Different moments in the participatory stage of the secondary students’ abstraction of mathematical conceptions

This study provides support to the characteristics of participatory and anticipatory stages in secondary school pupils’ abstraction of mathematical conceptions. We carried out clinical task-based interviews with 71 secondary-school pupils to obtain evidence of the different constructed mathematical conceptions (Participatory Stage) and how they were used (Anticipatory Stage). We distinguish two moments in the Participatory Stage based on the coordination of information from particular cases by activity-effect reflection which, in some cases, lead to a change of focus enabling secondary-school pupils to achieve a reorganization of their knowledge. We argue that (a) the capacity of perceiving regularities in sets of particular cases is a characteristic of activity-effect reflection in the abstraction of mathematical conceptions in secondary school, and (b) the coordination of information by pupils provides opportunities for changing the attention-focus from the particular results to the structure of properties.

Students’ understanding of the function-derivative relationship when learning economic concepts

The aim of this study is to characterise students’ understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding of these economic concepts is linked to students’ capacity to perform conversions and treatments between the algebraic and graphic registers of the function-derivative relationship when extracting the economic meaning of concavity/convexity in graphs of functions using the second derivative.

Developing pre-service teachers’ noticing of students’ understanding of the derivative concept

This research study examines the development of the ability of pre-service teachers to notice signs of students’ understanding of the derivative concept. It analyses preservice teachers’ interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers’ progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

How can directories of open access repositories improve the reuse of learning objects in building engineering?

This paper studies the use of directories of open access repositories worldwide (DOARW) to search Spanish repositories containing learning objects in the field of building engineering (BE). Results show that DOARW are powerful tools, but deficiencies (indicated in this study) have to be solved in order to obtain more accurate searches, and to facilitate repository-finding for potential users who are seeking learning objects (LOs) for reuse. Aiming to contribute to the promotion of the reuse of Spanish LOs, this study exposes to the academic community all existing Spanish repositories with LOs, and in particular, the repositories that contain LOs in the field of BE. This paper also studies the critical mass of available content (LOs) in the field of BE in Spain. It has been found to be low.

Coordination of aproximations in secondary school students’ understanding of limit concept

The aim of this research is to characterize the coordination of the processes of approximation related to the understanding of the limit of a function. We analyze the answers of 64 post-secondary school students to 7 problems considering the dynamic and metric conception of limit of a function. Results indicate that the metric understanding of the limit in terms of inequality supports that the student is capable of coordinating the approximations in the domain and in the range when lateral approximations coincide. However, the student is not capable of this coordination when lateral approximations do not coincide. This indicates that the metric understanding of the limit begins with the previous construction of the dynamic conception in case of coincidence of the lateral approximations in the range.

A quantitative assessment of students’ experiences of studying music: a Spanish perspective on the European credit transfer system (ECTS)

The purpose of this investigation is to evaluate whether or not the allocation of time proposed in the Music Study Guide, adapted from the European Higher Education Area (EHEA) guidelines, is consistent and adequate for students with minimal musical knowledge. The report takes into account the importance of students’ previous knowledge and the relation this has to the time and effort expended by students in acquiring appropriate knowledge and skills. This is related also to the adequacy of the course specification to meet the demands of university study and the labour market. Results show that those students who enrolled at university without any previous musical knowledge are likely to experience significant difficulty in the acquisition of certain musical and professional competences. This highlights a need to reinforce the music curriculum, or establish zero-level courses, in order to enable such students to succeed in the subject.

Profiles of emotional intelligence and learning strategies in a sample of Chilean students

In the last few years, one of the lines of research of great interest in the field of emotional intelligence (EI) has been the analysis of the role of emotions in the educational context and, in particular, their influence on learning strategies. The aims of this study are to identify the existence of different EI profiles and to determine possible statistically significant differences in learning strategies between the obtained profiles. The study involved 1253 Chilean school students from 14 to 18 years (M = 15.10, SD = 1.30), who completed the Trait Meta-Mood Scale-24 (TMMS-24) and the Inventory of Learning and Study Strategies—High School version (LASSI-HS). Cluster analysis identified four EI profiles: a group of adolescents with a high EI profile, a group with predominance of low emotional attention and high repair skills, a group with high scores on attention and low scores on clarity and repair, and a final group of adolescents with low EI. Also, students in groups with high overall scores in EI and low attention and high repair emotional obtained higher scores on the different learning strategies; however, the effect size analysis showed that these differences had no empirical relevance.