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.     

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.     

Spiral and Project-Based Learning with Peer Assessment in a Computer Science Project Management Course

Different learning methods such as project-based learning, spiral learning and peer assessment have been implemented in science disciplines with different outcomes. This paper presents a proposal for a project management course in the context of a computer science degree. Our proposal combines three well-known methods: project-based learning, spiral learning and peer assessment. Namely, the course is articulated during a semester through the structured (progressive and incremental) development of a sequence of four projects, whose duration, scope and difficulty of management increase as the student gains theoretical and instrumental knowledge related to planning, monitoring and controlling projects. Moreover, the proposal is complemented using peer assessment. The proposal has already been implemented and validated for the last 3 years in two different universities. In the first year, project-based learning and spiral learning methods were combined. Such a combination was also employed in the other 2 years; but additionally, students had the opportunity to assess projects developed by university partners and by students of the other university. A total of 154 students have participated in the study. We obtain a gain in the quality of the subsequently projects derived from the spiral project-based learning. Moreover, this gain is significantly bigger when peer assessment is introduced. In addition, high-performance students take advantage of peer assessment from the first moment, whereas the improvement in poor-performance students is delayed.     

Evolution in Freedom? The Meanings of ‘Free School’ in Chile

This article examines the background in which enterprises called free schools, as well as complementary educational activities, have taken root in Chile. Two kinds of recently burgeoning free schools are identified; one supplementing regular schooling with a social justice focus, and another that is a fully fledged alternative to other schooling. The history of freedom itself in Chile is explored from a historical perspective, contrasting somewhat with freedom as it is understood in more developed countries. Parallels to Anglophone free schools such as AS Neill’s Summerhill are also discussed, as well as the sociopolitical context in which Chilean free schools continue to develop.     

Automated summary evaluation with inbuilt rubric method: An alternative to constructed responses and multiple-choice tests assessments

Automated summary evaluation is proposed as an alternative to rubrics and multiple-choice tests in knowledge assessment. Inbuilt rubric is a recent Latent Semantic Analysis (LSA) method that implements rubrics in an artificially-generated semantic space. It was compared with classical LSA’s cosine-based methods assessing knowledge in a within-subjects design regarding two validation sources: a comparison with the results of rubric scores and multiple-choice tests, and the sensitivity of predicting the academic level of the test-taker. Results showed a higher reliability for inbuilt rubric (from Pearson correlation coefficient .81 to .49) over the classical LSA method (from .61 to .34), and a higher sensitivity using binary logistic regressions and effect sizes to predict academic level. It is concluded that inbuilt rubric has a qualitatively higher reliability and validity than classical LSA methods in a way that is complementary to models based on semantic networks. Thus, it is concluded that new automated summary evaluation approaches such as the inbuilt rubric method can be practical in terms of reliability and efficiency, and, thus, they can offer an affordable and valuable form of knowledge assessment in different educational levels.     

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.     

COLLEGE RANKINGS: Democratized College Knowledge for Whom?

Every fall the opening of the academic year is heralded by an ever increasing number of newsmagazines that rank colleges. In addition to the standard bearers of this market — U.S. News and World Report and Money — magazines that offer their readers advice on how to choose a college are proliferating. For example, one can find lists of the "best colleges" and "best buys" accompanied on newstands by the top jock schools (Sports Illustrated), the best party schools (Playboy), and the best colleges for Asian Americans (A. Magazine). This paper is a study of who uses the contentious and seemingly influential newsmagazine rankings of U.S. colleges and universities, and an analysis of what types of freshmen find these rankings useful in making their choice of college. Equally important, it is a discussion of why reputations are important and how they can serve as a hedge against uncertainty. Finally, the paper provides an analysis of the for-profit sector's encroachment into a critical educational equity arena-college access-embedded within a discussion of whether widely available college rankings result in democratized college knowledge.     

The Effectiveness of Teaching Geometry to Enhance Mathematical Understanding in Children with Down Syndrome

ABSTRACT

It is widely known that people with Down syndrome have difficulties transitioning from a basic understanding of counting and cardinality to more advanced arithmetic skills. This is commonly addressed by resorting to the mechanical use of algorithms, which hinders the acquisition of mathematical concepts. For this reason some authors have recently proposed a shift in the focus of learning from arithmetic to more fertile fields, in terms of understanding. In this paper we claim geometry fits this profile, especially suited for initiating children with Down syndrome into mathematics. To support this we resort to historical, epistemological, and cognitive reasons: the work of Séguin and his intuition on the central role of geometry in the development of abstract thinking in the so-called idiot children, the ideas of René Thom about the role of continuum intuition in the emergence of conscious thinking, and finally the two strengths people with Down syndrome display: visual learning abilities and interest in abstract symbols. To support these ideas we present the main findings of qualitative research on elementary mathematics teaching to a group of seven children (3–8) with Down syndrome in Spain. The didactic method used, naturally enhance their naïve geometrical conceptions.     

Anatomy 3.0: Rediscovering Theatrum Anatomicum in the wake of Covid-19

The Covid-19 pandemic has challenged medical educators internationally to confront the challenges of adapting their present educational activities to a rapidly evolving digital world. In this article, the authors use anatomy education as proxy to reflect on and remap the past, present, and future of medical education in the face of these disruptions. Inspired by the historical Theatrum Anatomicum (Anatomy 1.0), the authors argue replacing current anatomy dissection laboratory (Anatomy 2.0) with a prototype anatomy studio (Anatomy 3.0). In this studio, anatomists are web-performers who not only collaborate with other foundational science educators to devise meaningful and interactive content but who also partner with actors, directors, web-designers, computer engineers, information technologists, and visual artists to master online interactions and processes in order to optimize students' engagement and learning. This anatomy studio also offers students opportunities to create their own online content and thus reposition themselves digitally, a step into developing a new competency of stage presence within medical education. So restructured, Anatomy 3.0 will prepare students with the skills to navigate an emergent era of tele and digital medicine as well as help to foreshadow forthcoming changes in medical education.