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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]

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]

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