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".

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.

An examination of grade three mathematics textbooks for problem solving strategies

Three grade three mathematics textbooks were selected arbitrarily (every other) from a total of six currently used in the schools of Ontario. These textbooks were examined through content analysis in order to determine the extent (i. e., the frequency of occurrence) to which problem solving strategies appear in the problems and exercises of grade three mathematics textbooks, and how well they carry through the Ministry's educational goals set out in The Formative Years. Based on Polya's heuristic model, a checklist was developed by the researcher. The checklist had two main categories, textbook problems and process problems and a finer classification according to the difficulty level of a textbook problem; also six commonly used problem solving strategies for the analysis of a process problem. Topics to be analyzed were selected from the subject guideline The Formative Years, and the same topics were selected from each textbook. Frequencies of analyzed problems and exercises were compiled and tabulated textbook by textbook and topic by topic. In making comparisons, simple frequency count and percentage were used in the absence of any known criteria available for judging highor low frequency. Each textbook was coded by three coders trained to use the checklist. The results of analysis showed that while there were large numbers of exercises in each textbook, not very many were framed as problems according to Polya' s model and that process problems form a small fraction of the number of analyzed problems and exercises. There was no pattern observed as to the systematic placement of problems in the textbooks.

The effects of teaching a mathematics problem solving strategy on the problem solving ability of grade nine students

Forty grade 9 students were selected from a small rural board in southern Ontario. The students were in two classes and were treated as two groups. The treatment group received instruction in the Logical Numerical Problem Solving Strategy every day for 37 minutes over a 6 week period. The control group received instruction in problem solving without this strategy over the same time period. Then the control group received the treat~ent and the treatment group received the instruction without the strategy. Quite a large variance was found in the problem solving ability of students in grade 9. It was also found that the growth of the problem solving ability achievement of students could be measured using growth strands based upon the results of the pilot study. The analysis of the results of the study using t-tests and a MANOVA demonstrated that the teaching of the strategy did not significaritly (at p s 0.05) increase the problem solving achievement of the students. However, there was an encouraging trend seen in the data.

The quality of the mother-child relationship during collaborative problem solving /

The quality of the mother-child relationship was examined in relation to joint planning, maternal teaching strategies, maternal emotional support, mutual positive affect and attachment security. Fifty-five grade five children and their mothers participated in a laboratory session comprised of various activities and completed questionnaires to evaluate attachment security. Joint planning and social problem solving were assessed observationally during an origami task. Problem solving effectiveness was unrelated to maternal teaching strategies, maternal encouragement and mutual positive affect. A marginally significant relationship was found between maternal encouragement and active child participation. Attachment security was found to be significantly related to sharing of responsibility during local planning, but only for child autonomous performance. An examination of conditional probabilities revealed that mutual positive affect did not increase the likelihood of subsequent mother-child dyadic regulation. However, mutual positive affect was found to be significantly related to both active child participation and dyadic regulation. The hypothesis predicting a mediational model was not supported. The implications of these findings in the theoretical and empirical literature were considered and suggestions for future research were made.

Hurry up and slow down : education to close the ingenuity gap /

To explore the idea of education to close the ingenuity gap I use Thomas Homer-Dixon's work to define ingenuity. The notion that the supply of ingenuity to solve our technical and social problems is not keeping pace with the ingenuity required to solve those problems is called the ingenuity gap. Man-made technological developments are increasing the density, intensity, and pace of globalisation. People must reorganise decision-making organisations and problem-solving methods to pragmatically combat the growing ingenuity gap. John Dewey's work illustrates the fundamental attitudes for the thinking and judgment associated with educating for ingenuity. Howard Gardner's idea that truth, beauty, and morality ought to form the core values and tenets of the philosophy of educating for ingenuity is integral to this thesis. The act of teaching facilitates the invitation to the communication necessary to foster ingenuity. John Novak-discusses the five relationships of educational leadership that enhance an environment of ingenuity. The International Baccalaureate (IB) is an existing model of global education, one that defines some of the school experiences and academic development of core values of educating for ingenuity. Expanding upon the structure of the IB and other research within this thesis, I speculate upon what my school, where educating for ingenuity so as to close the ingenuity gap is the goal, would be like.

The effect of calculators on the numerical problem-solving skills and attitudes of primary students towards mathematics /

The purpose of this study was to determine the effect that calculators have on the attitudes and numerical problem-solving skills of primary students. The sample used for this research was one of convenience. The sample consisted of two grade 3 classes within the York Region District School Board. The students in the experimental group used calculators for this problem-solving unit. The students in the control group completed the same numerical problem-solving unit without the use of calculators. The pretest-posttest control group design was used for this study. All students involved in this study completed a computational pretest and an attitude pretest. At the end of the study, the students completed a computational posttest. Five students from the experimental group and five students from the control group received their posttests in the form of a taped interview. At the end of the unit, all students completed the attitude scale that they had received before the numerical problem-solving unit once again. Data for qualitative analysis included anecdotal observations, journal entries, and transcribed interviews. The constant comparative method was used to analyze the qualitative data. A t test was also performed on the data to determine whether there were changes in test and attitude scores between the control and experimental group. Overall, the findings of this study support the hypothesis that calculators improve the attitudes of primary students toward mathematics. Also, there is some evidence to suggest that calculators improve the computational skills of grade 3 students.

Predictors of academic achievement and social competence in adolescence : facilitation, inhibition and general cognitive processing /

The relevance of attentional measures to cognitive and social adaptive behaviour was examined in an adolescent sample. Unlike previous research, the influence of both inhibitory and facilitory aspects of attention were studied. In addition, contributions made by these attentional processes were compared with traditional psychometric measures of cognitive functioning. Data were gathered from 36 grade 10 and 1 1 high school students (20 male and 16 female students) with a variety of learning and attentional difficulties. Data collection was conducted in the course of two testing sessions. In the first session, students completed questionnaires regarding their medical history, and everyday behaviours (the Brock Adaptive Functioning Questionnaire), along with non-verbal problem solving tasks and motor speed tasks. In the second session, students performed working memory measures and computer-administered tasks assessing inhibitory and facilitory aspects of attention. Grades and teacher-rated measures of cognitive and social impulsivity were also gathered. Results indicate that attentional control has both cognitive and social/emotional implications. Performance on negative priming and facilitation trials from the Flanker task predicted grades in core courses, social functioning measures, and cognitive and social impulsivity ratings. However, beneficial effects for academic and social functioning associated with inhibition were less prevalent in those demonstrating a greater ability to respond to facilitory cues. There was also some evidence that high levels of facilitation were less beneficial to academic performance, and female students were more likely to exceed optimal levels of facilitory processing. Furthermore, lower negative priming was ''S'K 'i\':y-: -'*' - r " j«v ; ''*.' iij^y Inhibition, Facilitation and Social Competence 3 associated with classroom-rated distraction and hyperactivity, but the relationship between inhibition and social aspects of impulsivity was stronger for adolescents with learning or reading problems, and the relationship between inhibition and cognitive impulsivity was stronger for male students. In most cases, attentional measures were predictive of performance outcomes independent of traditional psychometric measures of cognitive functioning. >,, These findings provide support for neuropsychological models linking inhibition to control of interference and arousal, and emphasize the fundamental role of attention in everyday adolescent activities. The findings also warrant further investigation into the ways which inhibitory and facilitory attentional processes interact, and the contextdependent nature of attentional control.associated with classroom-rated distraction and hyperactivity, but the relationship between inhibition and social aspects of impulsivity was stronger for adolescents with learning or reading problems, and the relationship between inhibition and cognitive impulsivity was stronger for male students. In most cases, attentional measures were predictive of performance outcomes independent of traditional psychometric measures of cognitive functioning. >,, These findings provide support for neuropsychological models linking inhibition to control of interference and arousal, and emphasize the fundamental role of attention in everyday adolescent activities. The findings also warrant further investigation into the ways which inhibitory and facilitory attentional processes interact, and the contextdependent nature of attentional control.

Problem solving and computer-assisted instruction in science education : analysis of research findings and the research process /

The quantitative component of this study examined the effect of computerassisted instruction (CAI) on science problem-solving performance, as well as the significance of logical reasoning ability to this relationship. I had the dual role of researcher and teacher, as I conducted the study with 84 grade seven students to whom I simultaneously taught science on a rotary-basis. A two-treatment research design using this sample of convenience allowed for a comparison between the problem-solving performance of a CAI treatment group (n = 46) versus a laboratory-based control group (n = 38). Science problem-solving performance was measured by a pretest and posttest that I developed for this study. The validity of these tests was addressed through critical discussions with faculty members, colleagues, as well as through feedback gained in a pilot study. High reliability was revealed between the pretest and the posttest; in this way, students who tended to score high on the pretest also tended to score high on the posttest. Interrater reliability was found to be high for 30 randomly-selected test responses which were scored independently by two raters (i.e., myself and my faculty advisor). Results indicated that the form of computer-assisted instruction (CAI) used in this study did not significantly improve students' problem-solving performance. Logical reasoning ability was measured by an abbreviated version of the Group Assessment of Lx)gical Thinking (GALT). Logical reasoning ability was found to be correlated to problem-solving performance in that, students with high logical reasoning ability tended to do better on the problem-solving tests and vice versa. However, no significant difference was observed in problem-solving improvement, in the laboratory-based instruction group versus the CAI group, for students varying in level of logical reasoning ability.Insignificant trends were noted in results obtained from students of high logical reasoning ability, but require further study. It was acknowledged that conclusions drawn from the quantitative component of this study were limited, as further modifications of the tests were recommended, as well as the use of a larger sample size. The purpose of the qualitative component of the study was to provide a detailed description ofmy thesis research process as a Brock University Master of Education student. My research journal notes served as the data base for open coding analysis. This analysis revealed six main themes which best described my research experience: research interests, practical considerations, research design, research analysis, development of the problem-solving tests, and scoring scheme development. These important areas ofmy thesis research experience were recounted in the form of a personal narrative. It was noted that the research process was a form of problem solving in itself, as I made use of several problem-solving strategies to achieve desired thesis outcomes.

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.

Educating for love of wisdom : John Dewey and Simone Weil

The writings of John Dewey (1859-1952) and Simone Weil (1909-1943) were analyzed with a view to answering 3 main questions: What is wisdom? How is wisdom connected to experience? How does one educate for a love of wisdom? Using a dialectical method whereby Dewey (a pragmatist) was critiqued by Weil (a Christian Platonist) and vice versa, commonalities and differences were identified and clarified. For both, wisdom involved the application of thought to specific, concrete problems in order to secure a better way of life. For Weil, wisdom was centered on a love of truth that involved a certain way of applying one's attention to a concrete or theoretical problem. Weil believed that nature was subject to a divine wisdom and that a truly democratic society had supernatural roots. Dewey believed that any attempt to move beyond nature would stunt the growth of wisdom. For him, wisdom could be nourished only by natural streams-even if some ofthem were given a divine designation. For both, wisdom emerged through the discipline of work understood as intelligent activity, a coherent relationship between thinking and acting. Although Weil and Dewey differed on how they distinguished these 2 activities, they both advocated a type of education which involved practical experience and confronted concrete problems. Whereas Dewey viewed each problem optimistically with the hope of solving it, Weil saw wisdom in, contemplating insoluble contradictions. For both, educating for a love of wisdom meant cultivating a student's desire to keep thinking in line with acting-wanting to test ideas in action and striving to make sense of actions observed.

Anxiety and learning / response behaviour in the context of intellectual problem solving by young children

Twenty-eight grade four students were ca.tegorized as either high or low anxious subjects as per Gillis' Child Anxiety Scale (a self-report general measure). In determining impulsivity in their response tendencies, via Kagan's Ma.tching Familiar Figures Test, a significant difference between the two groups was not found to exist. Training procedures (verbal labelling plus rehearsal strategies) were introduced in modification of their learning behaviour on a visual sequential memory task. Significantly more reflective memory recall behaviour was noted by both groups as a result. Furthermore, transfer of the reflective quality of this learning strategy produced significantly less impulsive response behaviour for high and low anxious subjects with respect to response latency and for low anxious subjects with respect to response accuracy.

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 expression and development of teachers' capacities within two learning communities : a participant-observer case study

The learning community model has been an integral component of teacher development in Ontarian schools and beyond. This research was conducted to understand how teachers' personal capacity and professional, interpersonal, and organizational competencies are developed and expressed within this context. Nineteen elementary teachers and administrators participated in the study from November through January 2007. A qualitative case study methodology was used to investigate the role ofteachers' capacities and competencies in learning communities. Combined data sources from semistructured interviews, research journals, and document review were used to gather data about teachers' capacities and competencies. The study included 3 phases of analysis. In the final phase the analysis provided 3 qualities of the teachers at Jude and Mountain Schools (pseudonyms): identification as professionals, investment in others, and institutional affiliation that may explain how they differed from other educators. The data revealed these three themes, which provided an understanding of educators at Jude and Mountain Schools as dedicated professionals pushing practices to contribute to school life and address student learning needs, and as teachers who reflected on practices to continue expanding their skills. Teachers were heavily invested in creating a caring culture and in students' and team members' learning. Educators actively participated in solving problems and coplanning throughout the school levels and beyond, assumed collective responsibility for all pupils, and focused on generating school-wide consistent practices. These qualities and action patterns revealed teachers who invested time and effort in their colleagues, who committed to develop as professionals, and who affiliated closely with every aspect of school living.