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Context is a key element in statistics education. The objective of this study is to examine the capacity of 14- and 15-year-old students to work with real data, analyse statistical graphs and frequency tables and interpret statistical data in its context. The results of the descriptive, exploratory analysis show that most students were correctly able to analyse and interpret data presented through statistical graphs and tables. However, some students had difficulties when it came to identifying the represented variables. More difficulties arose when calculating and interpreting means and medians — generally produced from the use of class midpoints — and making decisions. Students made little use of the context the data were presented in. Results reinforce the importance of using context in the teaching of statistics, encouraging justified decision-making. [ABSTRACT FROM AUTHOR]

Previous research in mathematics education has explored teachers' conceptions of mathematics and its teaching and learning, and how their instructional tendencies (e.g., "traditional", "technological", "spontaneous" and "investigative") relate to these conceptions. However, empirical evidence on this topic from large samples of pre-service teachers is limited. This study adapts and validates an instrument originally designed for in-service teachers to analyse the conceptions of mathematics and mathematics teaching and learning. This was done in a sample of undergraduate students in several different degree programmes (primary education, mathematics, and the education itinerary in psychology) in a Spanish university. Existing theory about instructional tendencies and conceptions of mathematics teaching and learning that was developed in the context of in-service teachers is then re-examined in the context of empirical evidence from this sample of individuals (all potential future teachers) without teaching experience. Results show that items from the instrument can be separated into four factors focussed on investigative stances, the role of textbooks, the role of teachers and lesson planning. Individual participants are not characterised by single tendencies; rather, they can be described in terms of several combinations of tendencies, grouped into four clusters. In line with the previous literature on in-service teachers, results suggest that conceptions of mathematics and its teaching and learning are not best captured by rigid, sharply delineated profiles. Rather, individuals configure their own conceptions in terms of combinations of different characteristics of prototypical tendencies. [ABSTRACT FROM AUTHOR]

Background: Only a few months before starting university, more than 50% of Spanish high-school students do not know what course to choose. Data from the Ministry of Education show that dropout rates reach 40% in some Spanish communities. This study aims to analyse the most important reasons behind students’ choices of degree course and the sources of information they use to help them choose depending on the type of the school and the field of study chosen. Method: A sample of 2,254 students from all over Spain completed two previously validated questionnaires. Results: The results showed that in general terms, intrinsic motives were more highly valued. The sources of information that students used most and rated more highly were university websites and family advice. Students from private schools rated guidance activities organized by universities more highly than students from state schools. Mann-Whitney U and Kruskal-Wallis statistics showed that the intrinsic component was more highly valued by students who wanted to study degrees in the fields of Arts and Humanities or Services. Conclusions: These findings provide quality information that may be used to improve the effectiveness of guidance counselling activities. [ABSTRACT FROM AUTHOR]

The aim of this article is to reflect on the role of Twitter® as a professional development tool for mathematics teachers to teach statistics and probability in early childhood and primary education. Firstly, it addresses some of the main open questions about the teaching of statistics and probability at these stages: the purposes of teaching, teaching practices and the organisation of teaching. Considering these three elements, secondly, several threads on statistics and probability from the social network Twitter® are presented and analysed, containing both teaching sequences and mathematical activities. Finally, the possibilities and limitations of this platform to promote the professional development of teachers are described. [ABSTRACT FROM AUTHOR]

University dropout is a growing problem with considerable academic, social and economic consequences. Conclusions and limitations of previous studies highlight the difficulty of analyzing the phenomenon from a broad perspective and with bigger data sets. This paper proposes a new, machine-learning based method, able to examine the problem using a holistic approach. Advantages of this method include the lack of strong distribution hypothesis, the capacity for handling bigger data sets and the interpretability of the results. Results are consistent with previous research, showing the influence of personal and contextual variables and the importance of academic performance in the first year, but other factors are also highlighted with this model, such as the importance of dedication (part or full time), and the vulnerability of the students with respect to their age. Additionally, a comprehensive graphic output is included to make it easier to interpret the discovered rules. [ABSTRACT FROM AUTHOR]

Curricular issues of subject Applied Mathematics to Social Sciences are studied in relation to university entrance exams performed in several Spanish regions between 2009–2014. By using quantitative and qualitative analyses, it has been studied how these exams align with curriculum and how they produce a washback on curriculum and teachers’ work. Additionally, one questionnaire about teachers’ practices has been performed, in order to find out how the exams are influencing teaching methodology development. Main results obtained show that evaluation is producing a bias on the official curriculum, substantially simplifying the specific orientation that should guide applied mathematics. Furthermore, teachers’ practices are influenced by the exams, and they usually approach their teaching methodology to the frequent types of exams. Also, slight differences among the teachers lead to distinguish two behavioral subgroups. Results can also be useful in an international context, because of the importance of standardized exit exams in OECD countries. [ABSTRACT FROM AUTHOR]

Introduction: Searching for information is a necessary step for young people to decide what to study and prevent school drop-out. The aim of this study is to identify the main sources of information used by students in choosing a university career and to assess the degree of usefulness of these sources. Method: A new measuring instrument to assess the use and usefulness of the information sources used in choosing university studies was developed. 2,005 high school students aged 17 to 24 (M = 17.56, SD = .77) participated in the study, representing 44.95 % of the total of school centers of the Principality of Asturias (Spain). Results: The new instrument has adequate psychometric properties and shows that the information from parents and web pages by universities are the most used and most useful information sources for pre-university students. Conclusions: Obtaining this type of information is very important, as it encourages investing in those activities or resources that are important for pre-university students. [ABSTRACT FROM AUTHOR]

This paper presents a model for discovering user preferences from item characteristics. Based on the theory of evidence, the model estimates a probability interval for an item represented by a set of features. This interval represents the item preference within a group of users and it is computed according to preferences expressed in the past. Additionally, a method for moving among different domains and fusing information is outlined. The issue of efficient search subsets of interest within the inclusion lattice is investigated and algorithms are presented. [ABSTRACT FROM AUTHOR]

Abstract: A mathematical framework to model the Bayesian analysis of single-stage decision problems with imprecise utilities is proposed. The main advantage of this model with respect to previous models for such a problem, is that product measurability of the utility function is not necessary, since this model involves iterated expectations instead of an integral over a product space. Conditions for the equivalence between the extensive and normal forms of the Bayesian analysis, within the proposed framework, are obtained. The model is illustrated with an example in which the utility function is not product measurable. [Copyright &y& Elsevier]

In this paper we establish sufficient conditions to guarantee the exchange of the fuzzy expected value for a fuzzy random variable depending on certain parameter and its Hukuhara derivative with respect to the parameter. Main results are obtained for two different sets of general conditions, one of them requiring measurability conditions with respect to the product space the fuzzy random variable is defined from, and the second one just requiring conditions over the projections of the fuzzy random variables. [Copyright &y& Elsevier]

The emergency caused by coronavirus disease 2019 (COVID-19) has revealed significant deficiencies in citizens' statistical and probabilistic knowledge and in people's understanding of mathematical and, particularly, stochastic models, which may lead to wrong personal or institutional choices, with critical consequences for the entire population. Mathematics teachers play an essential role in ensuring citizens' statistical and probabilistic literacy. This study aimed at analyzing the pedagogical content knowledge that teachers utilized to teach statistics and probability through considering contextualized situations. In order to accomplish this purpose, fourteen secondary mathematics teachers participated in a formative and evaluative activity that was designed using the transformational professional competence model. During each evaluative phase, a group discussion was conducted. Participants were asked to reflect on their actions when promoting statistical and probabilistic literacy by considering a range of topics (data science, didactic resources, and methodological approaches) that were addressed during the training phase. A mixed, quantitative–qualitative methodological design was used for the data collection and analysis, which involved open-ended, multiple-choice, or scale-type questions that were moderated by the Metaplan® approach and the Mentimeter® software. The main ideas that emerged from the results indicated the need to reinforce the use of real data, technological resources to handle the visualization of information, the elaboration of different types of graphs besides the classical ones, and the formulation of hypotheses. The initial diagnosis will continue within a research and practice community made up of teachers and researchers. Therefore, a working proposal based on examples and models contextualized within the COVID-19 crisis is presented in order to enhance secondary mathematics teachers' pedagogical content knowledge. [ABSTRACT FROM AUTHOR]

Quantum computing (QC) is one of the most promising new technologies for High Performance Computing. Its potential use in High Energy Physics has lead CERN, one of the top world users of large-scale distributed computing, to start programmes such as the Quantum Technology Initiative (QTI) to further assess and explore the applications of QC. As a part of QTI, CERN offered, in November–December 2020, a free, online series of lectures on quantum computing. In this paper, we report on the experience of designing and delivering these lectures, evaluating them in the broader context of computing education and training. Traditional textbooks and courses on QC usually focus on physical concepts and assume some knowledge of advanced mathematical and physical topics from the student. Our lectures were designed with the objective of reducing the prerequisites to the bare minimum as well as focusing on hands-on, practical aspects of programming quantum computers and not on the mathematical analysis of the algorithms. This also allowed us to include contents that are not usually covered in introductory courses, such as quantum machine learning and quantum annealing. The evaluation of the reception of the lectures shows that participants significantly increased their knowledge, validating the proposed approach not focused on mathematics and physics but on algorithmic and implementation aspects. [ABSTRACT FROM AUTHOR]

More and more distribution companies need a model to efficiently retrieve physical technological systems. Building ontologies as knowledge representation models with respect to technological systems information is increasingly seen as a key to enable interoperability between software agents and people on the Web or through to network connections. This work presents a first step for the development of an ontological model for technological systems structure representation composed by physical artifacts. The goal of the work is twofold. First, the structure of these systems is described. Besides, a model to adapt the known Bill of Materials (BOM) to the needs of distribution companies focused not only on selling physical artifacts but also to correctly configure a technological system is presented. Finally, our approach proposes a mereotopological relationships set to model the interactions between the parts that make up the structure. [ABSTRACT FROM AUTHOR]

Initial teacher education programmes provide student teachers with the desired competences to develop themselves as teachers. Although a generic framework for teaching competences is available covering all school subjects in Spain, the initial teacher education programmes curriculum does not specify which competences secondary mathematics student teachers should acquire during their initial teacher education. This explains why this study aimed at developing and validating a competence framework for secondary mathematics student teachers in Spain. Building on existing models and international frameworks, a preliminary list of competences was drawn up. The validation process was based on a Delphi method. In addition experts expressed their opinions about the formulation of the chosen competences. A comprehensive framework of 33 competences for secondary mathematics student teachers could then be validated. [ABSTRACT FROM PUBLISHER]

A correction to this paper has been published: https://doi.org/10.1007/s11227-021-03923-0 [ABSTRACT FROM AUTHOR]

Classification is a long standing problem in computing. There are two broad kinds of classifiers, frequency based and geometry based. Frequency based classifiers often ignore the geometry underlying the data. Conversely, geometry based classifiers take into account the frequency only indirectly. This paper presents a classification algorithm which considers explicitly geometric and statistical characteristics of the data and combines them into a class representation. Reported here are initial experiments with this algorithm using two well known data sets, both with and without noise. The results show that the proposed algorithm is less sensitive to the training data set than other classifiers. [ABSTRACT FROM AUTHOR]

The teaching of probability is conditioned by teachers' mathematical knowledge. In this paper, an exploratory study is carried out with prospective teachers. A training task was designed requiring them to create and solve a probability problem using the values of euro coins, which was adapted to students aged 11 to 12. The study aimed at determining what mathematical knowledge prospective teachers show when dealing with the task. The data were collected through the Moodle online Campus. We framed the data analysis in the Mathematical Knowledge for Teaching model and we used content analysis as the methodological approach. The results indicate that, despite finding evidence of adequate common and specialised mathematical knowledge, in approximately half of the prospective teachers participating in the study, too many of them still show a lack of knowledge in both subdomains. There was also little evidence of knowledge of the curriculum. The main finding of the research is that, when prospective teachers get involved in complex creative tasks, they mobilised together specialised and common mathematical knowledge, working into different mathematical processes such as problem posing and solving, communication, and argumentation, which reinforces the need to continue working on these types of complex tasks. [ABSTRACT FROM AUTHOR]