This investigation concerns the ways in which young children (ages 5 to 8) compare quantities and how they work out the difference between them. The experiments involved children's understanding of mathematical problems and their ability to make use of graphical information in such problems. Each child was shown a series of illustrations, each representing two sets of quantities where the numerical difference was represented either discontinuously or continuously. The children were asked Equalize and Compare questions about each illustration and had to choose the correct answer from the set which represented the choice stimuli. Children's use of strategies was observed. In Experiment 1 (5-to-8-year-olds), only the younger children (5-to-6-year-olds) were observed to perform much more accurately on the Equalize-type question than on the Compare in both discontinuous and continuous conditions. The 7-to-8-year-olds reached a ceiling effect in performance, suggesting that by this age they can already deal with different types of arithmetic problems and with different types of graphical information. Experiment 2 (5-to-6-year-olds) repeated the first experiment presenting the graphical information on a microcomputer, but the discontinuous and continuous conditions were subdivided on the basis of the use of the comparative term "more" or "less". Children are helped significantly by the use of discontinuous material and by the use of "more" in Equalize-type questions only. These results did not support those of Experiment 1 where the Equalize and Compare difference was significant with both discontinuous and continuous material. Experiment 3 introduced part-whole manipulations in order to find out why Compare questions are more difficult to solve than Equalize questions. Five-to-6-year-olds' performance on Compare word problems was not affected by this type of manipulation. Experiment 4 explored the Equalize and Compare difference by presenting the material in a story-telling context. Again, the 5-to-6-year-olds' performance on Compare word problems was not affected by this type of manipulation. However, Equalize questions were helped by the use of the comparative term "more", as in Experiments 2 and 3, and by the presentation of discontinuous material, as in Experiment 2. Experiments 5 and 6 explored children's (5-to-8-year-olds) performance on Equalize- and Compare-type questions using spatial imagery manipulations. Experiment 5 involved manipulations of display in order to examine children's relative ease with Equalize word problems. Again, children's performance was not affected by this type of manipulation. In addition to the display manipulations, Experiment 6 introduced different level manipulations. However, in this experiment, the comparative pair was not represented in the choice stimuli. Children's performance on Compare word problems improved. There was no sign of the Equalize and Compare distinction which may be due to the fact that there was no representation of the comparative pair. The results show that the Equalize and Compare difference is due to a combination of their inherent structural and linguistic factors. Furthermore, the difficulty children have with Compare word problems is non-number-specific, but their relative ease with Equalize word problems is number-specific. Such type results indicate that children represent these two problems very differently.

No description available.

The Devereux Early Childhood Assessment (DECA; L.eBuffe & Naglieri, 1999), a standardized strength-based measure, was used with 125 kindergarten children from two different regions in British Columbia to investigate the relationship between mother and teacher ratings of students’ strengths and behaviour problems. Results suggest that the level of agreement between mother and teacher ratings for children’s strengths is similar to the level of agreement between mother and teacher ratings for children’s problem behaviours. The level of agreement between motherreported and teacher-reported scores was found to be low for all DECA scales and most DECA items, with some differences found upon examination of the sample by gender. The findings revealed three main trends: first, a higher degree of correspondence and a lower degree of difference was found between mother and teacher ratings for the Self-Control scale and items, compared to the other scales and items; second, a lower degree of correspondence and a higher degree of difference was found between mother and teacher ratings for the Attachment scale and items, compared to other scales and items; third, the level of agreement between mothers and teachers ratings was higher for boys than for girls. These patterns of cross-informant correspondences and differences are discussed in the context of the need for practitioners to obtain rating information from both mothers and teachers, since each rater provides a unique perspective. Furthermore, the importance of highlighting children’s strengths in the assessment process is emphasized. / Education, Faculty of / Educational and Counselling Psychology, and Special Education (ECPS), Department of / Graduate

Students who are learning English as a second language (ESL) have lower performance on mathematics problems based in language than students who are fully fluent in English. Students’ performance on word-based mathematics problems is directly related to their English reading comprehension and language fluency (Abedi & Lord, 2001; Brown, 2005; Hofstetter, 2003). This places students who are not fully fluent in English at a disadvantage in the mathematics classroom. Students’ self-efficacy beliefs also impacts their mathematics performance and motivation. The self-efficacy of students who are not fluent in English may be negatively impacted by their struggle with language. For this exploratory study, image-based mathematics problems were created to communicate problem solving questions with pictures instead of language or computational symbols. This problem format was investigated as a potential alternative to word-based or computation-based problems. Grade 6 students registered in ESL level 2, ESL level 4, and not registered in ESL, completed a mathematics task with four computation problems, four language-based problems, and four image-based problems. During a follow-up interview, students’ solution strategies and thought processes were explored further. The results of this study indicated that the inclusion of wordless mathematics problems, such as image-based problems, assisted some of the students who were learning basic English interpersonal communication skills. As nonroutine problems, image-based mathematics also encouraged complex thought and mathematics understanding. Students in ESL Level 2 demonstrated higher self-efficacy beliefs on image-based problems than word problems. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

No description available.

"Social Welfare" is of great, and growing, importance in the modern world, and it constantly demands definition. Statistical resources are needed (a) as aids in the definition of welfare problems, (b) to determine the nature and distribution of welfare needs, and (c) for evaluating the appropriateness and effectiveness of existing welfare services and planning the development of new services. As a background, the main types and sources of welfare measurements are reviewed in the light of the increasing volume of studies In Great Britain, the United States and Canada during the present century. To focus on the problem of adequate provincial statistics, an exploratory examination is made of two major groups of data: (a) demographic data from the Census and related sources; (b) the current standard measurements of the recipients of provincial public welfare services, abstracted from the annual reports of the Department of Social Welfare of the Province of British Columbia. The first group includes population trends, age-composition and family formation. The second group gives particular attention to the "categorical assistance programmes", the aged, social allowances, and provincial family services. There is now available a larger body of socio-economic data than ever before, but it is not being fully utilized for welfare interpretation or social service planning. A serious barrier to intensive analysis on a provincial basis is the lack of standardization of a set of regions covering the total geographical area, (as between Departmental Regions, administrative units and census districts). Variations In reporting procedure and insufficient development of socio-economic data and of components or causal factors in dependency are the greatest weaknesses in existing materials. Other areas of welfare in which new measurements as well as the co-ordination or modification of existing data are needed, are only briefly indicated in the present study. "Welfare", today, is more important than ever, and so is welfare research that provides the base for the improvement of existing services and creation of new ones, through broad, statistical measurements as well as special counts and studies. / Arts, Faculty of / Social Work, School of / Graduate

"Factors Associated With Crime and Juvenile Delinquency, Economic Dependency, and Inadequate Child Care In Multi-Problem Families". A thesis presented by Collin Carlile, John Cushnie, Roy Fong, Kenneth Pauli, Helen Ruckle, Ailsa Walker and Arthur Veroba. The purpose of this study was to explore associations between the factors of child care, crime and juvenile delinquency, and economic dependency, and selected family functioning variables. These family functioning variables were chosen from the scale utilized by Geismar-Ayres in the St. Paul Study on Multi-Problem Families. Simple random sampling was used to select 100 cases from a group of 250 cases previously selected and in use by the Vancouver Area Development Project. The source material consisted of Area Development Project case profiles and score sheets, and selected case file material. The collected data was sorted and tabulated in such a manner as to allow comparison of the association between the specific variables. The reliability of the ratings used was assumed as all data was previously recorded by Vancouver Area Development Project Staff who had been trained in utilizing the rating scale. This study was an "ex-post-facto” survey and therefore was not intended to necessarily delineate any complex etiological patterns. No factors were found to be highly associated with any of the family functioning variables though several incidents of moderate association were found. The family functioning factor most closely associated with economic dependency was the absence of one parent from the home. The factor most closely associated with inadequate child care was the inadequate behaviour of the mother. The factor most closely associated with delinquency and crime was inadequacy in the behaviour of the mother and inadequacy in marital relationships respectively. The major significant findings of this study would seem to indicate that it has fulfilled its purpose by underlining the need for further studies of family functioning variables within the context of multi-problem families. Such future studies would necessarily be intensified both in depth and focus. / Arts, Faculty of / Social Work, School of / Graduate

Let f(z) be a complex-valued function of the complex variable z which is regular at the origin, has radius of convergence R > 1 , and satisfies the condition f(1) = 1 . If we write [ equation omitted ]and [ equation omitted ], n=0,1,2,..., the matrix [ equation omitted ] leads to a summation method generally known as a Sonnenschein method. The utility of these methods lies in the fact that much can be said about them simply from a knowledge of the function f(z) . In the present work we are concerned with the three methods associated with the three functions f(z) = (1-r) + rz , f(z) = (1-r)+rz² and f(z) = (1-r)z + rz³ where r≠ 0 is an arbitrary complex parameter (generally, 0 < r < 1). The method based on the function (1-r) + rz leads to the well-known Euler-Knopp method which has already been extensively studied. We show that there exist simple recursion relations between the various rows of the matrix F and we make a detailed study of the domain Dᵣ on which these methods sum the geometric series [ equation omitted ].A more general sub-class of Sonnenschein methods called the (E,r,α,β) methods is then defined and some of the well-known theorems applicable to the (E,r) method are shown to hold for this sub-class. The practical application of the above three methods to the two- and three-body problems of classical mechanics forms the major portions of Chapters II and III . Much use is made in these chapters of a theorem, stated in Chapter I , which allows us to construct a domain Dr(a) on which one of the above methods sums an arbitrary function a(z) regular at the origin. On the limited Intervals for which the above methods are applicable, it is shown that they provide effective methods for obtaining the solution to the two-and three-body problems. Comparison is always made with similar results obtained by V. A. Brumberg and it is shown that the methods used here have certain advantages over his. The Sundman series for the three-body problem are also set up and utilized. Although the series are not very effective, the convergence is not as bad as is generally supposed. An interesting argument based on numerical evidence shows that the width of the strip about the real axis, in which the solution to the regularized three-body problem is known to be analytic, is not as narrow as Sundman's estimates give. Finally, a theorem is proved for the problem of the motion of a heavy rigid body about a fixed point showing that this problem can be treated in the complex plane in the same way as the two-body problem and regularized three-body problem. / Science, Faculty of / Mathematics, Department of / Graduate

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We demonstrate the schema and ontology matching tool COMA++. It extends our previous prototype COMA utilizing a composite approach to combine different match algorithms [3]. COMA++ implements significant improvements and offers a comprehensive infrastructure to solve large real-world match problems. It comes with a graphical interface enabling a variety of user interactions. Using a generic data representation, COMA++ uniformly supports schemas and ontologies, e.g. the powerful standard languages W3C XML Schema and OWL. COMA++ includes new approaches for ontology matching, in particular the utilization of shared taxonomies. Furthermore, different match strategies can be applied including various forms of reusing previously determined match results and a so-called fragmentbased match approach which decomposes a large match problem into smaller problems. Finally, COMA++ cannot only be used to solve match problems but also to comparatively evaluate the effectiveness of different match algorithms and strategies.