Making the transition to formal proof

This study examined the cognitive difficulties that university students experience in learning to do formal mathematical proofs. Two preliminary studies and the main study were conducted in undergraduate mathematics courses at the University of Georgia in 1989. The students in these courses were majoring in mathematics or mathematics education. The data were collected primarily through daily nonparticipant observation of class, tutorial sessions with the students, and interviews with the professor and the students. An inductive analysis of the data revealed three major sources of the students' difficulties: (a) concept understanding, (b) mathematical language and notation, and (c) getting started on a proof. Also, the students' perceptions of mathematics and proof influenced their proof writing. Their difficulties with concept understanding are discussed in terms of a concept-understanding scheme involving concept definitions, concept images, and concept usage. The other major sources of difficulty are discussed in relation to this scheme.This article is based on the author's doctoral dissertation completed in 1990 at the University of Georgia under the direction of Jeremy Kilpatrick.     

Learning from Texts and Visual Aids: a Developmental Perspective

The aims of this research were to investigate the ways in which students in primary and secondary schools process texts and accompanying visual aids and to ascertain any developmental patterns. Think-aloud protocols were gathered from 119 Grade 5, Grade 7 and Grade 9 students while they read and studied grade-appropriate History and Science materials which contained both text and visual aids (tables, diagrams). Analyses of the think-aloud protocols yielded over 50 different processes, subsumed under 10 major categories. While the History results showed no reliable grade differences in the 10 think-aloud categories, the Science results showed developmental differences. Older students demonstrated a more diverse array of strategies, and explicit linking of text and visual aid information was not as evident in the younger students. ANOVAs following cluster analyses showed weak relationships between cluster membership and outcomes. Implications for instruction are discussed.     

Reciprocal Teaching of Comprehension‐fostering and Comprehension‐monitoring Activities with Ten Primary School Girls

Abstract This paper reports an experimental evaluation of a direct instruction procedure in which children are taught and practise activities to both foster and monitor their comprehension while reading. Three different class groups of low comprehenders, Standard 4, Form 1 and Form 2, were serially exposed to 21 days of 20‐25 minutes instruction in four study activities: summarising, questioning, clarifying and predicting. Instruction was by reciprocal teaching whereby the adult tutor and children took turns leading a dialogue centred around the important topics of the instructional text. The design of this study incorporated both with‐subjects multiple baseline and between‐subjects comparisons, the no treatment comparison groups being average and above average comprehending class peers. Daily comprehension assessment on a different text at the same difficulty level as that used for reciprocal teaching and pre and post intervention scores on a reading comprehension test served as the dependent measures for the study. Results show significant increases in accuracy on comprehension tests for all experimental groups upon introduction of the reciprocal teaching procedure. On completion of the intervention two of these groups scores matched those of the above average controls. Follow‐up probes eight weeks later showed that all groups had maintained their comprehension gains.     

Adopting birth philosophies to guide successful birth practices and outcomes

Research studies conducted recently in hospitals located in Switzerland and Canada reveal the importance of birth philosophies in attaining successful birth practices and outcomes.     

The Effects of an Introductory Provision of Context on the Oral Reading Behaviour of an Above Average Reader

Abstract Previous studies have shown that prior discussion, or the provision of context, both decrease oral reading errors and increase self‐correction amongst low‐progress and mentally retarded readers. This study investigated the effects of prior provision of context upon the reading behaviour of an above average reader. The results indicate that discussion of context (through examination of the relevant illustrations, asking and answering questions, and the verbal introduction of some new words in the text) both significantly decreased errors, and slightly increased the amount of self‐correction for this subject.     

The existence and extent of spatial working memory ability in honeybees

Honeybees foraged from six locations, each of which was baited with sugar solution prior to each experimental trial. Under a variety of conditions, bees exhibited a small but reliable tendency to avoid revisits to locations that they had visited earlier during the experimental trial. These results replicate those of Brown and Demas (1994), who concluded that bees use working memory to discriminate previously visited locations from those not yet visited. The present experiments included procedures that allowed alternatives to this explanation to be more completely ruled out. The extent of spatial working memory performance exhibited by honeybees in these experiments appears to be limited by a process other than working memory capacity, perhaps the ability of bees to discriminate among several locations in close proximity to one another.     

Routes into English teaching: beginning teachers' reflections on college‐based and school‐based Initial Teacher Education programmes

This article compares student and trainee teachers' experiences of three different routes into secondary English teaching: the standard one‐year PGCE; the newer ‘flexible’ PGCE; and the employment‐based Graduate Teacher Programme. As part of a two‐year study involving over 80 beginning teachers the authors invite students and trainees to reflect on the perceived advantages and disadvantages of their chosen route. This article focuses on a small number of interviews with individuals from the sample as they near completion of their training. It sets the findings of the study in the wider political context of New Labour's agenda for school reform and the future development of Initial Teacher Education.     

Emotional risk to children caught in violent marital conflict—The Basildon treatment project

This paper outlines the work of the Basildon Marital/Family Violence Project set up as a result of two studies undertaken by the National Society for the Prevention of Cruelty to Children (N.S.P.C.C.) School of Social Work, which looked at the effect of marital violence upon the children involved. These effects were classified under the following headings: (1) the children were scapegoated; (2) used as pawns in the marital battles; (3) turned agression against themselves; (4) had relationship problems at school; (5) were physically assaulted by the parents in 25% of the cases. The project, which is now in its 4th year, has offered social work services, consultation, training courses and research. Work with the families, and particularly with the children, has further emphasised the severe emotional damage that marital violence can have upon the children. The paper optimistically reports that after intensive work using a five-point treatment programme, and direct work with the children, there has been considerable diminution of violence in many of the cases and in some cases no repetition of such violence at all. The worker's approach, it is suggested, should be characterised by optimism combined with indestructible calm, genuine empathy combined with 24-hour access, persistence in the face of lack of progress, enhancement of parents' low self-esteem, regular contact and an ability to contain destructiveness.