Theorema aureum — 2

In the first part of this article, we had introduced the notion of quadratic reciprocity and dwelt briefly on its history, which goes back all the way to the work of Fermat. Then we discussed the Law of Quadratic Reciprocity (‘QRL’), which Gauss named Theorema Aureum. Following this, we gave a not too well known proof of the QRL, due to G Rousseau. Now we give two more proofs of the QRL, drawing respectively from ideas in linear algebra and field extensions; they too are not very well known. Shivam Kumar graduated from Indian Statistical Institute, Bangalore and is joining the London School of Economics for MSc in applicable mathematics. His interest lies in expanding the existing applied paradigm of mathematics from stock market to unchartered subjects such as sociometrics.     

Learning words through overhearing

Recent research indicates that toddlers can monitor others' conversations, raising the possibility that they can acquire vocabulary in this way. Three studies examined 2-year-olds' (N = 88) ability to learn novel words when overhearing these words used by others. Children aged 2,6 were equally good at learning novel words-both object labels and action verbs-when they were overhearers as when they were directly addressed. For younger 2-year-olds (2,1), this was true for object labels, but the results were less clear for verbs. The findings demonstrate that 2-year-olds can acquire novel words from overheard speech, and highlight the active role played by toddlers in vocabulary acquisition.     

Scalars vectors in physics - II

In Part I, the nature of scalars and vectors was discussed for the Newtonian world. However, in the relativistic world, physical quantities follow Lorentz transformations. This change of transformation from Galilean to Lorentz results in interesting distinctions in their properties: mass and time are no longer scalars, time and space become intertwined, etc. This part discusses the nature of scalars and vectors in the relativistic world.     

Priority Education Zones in Mauritius

This article discusses the Priority Education Zones project (ZEP) in Mauritius. The original and innovative dimensions of the project are described, together with the difficulties encountered during the setting-up of the ZEP schools. The article covers five main issues: the status of the ZEP project; the minimal conditions for success; the implications concerning the teachers; the obstacles faced; and the strategy devised to implement the ZEP project, while overcoming the obstacles.

Assessment of expert-novice chemistry problem solving using HyperCard: Early findings

Results of a HyperCard method for assessing the performance of expert and novice high school chemistry students solving stoichiometric chemistry problems (balancing chemical equations) have been reported. The assessment involved the use of a HyperCard instrument (Hyperequation) developed on a Macintosh platform to administer a set of five chemistry problems, register student responses, and collect data related to student performance. The chemistry problems have been previously tested and validated in traditional (pen-paper) assessment settings by other researchers. MANOVA results indicate a significant difference between the performance of expert and novice students solving the five stoichiometric chemistry problems using the Hyperequation. The study shows promise in that a HyperCard assessment method could differentiate between the performance of experts and novices in problem solving. The implication is that HyperCard might be a suitable technology for developing performance assessment methods not only in chemistry but also in other science disciplines.     

A qualitative study of perceptions of bullying in Irish primary schools

This small-scale research examined young children’s, aged six to seven (n = 8), perceptions and understanding of bullying in Irish primary schools. It also included the views of the children’s parents (n = 8) and teachers (n = 2) on bullying. The participants’ views were obtained through semi-structured interviews which were analysed using the constant comparative method as per grounded theory approach. The results revealed the complexity of young children’s interactions in school and the difficulty that the adults around them have in accurately defining and addressing bullying behaviour. The data indicate the need for parents and teachers to listen attentively and sensitively to children’s accounts of bullying and to provide consistent advice on how to address bullying.     

A small-scale pilot study into language difficulties in children who offend

This small-scale pilot research project investigates the prevalence of Speech Language and Communication Difficulties in a sample of children attending a Youth Offending Service in the UK. Using the CELF-4, approximately 90% of the sample displayed some form of language difficulty and, overall, this population displayed mild to moderate difficulties in this area. Youth Offending Team staff questionnaires were also analysed and it was found that staff have little understanding of the difficulties presented by the children on their caseloads, despite reporting that they felt confident in this area. Implications for practice and potential roles for educational psychologists are discussed.     

Transformation for adults in an Internet‐based learning environment—is it necessary to be self‐directed?

This research explores the relationships between self‐directed learning readiness and transformative learning theory (TLT) reflected by the Constructivist Internet‐based Learning Environment Scale (CILES). A questionnaire survey about adult learner's perceptions of Internet‐based learning was administered to adults enrolled in classes in community colleges in Taiwan. A total of 593 valid questionnaires were used for the structural equation modeling analysis. The findings confirmed a second‐order hierarchical factor relationship of TLT (technical, dialectical and emancipatory learning interests) from CILES. Moreover, the three domains of learning interests of transformative learning were proved to have a developmental relationship, moderated by the readiness of self‐directed learning for adult learners in Internet‐based learning.     

Responding to students' needs in special schools in Ireland and England: findings from two schools

As more students with special educational needs attend mainstream schools, it is critical that the role and operation of special schools be examined. This article reports on two case studies, one special school in England and one in Ireland, which formed part of a national review of the role of special schools and special classes in Ireland. Two students, in each case study school, were shadowed and observed during two‐day visits by the research team. These students, and everyone belonging to them, were interviewed and relevant documents were analysed. Findings are discussed in terms of responding to students' needs through: organization of teaching and learning, curriculum, leadership, specialist staff, collaboration and links outside the special school. The implications are considered with reference to research, policy and practice and the authors conclude that the evidence provides support for maintaining the special school as an integral part of the continuum of educational provision for students with special educational needs.