Secondary School Students’ Errors in the Translation of Algebraic Statements

In this article, we present the results of a research study that explores secondary students’ capacity to perform translations of algebraic statements between the verbal and symbolic representation systems through the lens of errors. We classify and compare the errors made by 2 groups of students: 1 at the beginning of their studies in school algebra and another 1 completing their studies on algebra in compulsory education. This comparison allows us to detect errors which require specific attention in instruction due to its persistence and to identify errors that disappear as students advance in their study of algebra. The results and conclusions have a pedagogic value to inform instruction and also lead to backed conjectures and research questions to push forward research on student’s translation capacity and students’ knowledge of algebraic symbolism.     

Does generating examples aid proof production?

Many mathematics education researchers have suggested that asking learners to generate examples of mathematical concepts is an effective way of learning about novel concepts. To date, however, this suggestion has limited empirical support. We asked undergraduate students to study a novel concept by either tackling example generation tasks or reading worked solutions to these tasks. Contrary to suggestions in the literature, we found no advantage for the example generation group on subsequent proof production tasks. From a second study, we found that undergraduate students overwhelmingly adopt a trial and error approach to example generation and suggest that different example generation strategies may result in different learning gains. We conclude by arguing that the teaching strategy of example generation is not yet understood well enough to be a viable pedagogical recommendation.     

Reconsidering the Urban in Urban Education: Interdisciplinary Conversations

The field of education has become comfortable in its use of the construct urban to describe particular schools in particular metropolitan places. This article argues that the construct has come to signify not just place but also to denote particular meanings of ‘urban’ populations. It analyzes how literary and social-scientific practices converged to anchor this construct paradigmatically in the registers of educational practitioners and researchers. Drawing from cultural geography, the article then demonstrates why the framework of the urban, and its other implicit pole the suburban, is no longer satisfactory for conceptualizing empirical questions about metropolitan schools. Lastly, the author identifies and discusses exemplars within the field of educational research that help us to remap our theoretical and empirical work.     

Placing Immigrant and Minority Family and Community Members at the School's Centre: the role of community participation

Schools alone cannot reverse the high rates of school failure in the poorest communities in Europe; they need the contributions of the entire community. Coordination between families, the larger community, and the school has proven crucial to enhance student learning and achievement, especially for minority and disadvantaged families. However, families from such backgrounds often participate in their schools only peripherally because the schools take a ‘tourist’ approach, call parents to inform them about school projects and teachers' programmes, or consult them about decisions to be made by professionals, rather than engaging them in their children's education. In contrast, the INCLUD-ED project studied schools across Europe whose students are culturally diverse and from low SES backgrounds; here, the communities are deeply involved in the schools and the students do well academically. This article focuses on three strategies used by these successful schools to engage immigrant and minority community members in more active, decisive, and intellectual ways and thus have greater impact on the school and the students' learning. It also describes some specific practices of involvement grounded in those strategies and the improvements they generate. Though the schools studied use different practices, the three strategies have been found to contribute to a transformative result in all schools: moving minority and disadvantaged families from the periphery of school participation to the centre.

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Guidance for older workers in Denmark and Spain

Guidance has a role to play in helping older workers to lead meaningful and fruitful lives; inside, outside, on the edge of the labour market, or in voluntary work with examples from two very different European countries: Denmark and Spain. This paper aims to draw attention to older workers guidance from an economic policy approach. It will be demonstrated that there is a need for more policy making for older workers’ guidance in both countries.     

Fostering active processing of instructional explanations of learners with high and low prior knowledge

Despite the potential advantages of instructional explanations, evidence indicates that they are usually ineffective. Subsequent work has shown that in order to make instructional explanations effective indeed, one successful strategy is to combine them with indications of the limitations in learners' understanding that they are intended to revise, which makes learners deeply process the explanations. We explored whether this is so for both learners with low and those with high prior domain knowledge. In one experiment, 77 participants with low and high prior knowledge learned about plate tectonics from a multimedia presentation. In addition to the presentation, half the participants received instructional explanations combined with indications, whereas the rest received instructional explanations with no indications. After using the materials, the participants solved retention and transfer tests. Results showed that low prior knowledge learners learned more from explanations including indications of their misunderstandings, whereas high prior knowledge learners profited from instructional explanations either with or without the indications. We discussed theoretical and practical implications.     

Engineers’ spatial orientation ability development at the European Space for Higher Education

The aim of this research was to determine whether the new geographic information technologies, included as teaching objectives in the new European Space for Higher Education Engineering degrees, develop spatial abilities. Bearing this in mind, a first year seminar using the INSPIRE Geoportal (Infrastructure for Spatial Information in Europe) was designed, involving 46 engineering students from the University of La Laguna. The spatial orientation ability development was analysed through statistical inference methods, using the Perspective Taking/Spatial Orientation Test.     

Engineering education at a new public university in Brazil: first students’ contact with engineering methods

This paper describes the experience of an introductory discipline to the engineering curricula at the Brazilian Federal University of ABC (UFABC). The university offers a common basic curriculum that must be accomplished by every student and can be followed by professionalising courses. The discipline ‘Introduction to Engineering’ presents the basis of the engineering career, methods and thinking together with professional commitments and regulations. The objective is to help students to consciously choose their careers, minimising the precocity problem in deciding a professional future. The discipline methodology includes activities proposed by the TryEngineering website and from Brazilian engineering councils. Lectures with invited professors introduce UFABC engineering specialities: Aerospace, Bioengineering, Energy, Environmental & Urban, Information, Instrumentation & Automation & Robotics, Management, Materials. This paper reports the proposed activities, results obtained by the students, a methodology critical analysis and the impacts on the following steps of students embracing an engineering career.     

Listening to grandmothers

In this column, three proud grandmothers share their unique stories and eloquently describe the transforming experience of becoming a grandmother and the joy associated with witnessing their daughters giving birth.     

含左手介质非对称三层平板波导的模式特性研究

基于三层平板波导TE模的色散关系,分析覆盖层为左手介质而其他层为右手介质的非对称三层平板波导的模式特性.结果表明,只有满足一定条件TE0才存在,而高次模的截止频率随着非对称因子a增大而减小.