The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

The dual role of students with behavioural problems: an analysis of their experiences as bullies and victims /

The present study examined the bullying experiences of a group of students, age 10-14 years, identified as having behaviour problems. A total often students participated in a series of mixed methodology activities, including self-report questionnaires, story telling exercises, and interview style joumaling. The main research questions were related to the prevalence of bully/victims and the type of bullying experiences in this population. Questionnaires gathered information about their involvement in bullying, as well as about psychological risk factors including normative beliefs about antisocial acts, impulsivity, problem solving, and coping strategies. Journal questions expanded on these themes and allowed students to explain their personal experiences as bullies and victims as well as provide suggestions for intervention. The overall results indicated that all of the ten students in this sample have participated in bullying as both a bully and a victim. This high prevalence of bully/victim involvement in students from behavioural classrooms is in sharp contrast with the general population where the prevalence is about 33%. In addition, a common thread was found that indicated that these students who participated in this study demonstrate characteristics of emotionally dysregulated reactive bullies. Theoretical implication and educational practices are discussed.

Foraging ecology and parental care of common terns (Sterna hirundo) nesting in Windermere Basin, Lake Ontario

The relationships among chick feeding, size and type of prey item, and foraging time away from the brood have not been well studied in seabirds. This study investigated spatial and temporal patterns of foraging and chick-provisioning among 23 radio-tagged male common terns nesting at Hamilton Harbour, Lake Ontario during 1991 and 1992. Telemetry data were collected concurrently with behavioural observations from an elevated blind. Terns fitted with transmitters did not differ from controls with respect to either brood attendance, patterns of chick mortality, species and size distributions of prey delivered to offspring, or chick-provisioning rates. There was a clear separation of parental roles: males were primarily responsible for feeding chicks while females allocated more time to brood attendance. The prey species most commonly delivered to chicks by adults were rainbow smelt (Osmerus mordax) and alewife (A/osa pseudoharengus), followed in importance by larval fish, emerald shiner (Notropis antherinoides), salmonids, and fathead minnows (Pimepha/es prome/as). The relative proportions of various fish speCies delivered to chicks by males differed over the course of each breeding season, and there was also much variability in species composition of prey between years. Sizes of prey delivered to chicks also differed between sampling periods. The modal size of fish brought to chicks during Peak 1991 was 1.5 bill lengths, while the majority of prey in Late 1991 were small larval fish. The reverse trend occurred in 1992 when small fish were delivered to chicks predominantly during the Peak nesting period. During periods when predominantly small fish were delivered to chicks, the foraging activity of radio-tagged males was concentrated within a two kilometer radius of the colony. The observed variation in prey composition and foraging locations during the study likely reflects temporal variation in the availability of prey in the vicinity of the colony. Males delivered fish to chicks at a constant rate, while females 4 increased their feeding frequency over the first six to ten brood days. The mean length of fish delivered to chicks by adults increased significantly with increasing chick age. As a group, within each nesting period, transmittered males either foraged predominantly in the same directional bearing (north during Peak 1991, south during Late 1992), or concentrated foraging activity in the immediate vicinity of the colony (Late 1991, Peak 1992). However, individual radio-tagged males exhibited unique and predictable foraging patterns, often favouring specific locations within these areas and differing in their secondary foraging patterns. Overall, the Lake Ontario shoreline between NCB Bay" (3.5 km south of colony) and the lift bridge canal (4 km north of colony) was the foraging area used most frequently by radiotagged males during the chick-rearing period. Foraging patterns of transmittered males at Windermere Basin are similar to patterns of peak-nesting common terns, but differ from those of late-nesters, at a nearby colony (Port Colborne, Lake Erie). Differences between the foraging patterns of late-nesting terns at these colonies likely reflect differences in annual patterns of fish availability between the two locations. No relationship was found between foraging proficiency of adults and survival of offspring. Stochastic factors, such as predation by black-crowned nightherons (Nycticorax nycticorax) and adverse weather conditions during the early stages of chick rearing, may be more important determinants of common tern breeding success than parental quality or fish availability.

Zero-sum problems in finite cyclic groups

The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zero-sum theory. A zero-sequence in a finite cyclic group G is said to have the basic property if it is equivalent under group automorphism to one which has sum precisely IGI when this sum is viewed as an integer. This thesis investigates two major problems, the first of which is referred to as the basic pair problem. This problem seeks to determine conditions for which every zero-sequence of a given length in a finite abelian group has the basic property. We resolve an open problem regarding basic pairs in cyclic groups by demonstrating that every sequence of length four in Zp has the basic property, and we conjecture on the complete solution of this problem. The second problem is a 1988 conjecture of Kleitman and Lemke, part of which claims that every sequence of length n in Zn has a subsequence with the basic property. If one considers the special case where n is an odd integer we believe this conjecture to hold true. We verify this is the case for all prime integers less than 40, and all odd integers less than 26. In addition, we resolve the Kleitman-Lemke conjecture for general n in the negative. That is, we demonstrate a sequence in any finite abelian group isomorphic to Z2p (for p ~ 11 a prime) containing no subsequence with the basic property. These results, as well as the results found along the way, contribute to many other problems in zero-sum theory.

The nesting biology of Ceratina (Hymenoptera: Apidae) in the Niagara Region : new species, nest site selection and parasitism

One of the most common bee genera in the Niagara Region, the genus Ceratina (Hymenoptera: Apidae) is composed of four species, C. dupla, C. calcarata, the very rare C. strenua, and a previously unknown species provisionally named C. near dupla. The primary goal of this thesis was to investigate how these closely related species coexist with one another in the Niagara ~ee community. The first necessary step was to describe and compare the nesting biologies and life histories of the three most common species, C. dupla, C. calcarata and the new C. near dupla, which was conducted in 2008 via nest collections and pan trapping. Ceratina dupla and C. calcarata were common, each comprising 49% of the population, while C. near dupla was rare, comprising only 2% of the population. Ceratina dupla and C. near dupla both nested more commonly in teasel (Dipsacus sp.) in the sun, occasionally in raspberry (Rubus sp.) in the shade, and never in shady sumac (Rhus sp.), while C. calcarata nested most commonly in raspberry and sumac (shaded) and occasionally in teasel (sunny). Ceratina near dupla differed from both C. dupla and C. calcarata in that it appeared to be partially bivoltine, with some females founding nests very early and then again very late in the season. To examine the interactions and possible competition for nests that may be taking place between C. dupla and C. calcarata, a nest choice experiment was conducted in 2009. This experiment allowed both species to choose among twigs from all three substrates in the sun and in the shade. I then compared the results from 2008 (where bees chose from what was available), to where they nested when given all options (2009 experiment). Both C. dupla and C. calcarata had the same preferences for microhabitat and nest substrate in 2009, that being raspberry and sumac twigs in the sun. As that microhabitat and nest substrate combination is extremely rare in nature, both species must make a choice. In nature Ceratina dupla nests more often in the preferred microhabitat (sun), while C. calcarata nests in the preferred substrate (raspberry). Nesting in the shade also leads to smaller clutch sizes, higher parasitism and lower numbers of live brood in C. calcarata, suggesting that C. dupla may be outcompeting C. calcarata for the sunny nesting sites. The development and host preferences of Ceratina parasitoids were also examined. Ceratina species in Niagara were parasitized by no less than eight species of arthropod. Six of these were wasps from the superfamily Chalcidoidea (Hymenoptera), one was a wasp from the family Ichneumonidae (Hymenoptera) and one was a physogastric mite from the family Pyemotidae (Acari). Parasites shared a wide range of developmental strategies, from ichneumonid larvae that needed to consume multiple Ceratina immatures to complete development, to the species from the Eulophidae (Baryscapus) and Encyrtidae (Coelopencyrtus), in which multiple individuals completed development inside a single Ceratina host. Biological data on parasitoids is scarce in the scientific literature, and this Chapter documents these interactions for future research.

Repertory grid adaptations in detecting connotative trends and social behaviour problems in education

Please consult the paper edition of this thesis to read. It is available on the 5th Floor of the Library at Call Number: Z 9999 E38 K66 1983

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

A Study of Ordered Gene Problems Featuring DNA Error Correction and DNA Fragment Assembly with a Variety of Heuristics, Genetic Algorithm Variations, and Dynamic Representations

Ordered gene problems are a very common classification of optimization problems. Because of their popularity countless algorithms have been developed in an attempt to find high quality solutions to the problems. It is also common to see many different types of problems reduced to ordered gene style problems as there are many popular heuristics and metaheuristics for them due to their popularity. Multiple ordered gene problems are studied, namely, the travelling salesman problem, bin packing problem, and graph colouring problem. In addition, two bioinformatics problems not traditionally seen as ordered gene problems are studied: DNA error correction and DNA fragment assembly. These problems are studied with multiple variations and combinations of heuristics and metaheuristics with two distinct types or representations. The majority of the algorithms are built around the Recentering- Restarting Genetic Algorithm. The algorithm variations were successful on all problems studied, and particularly for the two bioinformatics problems. For DNA Error Correction multiple cases were found with 100% of the codes being corrected. The algorithm variations were also able to beat all other state-of-the-art DNA Fragment Assemblers on 13 out of 16 benchmark problem instances.

Palmer's Pocket Scale with Rules for its Use in Solving Arithmetical and Geometrical Problems

The book is signed by S.D. Woodruff. A label the book indicates that it was also owned by "Band, of De Vere Gardens in Toronto".

Letter to Henry Nelles from Michael Harris regarding estate problems

Letter to Henry Nelles from Michael Harris regarding estate problems (3 pages, handwritten with writing going in 2 directions on the last page), May 30, 1821.