Who aspires to higher education? Axes of inequality,values of education and higher education aspirations in secondary schools in Luxembourg and the Swiss Canton of Bern

This article reports a study that investigated secondary school students’ higher education aspirations (towards university studies, ISCED 6 and above) and how these differ between student groups as well as how these are impacted by values of education. Panel data of more than 300 secondary school students in two countries, Luxembourg and Switzerland (the Swiss Canton of Bern) was analysed. Schools are structured differently in the education systems of Luxembourg and the Swiss Canton of Bern. The results of our analysis show that students in the Luxembourgish sample more often aspire to higher education than in the Swiss sample. Disparities in higher education aspirations were also more pronounced in the Luxembourgish sample, boys and students from families of low socio‐economic status (SES) were less likely to aspire to higher education. While the effects of values of education are generally scarce, stimulation in terms of anticipated enjoyment and interest derived from participation in higher education seems to have a positive effect on higher education aspirations.     

Non-parametric adaptive locally asymptotically optimum detection in additive noise

In this paper, a new approach to non-parametric signal detection with independent noise sampling is presented. The present approach is based on the locally asymptotically optimum (LAO) methodology, which is valid for vanishingly small signals and very large sample sizes, and on semi-parametric statistics. Its unique feature and essential difference from other techniques is that LAO non-parametric detectors are optimum according to the Neyman-Pearson criterion by being asymptotically uniformly most powerful at false alarm level α (AUMP (α)) and adaptive in the sense that no loss in Fisher's information number is incurred when the underlying noise process is no longer parametrically defined. Accordingly, they are robust against deviations from the postulated noise model and, unlike other non-parametric detectors, are distribution-free under both hypotheses H₀ (“noise only present”) and H₁ (“signal and noise present”). Non-parametric LAO detectors are derived from an asymptotic stochastic expansion of the log-likelihood ratio for coherent and narrowband incoherent “on-off” signals. Moreover, under the present framework it is shown that, in direct contrast to already known results, the non-parametric sign detector is AUMP (α) and adaptive even for non-constant signal samples.     

Using intellectual capital statements to determine value drivers and priorities for organizational change: a portfolio selection approach

Ex post examination of a firm's performance in key intellectual capital indicators can demonstrate the value-creating potential and the organizational change aspect of intellectual capital reporting and management. These insights form the basis of an intellectual capital portfolio selection problem. Portfolio selection takes place in two stages. First, we calculate mean returns and variances for each market-valued portion of intellectual capital. Based on these estimations, we set up a portfolio selection problem. The solution to this portfolio selection problem provides priorities for organizational change. In this framework, the portfolio weights stand for organizational priorities, the weight constraints represent organizational barriers for change and the correlation of returns stands for the organizational interdependence of the intellectual capital components.     

Introducing a symbolic interactionist approach on teaching mathematics: the case of revoicing as an interactional strategy in the teaching of probability

This study examines an interactional view on teaching mathematics, whereby meaning is co-produced with the students through a process of negotiation. Further, teaching is viewed from a symbolic interactionism perspective, allowing the analysis to focus on the teacher’s role in the negotiation of meaning. Using methods inspired by grounded theory, patterns of teachers’ interaction are categorized. The results show how teachers’ actions, interpretations and intentions form interactional strategies that guide the negotiation of meaning in the classroom. The theoretical case of revoicing as a teacher action, together with interpretations of mathematical objects from probability theory, is used to exemplify conclusions from the proposed perspective. Data are generated from a lesson sequence with two teachers working with known and unknown constant sample spaces with their classes. In the lessons presented in this article, the focus is on negotiations of the meaning of chance. The analysis revealed how the teachers indicate their interpretations of mathematical objects and intentions to the students to different degrees and, by doing so, create opportunities for the students to ascribe meaning to these objects. The discussion contrasts the findings with possible interpretations from other perspectives on teaching.     

Research-based interventions in the area of proof: the past,the present,and the future

The concept of proof has attracted considerable research attention over the pastdecades in part due to its indisputable importance to the discipline of mathematics and tostudents’ learning of mathematics. Yet, the teaching and learning of proof is an instructionallyarduous territory, with proof being recognized as a hard-to-teach and hard-to-learn concept atall levels of education. Prior research has examined, documented, and cast light on theprocesses underpinning different problems of classroom practice in the area of proof, buthas paid less emphasis on acting upon such problems to generate possible solutions throughresearch-based interventions in mathematics classrooms. In this Editorial, we first situate thecontributions in this Special Issue in a brief chronological account of scholarly work on research-based interventions in the area of proof, and we conclude with a proposal for somehigh-leverage directions for future research.     

Converging Subjective and Psychophysiological Measures of Cognitive Load to Study the Effects of Instructor‐Present Video

Many online videos feature an instructor on the screen to improve learners' engagement; however, the influence of this design on learners' cognitive load is underexplored. This study investigates the effects of instructor presence on learners' processing of information using both subjective and psychophysiological measures of cognitive load. Sixty university students watched a statistics instructional video either with or without instructor presence, while the spontaneous electrical activity of their brain was recorded using electroencephalography (EEG). At the conclusion of the video, they also self‐reported overall load, intrinsic load, extraneous load, and germane load they experienced during the video. Learning from the video was assessed via tests of retention and transfer. Results suggested the instructor‐present video improved learners' ability to transfer information and was associated with a lower self‐reported intrinsic and extraneous load. Event‐related changes in theta band activity also indicated lower cognitive load with instructor‐present video.     

Differentiating Different Types of Cognitive Load: a Comparison of Different Measures

Recent studies about learning and instruction use cognitive load measurement to pay attention to the human cognitive resources and to the consumption of these resources during the learning process. In order to validate different measures of cognitive load for different cognitive load factors, the present study compares three different methods of objective cognitive load measurement and one subjective method. An experimental three-group design (N = 78) was used, with exposure to seductive details (extraneous cognitive load factor), mental animation tasks (germane cognitive load factor), or the basic learning instruction (control group). Cognitive load was measured by the rhythm method (Park and Brünken 2015), the index of cognitive activity (ICA) (Marshall 2007), and the subjective ratings of mental effort and task difficulty (Paas 1992). Eye-tracking data were used to analyze the attention allocation and as an indicator for cognitive activity. The results show a significantly higher cognitive load for the mental animation group in contrast to the control and the seductive detail group, indicated by rhythm method and subjective ratings, as well as a higher cognitive activity, indicated by eye tracking. Furthermore, the mental animation group shows significantly higher comprehension performance in contrast to the seductive detail group and significantly higher transfer performance in contrast to the control group. The ICA values showed no significant differences in cognitive load. The results provide evidence for the benefits of combining eye-tracking analysis and the results of cognitive load ratings or secondary task performance for a direct and continuous cognitive load assessment and for a differentiating access to the single cognitive load factors.     

An examination of the roles of the teacher and students during a problem-based learning intervention: lessons learned from a study in a Taiwanese primary mathematics classroom

The benefits of problem-based learning (PBL) to student learning have prompted researchers to investigate this pedagogical approach over the past few decades. However, little research has examined how PBL can be applied to mathematics learning and teaching, especially in countries like Taiwan, where the majority of teachers are accustomed to lecture methods and students are used to this style of teaching. This study examines the actions of a teacher and her class of 35 fifth-grade students (10–11-year-olds) as they tried to take on and respond to the demands of their new roles as “facilitator” and “constructors”, respectively, during a one-year PBL intervention in a Taiwanese mathematics classroom. Our findings provide insights into classroom participants’ role transition, from a customary role to a new role, when engaging with PBL. We identify an interrelationship between the teacher and student roles and discuss implications for the implementation of PBL at the primary education level.