Elementary students’ metacognitive processes and post-performance calibration on mathematical problem-solving tasks

Calibration, or the correspondence between perceived performance and actual performance, is linked to students’ metacognitive and self-regulatory skills. Making students more aware of the quality of their performance is important in elementary school settings, and more so when math problems are involved. However, many students seem to be poorly calibrated, with a tendency towards over-confidence. The present study analyzes the relationship between post-performance calibration accuracy and the metacognitive process shown by 524 fifth- and sixth-grade students while solving two math problems. After calculating a calibration index and establishing the stability of students’ judgments and actual performance, differences in the metacognitive process exhibited by students with different calibration accuracy (Accurate vs. Inaccurate groups) were analyzed. The emergence of different calibration patterns and differences in the metacognitive process as a function of mathematics achievement and grade level were also examined. Results indicated that: (a) students in the overall sample were little calibrated and over-confident, showing high stability in their judgments and actual performance across problems; (b) inaccurate students reported using information representation sub-processes (drawing/summarizing) less frequently, but writing and reviewing (and also correcting mistakes) more frequently than their accurate peers; and (c) differences in calibration patterns and the metacognitive process were found when achievement level was considered, whereas grade level did not generate any important effect. These findings suggest the usefulness of process-based measures to examine the metacognitive processes involved in making post-performance judgments, considering achievement and its possible mediating role in this relationship.     

Islamic religious education and the plan against violent radicalization in Spain

ABSTRACT

This article analyses the importance of Islamic religious education in public schools in Spain as an instrument in the prevention and fight against violent radicalisation. In this article, we examine the legal status of Islamic religious education and the latest regulations on Islamic religious education that emphasise the fight against Islamist terrorism. We also study the regulation of teachers of Islamic religious education and their role in the counter-narrative required to deter the message of Islamist terrorists and prevent violent radicalisation.     

Proposing Questions for Scientific Inquiry and the Selection of Science Content in Initial Elementary Education Teacher Training

Research in Science Education - This article presents a qualitative study of the type and quality of questions formulated by prospective elementary teachers (PETs) when designing scientific inquiry...     

Using a fine-grained multiple-choice response format in educational drill-and-practice video games

When using educational video games, particularly drill-and-practice video games, there are several ways of providing an answer to a quiz. The majority of paper-based options can be classified as being either multiple-choice or constructed-response. Therefore, in the process of creating an educational drill-and-practice video game, one fundamental question to be answered is which is the most appropriate response format? This paper answers this question, proposing a hybrid format that we call fine-grained multiple-choice, where the player constructs their response one element at a time, with each element chosen from a pre-defined set. A comparative study was conducted with second grade students. When comparing the impact of an educational drill-and-practice video game that uses multiple-choice with one that uses fine-grained multiple-choice, we observe that the fine-grained multiple-choice game achieved better results. However, the multiple-choice game was substantially more successful at capturing the students' interest and motivation. Considering the widespread use of the multiple-choice format in game-based learning activities, as well as in interactive activities, this research suggests rethinking what the most suitable answer format might be for each area of the curriculum and for the different types of games.     

Three concepts or one? Students’ understanding of basic limit concepts

In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of very similar symbols, few connections between these notions are made explicitly and few papers in the large literature on student understanding of limit connect them. This paper examines the nature of connections made by students exposed to this fragmented curriculum. The study adopted a phenomenographic approach and used card sorting and comparison tasks to expose students to symbols representing these different types of limit. The findings suggest that, while some students treat limit cases as separate, some can draw connections, but often do so in ways which are at odds with the formal mathematics. In particular, while there are occasional, implicit uses of neighbourhood notions, no student in the study appeared to possess a unifying organisational framework for all three basic uses of limit.     

Cognitive,Motivational, and Volitional Dimensions of Learning: An Empirical Test of a Hypothetical Model

The principal aim of this research is to contrast empirically a hypothetical model developed on the basis of the fundamental assumptions of current self-regulated learning models. In line with evaluation criteria of model fit, a high rate of congruence between the hypothesized theoretical model and the empirical data was observed. Analysis of the effects between the variables of the model revealed the following relevant aspects: students' predisposition to feel responsible for the results of their academic behavior (internal attribution) is related to positive self-image (academic self-concept), both being important conditions for development of learning-oriented motivation (learning goals). All of this involves selection and use of learning strategies for deep information processing (deep learning strategies), which leads students to assume responsibility with high levels of persistence, perseverance, and tenacity so as to achieve goals defined by the motivational orientation. This persistence and effort to achieve the proposed goals has in turn a positive and significant effect on academic achievement.     

Indexical Expressions in Word Problems and their Influence on Multiple Referents of the Unknown

When translating word problems into equations, a common error consists of using the same letter to refer to two different quantities. This error, called multiple referents for the unknown, can be connected to the existence of deictic or indexical expressions within the problem statement. This paper aims to analyse the influence of indexical expressions on the incidence of the multiple referents for the unknown error. Results from a quantitative study with 117 Spanish secondary students show a significantly higher number of such type of error when the problem statement contains indexical expressions. The analysis of students’ performances in subsequent interviews indicates that this error may be due to the fragmented reading of statements.     

From diagrams to self-regulated learning: student teachers’ reflections on the construction of their PLE

This paper presents a study on the reflections on their PLEs by student teachers in an ICT subject of the fourth degree course in Teacher Education (Early Childhood Teacher Training) at the University of the Balearic Islands (UIB). There were four student teacher groups (n = 117) participating in this project, from the three Balearic Islands’ campuses (Mallorca, Menorca and Ibiza). The main research issues focused on in this study are: the topics highlighted from the reflections on the students’ PLEs and the reflection level achieved. To explore these issues, a content analysis technique has been used to interpret their final assignment of the students’ eportfolios, in which they had to carry out their reflections on their PLEs. For that purpose, two instruments have been designed: a system of categories and a rubric of assessment. Results show that the topics on which students reflect most are the conception of the PLE, its explicitness and its purpose. Although some improvement in students’ reflective skills was observed, conclusions lead us to the necessity of working further on the depth of reflections in order to adequately support self-regulated learning.     

Music Education at Hospital Schools in Spain and Sweden: Paths Between Governing and Knowledge

This paper focuses on some debates regarding music education within hospital schooling, an educational track that has developed in the course of the 20th century within Western education systems. Analysis and proposals are made with respect to the music education curriculum content in primary education, within hospital education tracks, in Spain and Sweden. In order to critically approach the changing definition of what is considered significant knowledge, we discuss how music education curriculum content is included in hospital schools located in the capitals Madrid and Stockholm.