same personal definition of function, yet used that definition differently within a task designed around the function concept. The task itself was novel in that it is presented in a non-algebraic context, namely a vending machine. As such, PSMTs were required to coordinate their personal definition and images within the novel context. Attending to PSMTs' concept images revealed that though they were working from the same personal definition, images they drew upon to determine whether or not an object is a function were varied.

Purpose: The purpose of this study is, First, to leverage the limitation of annotated data and to identify the cognitive level of learning objectives efficiently, this study adopts transfer learning by using word2vec and a bidirectional gated recurrent units (GRU) that can fully take into account the context and improves the classification of the model. This study adds a layer based on attention mechanism (AM), which captures the context vector and gives keywords higher weight for text classification. Second, this study explains the authors' model's results with local interpretable model-agnostic explanations (LIME). Design/methodology/approach: Bloom's taxonomy levels of cognition are commonly used as a reference standard for identifying e-learning contents. Many action verbs in Bloom's taxonomy, however, overlap at different levels of the hierarchy, causing uncertainty regarding the cognitive level expected. Some studies have looked into the cognitive classification of e-learning content but none has looked into learning objectives. On the other hand, most of these research papers just adopt classical machine learning algorithms. The main constraint of this study is the availability of annotated learning objectives data sets. This study managed to build a data set of 2,400 learning objectives, but this size remains limited. Findings: This study's experiments show that the proposed model achieves highest scores of accuracy: 90.62%, F1-score and loss. The proposed model succeeds in classifying learning objectives, which contain ambiguous verb from the Bloom's taxonomy action verbs, while the same model without the attention layer fails. This study's LIME explainer aids in visualizing the most essential features of the text, which contributes to justifying the final classification. Originality/value: In this study, the main objective is to propose a model that outperforms the baseline models for learning objectives classification based on the six cognitive levels of Bloom's taxonomy. In this sense, this study builds the bidirectional GRU (BiGRU)-attention model based on the combination of the BiGRU algorithm with the AM. This study feeds the architecture with word2vec embeddings. To prove the effectiveness of the proposed model, this study compares it with four classical machine learning algorithms that are widely used for the cognitive classification of text: Bayes naive, logistic regression, support vector machine and K-nearest neighbors and with GRU. The main constraint related to this study is the absence of annotated data; there is no annotated learning objective data set based on Bloom's taxonomy's cognitive levels. To overcome this problem, this study seemed to have no choice but to build the data set.

Personalized learning systems use several components in order to create courses adapted to the learners'characteristics. Current emphasis on the reduction of costs of development of new resources has motivated the reuse of the e-learning personalization components in the creation of new components. Several systems have been proposed in the literature. Each system implements a specific approach and includes a set of software components. However, many of these components are not easily reusable. This paper proposes an architecture, which aims to improve the representation of learning components in a reusable and interoperable way. As a result, these components could be integrated easily for the creation of personalized learning courses. This architecture consists of five main packages: learner model, adaptation model, reuse facilities, learner interface and pedagogical knowledge. An experiment is conducted to validate the proposed architecture. The obtained results illustrate the optimal composition of e-learning personalization components through an example.

This paper explores the associations between math-gender stereotypes and two dimensions of student engagement -- class engagement and disengagement -- among Russian engineering students. The data collected in three Russian universities (n = 2,074) were utilised. Structural equation modelling was employed to test hypotheses about relationships between key variables and their variations for male and female subsamples. We revealed that the students' attribution of math-gender stereotypes to faculty slightly decreased class engagement and increased disengagement for both male and female students. Therefore, we hypothesise that male students can be more overconfident about their future performance in exams on math-related subjects because of a better reputation in the eyes of instructors, which can result in less engagement and, as a consequence, lower academic outcomes. These findings demonstrate the high importance of faculty in encouraging engineering student engagement and providing a bias-free learning environment.

The student profile has become an important component of education systems. Many systems objectives, as e-recommendation, e-orientation, e-recruitment and dropout prediction are essentially based on the profile for decision support. Machine learning plays an important role in this context and several studies have been carried out either for classification, prediction or clustering purpose. In this paper, the authors present a comparative study between different boosting algorithms which have been used successfully in many fields and for many purposes. In addition, the authors applied feature selection methods Fisher Score, Information Gain combined with Recursive Feature Elimination to enhance the preprocessing task and models' performances. Using multi-label dataset predict the class of the student performance in mathematics, this article results show that the Light Gradient Boosting Machine (LightGBM) algorithm achieved the best performance when using Information gain with Recursive Feature Elimination method compared to the other boosting algorithms.

Learning mathematics is as much about developing relationships with mathematics as the development of mathematics concepts and skills. Mathematics clubs usually support learners to develop relationships with mathematics through engaging with challenging mathematics problems, exploring mathematical ideas, and communicating and sharing their ideas. This paper reports on research on such a mathematics club. Data sources included learners' mathematics results, short written responses after club sessions and interviews with club learners. Data were analysed quantitatively and qualitatively. The study shows that club learners' school results improved relative to non-club learners, that learners' experiences of mathematics in club and class were very different from each other and that the club supported different relationships with mathematics than learners experienced in class. The study suggests that mathematics clubs can support learners' positive relationships with mathematics.

In the disciplines of dance and mathematics, binary identities commonly split individuals into either (non)dance and/or (non)math people. However, these shorthand assessments become dangerous because they constrain disciplinary knowledge, and limiting one's identity and capabilities remains antithetical to broad education goals. Capitalizing on dance as a situated, embodied form of knowledge, as well as an engaging, interactive, and social endeavor, we facilitate instruction that uses a dance-based approach to teach geometric transformations in a teacher education program. In this paper, we discuss findings from a case study intervention in a graduate-level geometry education course where we engaged participants in this transformations dance activity. We ask: What disciplinary practices did participants use in a dance-based intervention on geometric transformations? And, how did they use them? We found that the parallel disciplinary practices that the participants engaged in, in dance and mathematics, sheds light on a need in education to resist binary identities and to encourage inquiry-based practices. We aim to inspire future professional development and collaborative teaching opportunities for dance teachers in math and math teachers in dance, along with research that investigates intersections of learning, practice, and identity, particularly in dance + math.

Shulman (1986) conceptualized pedagogical content knowledge (PCK) at the intersection of content knowledge and pedagogical knowledge. In this paper, I re-explore the intersection of content--in our case, mathematics--and pedagogy, not in terms of domains of knowledge, but in terms of domains of practice. I conceptualize, describe, and exemplify what ideas at the intersection of mathematical practices and pedagogical practices might mean--which I refer to as pedagogical mathematical practices (PMPs)--and then explore what the potential implications for such a construct might be in teacher education, and how it might be useful for, and used by, the field.