Word Equations and Related Topics. Independence, Decidability and Characterizations

The three main topics of this work are independent systems and chains of word equations, parametric solutions of word equations on three unknowns, and unique decipherability in the monoid of regular languages. The most important result about independent systems is a new method giving an upper bound for their sizes in the case of three unknowns. The bound depends on the length of the shortest equation. This result has generalizations for decreasing chains and for more than three unknowns. The method also leads to shorter proofs and generalizations of some old results. Hmelevksii’s theorem states that every word equation on three unknowns has a parametric solution. We give a significantly simplified proof for this theorem. As a new result we estimate the lengths of parametric solutions and get a bound for the length of the minimal nontrivial solution and for the complexity of deciding whether such a solution exists. The unique decipherability problem asks whether given elements of some monoid form a code, that is, whether they satisfy a nontrivial equation. We give characterizations for when a collection of unary regular languages is a code. We also prove that it is undecidable whether a collection of binary regular languages is a code.

Training graduate students to be teachers

Pedagogic education of graduate students, when and where it exists, is restricted to theoretical courses or to the participation of the students as teachers' assistants. This model is essentially reproductive and offers few opportunities for any significant curriculum innovation. To open an opportunity for novelty we have introduced a new approach in "Biochemistry Teaching", a course included in the Biochemistry Graduate Program of the Biochemistry Department (Universidade Estadual de Campinas and Universidade de São Paulo). The content of the course consists of a) choosing the theme, b) selecting and organizing the topics, c) preparing written material, d) establishing the methodological strategies, e) planning the evaluation tools and, finally, f) as teachers, conducting the course as an optional summer course for undergraduate students. During the first semester the graduate students establish general and specific educational objectives, select and organize contents, decide on the instructional strategies and plan evaluation tools. The contents are explored using a wide range of strategies, which include computer-aided instruction, laboratory classes, small group teaching, a few lectures and round table discussions. The graduate students also organize printed class notes to be used by the undergraduate students. Finally, as a group, they teach the summer course. In the three versions already developed, the themes chosen were Biochemistry of Exercise (UNICAMP), Biochemistry of Nutrition (UNICAMP) and Molecular Biology of Plants (USP). In all cases the number of registrations greatly exceeded the number of places and a selection had to be made. The evaluation of the experience by both graduate and undergraduate students was very positive. Graduate students considered this experience to be unique and recommended it to their schoolmates; the undergraduate students benefited from a more flexible curriculum (more options) and gave very high scores to both the courses and the teachers.

Classificações de signos de C.S.Peirce: de ‘On the Logic of Science’ ao ‘Syllabus of Certain Topics of Logic’

As classificações dos signos de C.S.Peirce começam a ser desenvolvidas em 1865 e se estendem a até, pelo menos, 1909. Vou apresentar o período que tem início em 1865, e possui dois momentos de intensa produção - "On a New List of Categories" e "On the Algebra of Logic: a contribution to the philosophy of notation". Em seguida apresento as dez classes de signos, uma morfologia que aparece no "Syllabus of Certain Topics of Logic", e é desenvolvida a partir de 1903. Meu propósito aqui é familiarizar o leitor com as intrincadas classificações sígnicas de Peirce.

Adolescent females' self-concept and physical education : a Q-sort analysis /

This research illuminates the relationship between female adolescents' self-concept and their experience of physical education. This was accomplished through three stages of interviews and a Qsort. The topics through which the research was categorized included peer support, teachers as significant others, meaningful connections to the body, and curriculum content. During stage one female physical education specialists, curriculum coordinators, and adolescents were interviewed to develop Q-items for the Q-sort. The second stage Involved two groups of females between the ages of 12 and 14 years who participated in the Q-sort. The final stage involved an insight group that consisted of four Q-sort participants who interpreted the highest ranking Q-items. Critical to this research was giving these adolescents the opportunity to voice what was important to them. The results of the research included descriptions of the elements in physical education that were deemed most important by female adolescent students. The topics of "peer support" and "meaningful connections to the body" were ranked the highest. By interpreting the rich insights of the discussion group, it was found that peers were most influential to these young girls. Perceiving and bestowing respect were imperative in this stage of their lives.

Cardiovascular health risk profiling of Niagara Region grade 9 students : implications for elementary curriculum /

The purpose of this study was to determine if Ontario's health and physical education curriculum contributes sufficiently to ensure the health of our children and young adults. To determine the curriculum effect, the health risk profile of Niagara Region's grade 9 students was compared to Canada's adolescent population. All subjects completed a "Heart Health Lifestyle" survey and were measured for height, weight, percent body fat, blood pressure, and total cholesterol and performed the 20-metre shuttle run test as part of their physical and health education classes. The Niagara Region grade 9 population had a healthy risk profile. Aerobic power was inversely related, and cholesterol levels were positively associated to body mass index and percent body fat in the whole group analysis. These results indicate that physical education can offer unique and essential aspects allowing individuals a means to learn and control body movements and keep physically fit while providing protection against modern disease. Ontario's health and physical education curriculum does contribute to the health of our children and adolescents; however, there is a need to implement a stronger mandate for daily vigorous physical activity.

An exploration of the experience of implementing the second step violence prevention curriculum in one primary general learning disabilities class /

Violence has always been a part of the human experience, and therefore, a popular topic for research. It is a controversial issue, mostly because the possible sources of violent behaviour are so varied, encompassing both biological and environmental factors. However, very little disagreement is found regarding the severity of this societal problem. Most researchers agree that the number and intensity of aggressive acts among adults and children is growing. Not surprisingly, many educational policies, programs, and curricula have been developed to address this concern. The research favours programs which address the root causes of violence and seek to prevent rather than provide consequences for the undesirable behaviour. But what makes a violence prevention program effective? How should educators choose among the many curricula on the market? After reviewing the literature surrounding violence prevention programs and their effectiveness, The Second Step Violence Prevention Curriculum surfaced as unique in many ways. It was designed to address the root causes of violence in an active, student-centred way. Empathy training, anger management, interpersonal cognitive problem solving, and behavioural social skills form the basis of this program. Published in 1992, the program has been the topic of limited research, almost entirely carried out using quantitative methodologies.The purpose of this study was to understand what happens when the Second Step Violence Prevention Curriculum is implemented with a group of students and teachers. I was not seeking a statistical correlation between the frequency of violence and program delivery, as in most prior research. Rather, I wished to gain a deeper understanding of the impact ofthe program through the eyes of the participants. The Second Step Program was taught to a small, primary level, general learning disabilities class by a teacher and student teacher. Data were gathered using interviews with the teachers, personal observations, staff reports, and my own journal. Common themes across the four types of data collection emerged during the study, and these themes were isolated and explored for meaning. Findings indicate that the program does not offer a "quick fix" to this serious problem. However, several important discoveries were made. The teachers feU that the program was effective despite a lack of concrete evidence to support this claim. They used the Second Step strategies outside their actual instructional time and felt it made them better educators and disciplinarians. The students did not display a marked change in their behaviour during or after the program implementation, but they were better able to speak about their actions, the source of their aggression, and the alternatives which were available. Although they were not yet transferring their knowledge into positive action,a heightened awareness was evident. Finally, staff reports and my own journal led me to a deeper understanding ofhow perception frames reality. The perception that the program was working led everyone to feel more empowered when a violent incident occurred, and efforts were made to address the cause rather than merely to offer consequences. A general feeling that we were addressing the problem in a productive way was prevalent among the staff and students involved. The findings from this investigation have many implications for research and practice. Further study into the realm of violence prevention is greatly needed, using a balance of quantitative and qualitative methodologies. Such a serious problem can only be effectively addressed with a greater understanding of its complexities. This study also demonstrates the overall positive impact of the Second Step Violence Prevention Curriculum and, therefore, supports its continued use in our schools.

Transforming curriculum leadership: vice principals in independent Christian elementary schools /

The literature on the vice principalship characterizes the position as one filled with clerical record keeping and student discipline and paints a picture of role conflict and general discontent. Research suggests that vice principals desire to take on a more significant role, specifically a role in curriculum leadership. Using open-ended interviews, a focus group interview, document analysis, and my research journal, I have explored the work ofa group of vice principals who have taken on the role of curriculum leader in independent Christian elementary schools in Ontario. When asked to explain their understanding of curriculum, the participants referred to written programs of study. However, their leadership activities reveal a broader understanding of curriculum as something that is in fact dynamic in nature. This leadership is enabled and shaped by their middle position on staff that combines the authority of an administrator and the credibility of a teacher. Although this dual identity creates tension, it also provides opportunities for genuine curriculum leadership. As middle leaders, the participants in this study often pull together or connect elements of the curriculum (teachers, principals, and programs) that have become separated. Such connective leadership is characterized by transformational (Van Brummelen, 2002) tendencies. This research suggests that the further along the continuum one goes from the understanding of curriculum as planned (Eisner, 1994) to acknowledging a lived curriculum (Aoki, 1993), the more transformational one's leadership style becomes.

The impact of scheduling on the implementation of the new Ontario curriculum: teachers' perceptions /

This qualitative study explored secondary teachers' perceptions of scheduling in relation to pedagogy, curriculum, and observation of student learning. Its objective was to determine the best way to organize the scheduling for the delivery of Ontario's new 4-year curriculum. Six participants were chosen. Two were teaching in a semestered timetable, 1 in a traditional timetable, and 3 had experience in both schedules. Participants related a pressure cooker "lived experience" with weaker students in the semester system experiencing a particularly harsh environment. The inadequate amount of time for review in content-heavy courses, gap scheduling problems, catch-up difficulties for students missing classes, and the fast pace of semestering are identified as factors negatively impacting on these students. Government testing adds to the pressure by shifting teachers' time and attention in the classroom from deeper learning to a superficial coverage of material, from curriculum as lived to curriculum as text to be covered. Scheduling choice should be available in public education to accommodate the needs of all students. Curriculum guidelines need to be revamped to reflect the content that teachers believe is necessary for a successful course delivery. Applied level courses need to be developed for students who are not academically inferior but learn differently.

Introducing e-learning in a large multisite academic health sciences centre: a case study of e-curriculum planning and educator support /

This qualitative study investigated how a team of 7 hospital educators collaborated to develop e-curriculum units to pilot for a newly acquired learning -r management system at a large, multisite academic health sciences centre. A case study approach was used to examine how the e-Curriculum Team was structured, how the educators worked together to develop strategies to better utilize e-leaming in their ovwi practice, what e-curriculum they chose to develop, and how they determined their priorities for e-curriculum development. It also inquired into how they planned to involve other educators in using e-leaming. One set of semistructured interviews with the 6 hospital educators involved in the project, as well as minutes of team meetings and the researcher's journal, were analyzed (the researcher was also a hospital educator on the team). Project management structure, educator support, and organizational pressures on the implementation project feature prominently in the case study. This study suggests that implementation of e-leaming will be more successful if (a) educators involved in the development of e-leaming curriculum are supported in their role as change agents, (b) the pain of vmleaming current educational practice is considered, (c) the limitations of the software being implemented are recognized, (d) time is spent leaming about best practice, and (e) the project is protected as much as possible from organizational pressures and distractions.

An aryne route to aporphine alkaloids and related topics / |nIjaz Ahmad Chanda. -- 260 St. Catharines, Ont. : [s. n.],

This research was directed towards the investigation and development of an aryne route to the syntheses of aporphi ne and dibenzopyrrocolinium (dibenzoindolizinium) alkaloids and to the stability of the latter under the conditions used for aryne formation. The work c an be divided into three main sections . i) - Synthesis of Glaucine 6-Bromo-3,4-dimethoxyphenylacetic acid, prepared by the action of bromine i n acetic acid on3,4-dimethoxyphenylacetic a cid, was converted into its acid chloride by t he action of thionyl chloride. This on treatment with 3,4- dimethoxyphenylethylamine pr ovided N-(3, 4-dimethoxyphenylethyl)- 2-(2-bromo-4,S-dimethoxyphenyl)-acetamide which on dehydration with phosphoryl chloride (Bischler Napieralski reaction) in dry benzene afforded l -(2-bromo-4,S-dimethoxybenzyl)- 3,4-dihydro-6,7-dimethoxyisoquinoline, isolated as hydrochl oride. A new method o f destroying the excess of phosphoryl chloride was developed which proved to be quite useful. Methylation of the dihydroisoquinoline'with methyl iodide in methanol , and subsequent reduction with sodium borohydride provided (±)-6-bromolaudanosine. Act ion of potassamide or sodamide in anhydrous liquid ammonia on (±)-6-bromolaudanosine yielded the corresponding amino derivative along with other products. Diazotization and ring closure of (±)-6-aminolaudanosine then a f forded (±)-glaucine which was isolated as methiodide. ii) - Intramolecular Capture of Aryne During Glaucine Synthesis, and Subsequent Reactions . This section deals with the by-products formed under the conditions of the aryne stage of t he glaucine synthesis. The crude product, obtained in the reaction of potassamide or sodamide in liquid ammonia on (±)-6-bromolaudanosine, was s eparated by chromatography, Three products were separated and identified. a ) - 5,6-Dimethoxy-2-( 3,4-dimethoxy-6-ethylphenyl)-lmethylindole. Two mechanisms are proposed for the formation of this interesting product. This compound also was prepared by the action of potassamide in l,iquid ammonia on 5,6 ,l2,l2atetrahydro- 2,3,9,lO-tetramethoxy-7-methyldibenz[b,g]indolizinium i odide . b) - 5,6-Dimethoxy-2-(3,4-dimethoxy-6-vinylphenyl)-lmethylindoline. Its formation represented a new method of Hofmann degradation . Further confirmation of structure was done by performing the normal Hofmann reaction on 5, 6,12,12a-tetrahydro -2/3,9,lO-tetramethoxy ~7-methyldibe nz[ b,g]indolizinium iodide. The indoline prepared i n this way was identical in all respects with that prepared above . c) - 1- (2-amino-4,5-dimethoxybenzyl ) -l,2,3,4-tetrahydro-2- methyl-6,7-dimethoxyisoquinoline, was converted t o glaucine as stated in section 1 . iii) - Attempt:,ed Sxnthesis of Liriodenine Piperonal was converted into 3,4-methylenedioxyinitrostyrene which on reduction with lithium aluminium hydride provided 3,4-methylenedioxyphenylethylamine. The method of extraction after the reduction was improved t o some extent. The amine on condensation with m-chlorophenylacetyl chloride, prepared by the action of oxalyl chloride on 3,4-methylenedioxyphenylacetic acid, provided N-[ ~ -(3,4-methylenedioxyphenyl)- e thyl)-3-chlorophenylacetamide. This on dehydration with phosphoryl chloride in dry benzene followed by air oxidation afforded l-(3-chlorobenzoyl)-6,7-methylenedioxyi soquinoline. This compound on r eaction with potassamide in liquid ammonia afforded a crude product from which. one product was separated by chromatography i n a pure condition . This yellow compound analysed as,c17Hl ON2021 and was t he main product i n the reaction ; a t entative structure is proposed. A second compound, not obtained in pure condition, was submitted to Pschorr reaction in the hope of obtaining liriodenine, but without success.

Measuring curriculum integration in the junior grades: the design of an instrument

This study \Alas initiated in response to the Junior Division Review (1985) publ ished by the Ministry of Education for the Province of Ontario. Curriculum integration is an element used within the educational paradigm designed by the Ontario Ministry of Education. It is a term frequent1y verbal ized b>' educators in this province, but because of 1 imi ted resource support regarding this methodology, it was open to broad interpretation resulting in an extreme v ar i at i on i nit simp 1 eme n tat i on • I n de ed, the Min i s try intimated that it was not occurring to any significant degree across the province. The objective of this thes is was· to define integration in the junior classroom and de-:.ign a meas.ur·ement in-:.tr-ument which would in turn high 1 i gh t indicators of curriculum integration. The :.tudy made a prel iminary, field-based survey of educa tiona 1 professionals in order to generate a relevant description of integrated curr-iculum programm i ng as def i ned in the j un i or classroom. The description was a compilation of views expressed by a random selection of teachers, consultants, supervisory officers and principals. The survey revea 1 ed a much more comprehens i ve vi et·<,l of the attributes of integrated programming than tradition would dictate and resulted in a functional definition tha t was broader than past prac t ices. Based on the information generated by this survey, an instrument ou t 1 in i ng program cr iter i a of was devised. an integrated junior cla~·sroom Th i s measuremen t i nstrumen t , designed for all levels of educators, was named uThe Han~.son I nstrumen t for the Measuremen t of Program Integrat ion in the Jun i or Cl assroom". It refl ected five categories intrinsic to the me thodol ogy of integration: Teacher Behaviour, Student Behaviour, Classroom Layout, Cl as~·r oom Environment and Progr amm i ng. Each category and the items therein were successfully tested in val idi ty and rel iabi 1 i ty checKs. Interestingly, the individual class was found to be the major variable programming in in the measuremen t the j un i or d i vis i on • of The integrated instrument demonstrated potential not onl)' a~· an initial measure of the degree of integrated curriculum, but as a guide to strategies to implement such a methodology.