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Of the eight hundred Ball State University freshman and sophomore students surveyed to determine the incidence of those who identified themselves as test anxious, approximately thirty percent indicated that they suffered from test anxiety. The thirty-eight students who agreed to participate in the experiment and were included in the final data analysis were students at Ball State University, Winter Quarter, 1970-1971, and described themselves as test anxious to the point of suffering moderate to severe discomfort in test-taking situations.After pre-testing, subjects in Group I (traditional SD) and Group II (modified SD) received two hours' relaxation training and visual imagery training, after which they underwent SD in the following manner: Group I received SD based on Wolpe's model. That is, while in a relaxed state they were exposed to a standard hierarchy based on items from the Suinn Test Anxiety Behavior Scale. Group I did not proceed to a new hierarchy item if more than one person indicated more than minimal anxiety after four exposures the item. In the six desensitization sessions, Group I was exposed to 13 of the 17 hierarchy items. Group II proceeded through the same standard hierarchy under the same conditions, but at a predetermined rate without repeating any items. They were exposed to the 17 hierarchy items in six sessions.Group III received relaxation training only with no presentation of hierarchy items. Group IV received no to treatment.A multi-factor analysis of variance was computed for pre- and post-test scores on the three measures for the four groups. Posteriori orthogonal comparisons were made for contrasts showing significant differences. Both methods of desensitization as well as relaxation training were effective in significantly reducing test anxiety as reflected by subjects' post-treatment STABS scores. All three experimental groups experienced significately greater reduction of test anxiety than the control group: Group II, F 31.1564; Group III, F 12.0813; and Group I, 6.0133. Group I and Group III were not significantly different from each other in terms of test anxiety reduction. However, Group II experienced significantly greater reduction of test anxiety than Group I as measured by mean difference STABS scores (F 9.7996).Significant changes did. not occur in scores in the other two measures used in the study, with one exception. There were no significant differences in pre- and post-test scores on the general anxiety measure (TMAS) for any of the groups. Group I showed a significant loss on the scholastic achievement measure, and the trend for the other groups was toward loss rather than gain. The reasons for this are not clear, but some possibilities are listed in the text of the dissertation.The results of the study indicate that the three experimental techniques for treatment of test anxiety as measured by the STABS were viable treatment methods. The modified SD method (Group II) appeared to be superior to the other two treatment methods in effectiveness.

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This thesis records an attempt to prove the two conjecture: Conjecture A: Every finite non-regular primitive permutation group of degree n contains permutations fixing one point but fixing at most $n^{1/2}$ points. Conjecture C: Every finite irreducible linear group of degree m > 1 contains an element whose fixed-point space has dimension at most m/2. Variants of these conjectures are formulated, and C is reduced to a special case of A. The main results of the investigation are: Theorem 2: Every finite non-regular primitive permutation group of degree n contains permutations which fix one point but fix fewer than (n+3)/4 points. Theorem 3: Every finite non-regular primitive soluble permutation group of degree n contains permutations which fix one point but fix fewer than $n^{7/18}$ points. Theorem 4: If H is a finite group, F is a field whose characteristic is 0 or does not divide the order of H, and M is a non-trivial irreducible H-module of dimension m over F, then there is an element h in H whose fixed-point space in M has dimension less than m/2. Theorem 5: If H is a finite soluble group, F is any field, and M is a non-trivial irreducible H-module of dimension m over F, then there is an element h in H whose fixed-point space in M has dimension less than 7m/18. Proofs of these assertions are to be found in Chapter II; examples which show the limitations on possible strenghtenings of the conjectures and results are marshalled in Chapter III. A detailed formulation of the problems and results is contained in section 1.

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Paper 1: The provision of Nurture Groups (NGs) has been recognised as an effective early intervention for children with social, emotional and behavioural difficulties (SEBD). ‘The high expectations of teachers in Nurture Groups can bring about amazing change’ in the lives of young emotionally disturbed children (Lucas, 1999, p.14). When the principles of NG are effectively applied by all staff in all areas of the school and when nurturing attitudes and practices develop throughout the school, teaching and learning become effective for all children (Lucas, 1999). This study aims to extend the understanding of the gains and costs that may be associated with the placement of children in NGs. The NG intervention’s contribution to the wider school system is also documented. However, this study aims to provide a deeper understanding on the impact of NG provision on the mainstream school it serves from the viewpoints of the different groups of participants involved and to look whether the ethos and approaches used in the nurture group are promoted in the wider school environment. A case study methodology with interpretive approaches was employed in a community primary school in an urban area in the South West of England. Quantitative (Boxall Profiles) and qualitative (interviews and observations) measures revealed that overall there have been improvements in NG children’s social, emotional and behavioural (SEB) functioning and academic development. However, findings also revealed a number of opportunity costs attached to children’s placement in the NG. Qualitative measures also showed that, while NG provision contributed to positive developments within the school, the NGs did not help the school in fully integrating their work in the wider approach to meeting all children’s needs. A number of disadvantages were also reported with regards to the impact of the NG upon the school. Abstract Paper 2: The provision of Nurture Groups has been recognised as an effective early intervention for children with SEBD. ‘The high expectations of teachers in Nurture Groups can bring about amazing change’ in the lives of young emotionally disturbed children (Lucas, 1999, p.14). When the principles of NG are effectively applied by all staff in all areas of the school and when nurturing attitudes and practices develop throughout the school, teaching and learning become effective for all children (Lucas, 1999). Communication between NG and mainstream staff is considered to be important for the effective running of the NGs and for developing a nurturing school ethos. Lack of collaborative partnership work can create tensions between NG and mainstream staff. Parental involvement is also recognised important in the NG. Research reveals that partnership relationships with parents contribute to positive social and emotional outcomes for children and to positive effects for parents in terms of their capacity to understand their children and apply NG practices outside of the NG. Despite the inherent power imbalance between NG staff and parents, there can be a positive outcome if the NG approaches are extended holistically to all school staff. The aim of this paper is to explore the quality of communication between NG and mainstream staff and the enablers and barriers of parental involvement in the NGs and the school. This qualitative study was conducted in a community primary school in an urban area in the South West of England and included 34 participants - 13 school staff, 8 parents, 9 children, and 4 professionals and governors. Semi-structured interview data revealed that while some communication existed between NG and mainstream staff there were subtle difficulties involved in creating a collaborative partnership work with regards to sharing information with each other. Despite developing a collaborative relationship and effective communication being seen as the most important enabler for parental involvement in the NGs and the rest of the school, there was a more structured communication and a more supportive support between the NGs and parents of the NG children than the rest of the school and parents.

This paper will be concerned mainly with automorphisms of groups. The concept of a group endomorphism will be used at various points in this paper.

This paper is an algebraic study of selected properties of semigroups. Since a semigroup is a result of weakening the group axioms, all groups are semigroups. One facet of the paper is to demonstrate various semigroup properties that induce the group axioms.