Students’ conception of infinite series

This is a report of a study of students’ understanding of infinite series. It has a three-fold purpose: to show that students may construct two essentially different notions of infinite series, to show that one of the constructions is particularly difficult for students, and to examine the way in which these two different constructions may be built so that we may uncover ways to help students improve their understanding. The theoretical framework consists of action–process–object–schema theory and the specific model of conceptions in Balacheff’s theory of conception, knowing, and concept. Approaching the problem from these two different theoretical perspectives allows us to provide different and at the same time complementary explanations of observed phenomena. The two different infinite series constructions are, briefly stated, series as an infinite unending process of addition and series as a sequence of partial sums. Students are found to have difficulty building an understanding of series as a sequence of partial sums and thus tend to have difficulty in problem situations that require this interpretation. The study uses semi-structured interviews with 10 graduate students. The interviews explore situations that might give insight into students’ notion of the sequence of partial sums.     

Personal learning environments: design and use / Los entornos personales de aprendizaje en la educación superior: del diseño al uso

Abstract

This study focuses on the uses that two groups of higher education students make of technological resources offered by an institution to build their own personal learning environments. The main thesis is that these uses depend on the techno-pedagogical design of the teaching and learning process in which the technological resources are framed. In order to explore and illustrate this thesis two instructional sequences have been analysed. Both use the same technological design, the Elgg platform, which allows users to select and organize a set of resources or widgets according to their interests and needs. The results show that in both cases the uses that students make of technology are related to the characteristics and requirements of the particular techno-pedagogical designs. We conclude that the key is not to offer technological resources to the students so they can build their own personal learning environments, but to design activities that attract and induce them to build these personal environments and to guide and support the process of construction.     

Who pays for standardised testing? A cost-benefit study of mandated testing in three Queensland secondary schools

This paper reports on an Australian study that explored the costs and benefits of the National Assessment Programme, Literacy and Numeracy (NAPLAN) testing, both tangible and intangible, of Year 9 students in three Queensland schools. The study commenced with a review of pertinent studies and other related material about standardised testing in Australia, the USA and UK. Information about NAPLAN testing and reporting, and the pedagogical impacts of standardised testing were identified, however little about administrative costs to schools was found. A social constructivist perspective and a multiple case study approach were used to explore the actions of school managers and teachers in three Brisbane secondary schools. The study found that the costs of NAPLAN testing to schools fell into two categories: preparation of students for the testing; and administration of the tests. Whilst many of the costs could not be quantified, they were substantial and varied according to the education sector in which the school operated. The benefits to schools of NAPLAN testing were found to be limited. The findings have implications for governments, curriculum authorities and schools, leading to the conclusion that, from a school perspective, the benefits of NAPLAN testing do not justify the costs.     

Which English? Standard English and Language Variety: Some Educational Perspectives

The aim of this paper is to provoke thought on the role of standard English in the early years of education. It examines the nature and function of a standard and highlights its close relationship with political aims and its potential for liberation and oppression. The reality of language variety and bilingualism is outlined and leads to a discussion of standard English and early schooling. The paper concludes with some suggestions for avoiding the standard English trap.