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.

Gender bias in the Trends in Mathematics and Science Study 2003 (TIMMS) for Canadian students /

This study is a secondary data analysis of the Trends in Mathematics and Science Study 2003 (TIMSS) to determine if there is a gender bias, unbalanced number of items suited to the cognitive skill of one gender, and to compare performance by location. Results of the Grade 8, math portion of the test were examined. Items were coded as verbal, spatial, verbal /spatial or neither and as conventional or unconventional. A Kruskal- Wallis was completed for each category, comparing performance of students from Ontario, Quebec, and Singapore. A Factor Analysis was completed to determine if there were item categories with similar characteristics. Gender differences favouring males were found in the verbal conventional category for Canadian students and in the spatial conventional category for students in Quebec. The greatest differences were by location, as students in Singapore outperformed students from Canada in all areas except for the spatial unconventional category. Finally, whether an item is conventional or unconventional is more important than whether the item is verbal or spatial. Results show the importance of fair assessment for the genders in both the classroom and on standardized tests.

Adolescent girls and mathematics: classroom performance, attitudes toward mathematics and perceptions of parental attitudes /

The purpose of this study was to determine the extent to which gender differences exist in student attitudes toward mathematics and in their performance in mathematics at the Grade Seven and Eight level. The study also questioned how parents influence the attitudes of this grade level of male and female students toward mathematics. Historically, the literature has demonstrated gender differences in the attitudes of students toward mathematics, and in parental support for classroom performance in mathematics. This study was an attempt to examine these differences at one senior public school in the Peel Board of Education. One hundred three Grade Seven and Eight students at a middle school in the Peel Board of Education volunteered to take part in a survey that examined their attitudes toward mathematics, their perceptions of their parents' attitudes toward mathematics and support for good performance in the mathematics classroom, parental expectations for education and future career choices. Gender differences related to performance levels in the mathematics classroom were examined using Pearson contingency analyses. Items from the survey that showed significant differences involved confidence in mathematics and confidence in writing mathematics tests, as well as a belief in the ability to work on mathematics problems. Male students in both the high and low performance groups demonstrated higher levels of confidence than the females in those groups. Female students, however, indicated interest in careers that would require training and knowledge of higher mathematics. Some of the reasons given to explain the gender differences in confidence levels included socialization pressures on females, peer acceptance, and attribution of success. Perceived parental support showed no significant differences across gender groups or performance levels. Possible explanations dealt with the family structure of the participants in the study. Studies that, in the past, have demonstrated gender differences in confidence levels were supported by this study, and discussed in detail. Studies that reported on differences in parental support for student performance, based on the gender of the parent, were not confirmed by this study, and reasons for this were also discussed. The implications for the classroom include: 1) build on the female students' strengths that will allow them to enjoy their experiences in mathematics; 2) stop using the boys as a comparison group; and 3) make students more aware of the need to continue studying mathematics to ensure a wider choice of future careers.

A case study of a high functioning autistic female in a games setting

This study detennined whether or not a high functioning autistic girl can develop game structure strategies that may allow her to become an active participant in a game or sport environment. This qualitative case study involved the in-depth observation and description of one high functioning autistic student whose experience in a game setting would be studied. The type of case study carried out was a combination of descriptive and evaluative. This experience was investigated through structured, individual programming. Through on-site observation, journal entries, and hands on instruction, I was able to describe what progress the autistic student made in tenns of skill development. The results of the study demonstrated that a high-functioning autistic female has the potential to develop the necessary motor skills to participate in the chosen sport of basketball. The observation results and field notes contributed to a movement profile which described her habits of body. Teaching strategies and frameworks utilized during the study were described and listed. Insights and commentary are further provided. A thorough examination of autism and games programming is provided in the literature review.

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.

Completing the picture: the effects of video game practice on verbal and performance I.Q. scores in high functioning children

The strength and nature of the video game practice effect on tests of visual and perceptual skills were examined using high functioning Grades Four and Five students who had been tested with the WISC-R .for the purpose of gifted identification and placement. The control group, who did not own and .play video games on a sustained basis, and the experimental group, who did own a video game system and had some mastery of video games, including the -Nintendo game, "Tetris", were each composed of 18 juniorg:r;-ade students and were chosen from pre-existing conditions. The experimental group corresponded to the control group in terms of age, sex, and community. Data on the Verbal and Performance I.Q. Scores were· collected for both groups and the author was interested in the difference between the Verbal and Performance Scores within each group, anticipating a P > V outcome for the experimental group. The results showed a significant P > V difference in the experimental, video game playing group, as expected, but no significant difference between the Performance $cores of the control and experimental groups. The results, thus, indicated lower Verbal I.Q. Scores in the experimental group relat'ive to 'the control group.' The study conclu~ed that information about a sUbject's video game experience and "learhing style pref~rence is important for a clear interpretation of the Verbal and Performance I.Q. Scores of the WISC-R. Although the time spent on video game play may, 'indeed, increase P~rformance Scores relative to Verbal Scores for an individual, the possibilities exist that the time borrowed and spent away from language based activities may retard verbal growth and/or that the cognitive style associated with some Performance I.Q.subtests may have a negative effect on the approach to the tasks on the Verbal I.Q. Scale. The study also discussed the possibility that exposure to ,the video game experience, in pre-puberty, can provide spatial instruction which will result in improved spatial skills. strong spatial skills have been linked to improved performance and preference in mathematics, science, and engineering and it was suggested that appropriate video game play might be a way to involve girls more in the fields of mathematics and science.

Cooperative learning and elaborative interrogation: effects on children's learning

This experimental study examined the effects of cooperative learning and a question-answering strategy called elaborative interrogation ("Why is this fact true?") on the learning of factual information about familiar animals. Retention gains were compared across four study conditions: elaborative-interrogation-plus-cooperative learning, cooperative-learning, elaborative-interrogation, and reading-control. Sixth-grade students (n=68) were randomly assigned to the four conditions. All participants were given initial training and practice in cooperative learning procedures via three 45-minute sessions. After studying 36 facts about six animals, students' retention gains were measured via immediate free recall, immediate matched association, 30-day, and GO-day matched association tests. A priori comparisons were made to analyze the data. For immediate free recall and immediate matched association, significant differences were found between students in the three experimental conditions versus those in the control condition. Elaborative-interrogation and elaborativeinterrogation- plus-cooperative-learning also promoted longterm retention (measured via 30-day matched association) of the material relative to repetitive reading with elaborative-interrogation promoting the most durable gains (measured via GO-day matched association). The relationship between the types of elaborative responses and probability of subsequent retention was also examined. Even when students were unable to provide adequate answers to the why questions, learning was facilitated more so than repetitive reading. In general, generation of adequate elaborations was associated with greater probability of recall than was provision of inadequate answers. The findings of the study demonstrate that cooperative learning and the use of elaborative interrogation, both individually and collaboratively, are effective classroom procedures for facilitating children's learning of new information.

Exploring the impact of a hands-on intervention on grade 7 girls and their feelings about self, mathematics, science, technology and related careers

Forty-five 12- and 13-year-old females attending Grade 7 in North York, Ontario were randomly selected from a group of 100 females who had volunteered to participate in a oneday hands-on workshop called It's Your Choice at Seneca College. The goals of this intervention were to broaden the career horizons of these students and to help them realize the need to continue mathematics and science through high school in order to keep occupational options unlimited. The young women were given a pre- and post-attitude survey to provide background information. In the month following participation in the workshop the students were interviewed in small groups (S students per group) to discover their perceptions of the impact of the workshop. The interviews revealed that participants felt that after the workshop their feelings of self-confidence increased, specifically with respect to working with their hands. Participants felt more aware of the usefulness and importance of the study of mathematics, science and technology, They also felt that It's Your Choice increased their interest in careers in these domains and helped them to see that these careers are viable choices for females. The interviews also revealed that many of the participants felt that in this society their roles and their choices were influenced and probably limited by the fact that they are female.

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 impact of integrated programming on student attitude and achievement in grade 9 academic mathematics and science

This research studioo the effect of integrated instruction in mathematics and~ science on student achievement in and attitude towards both mathematics and science. A group of grade 9 academic students received instruction in both science and mathematics in an integrated program specifically developed for the purposes of the research. This group was compared to a control group that had received science and mathematics instruction in a traditional, nonintegrated program. The findings showed that in all measures of attitude, there was no significant difference between the students who participated in the integrated science and mathematics program and those who participated in a traditional science and mathematics program. The findings also revealed that integration did improve achievement on some of the measures used. The performance on mathematics open-ended problem-solving tasks improved after participation in the integrated program, suggesting that the integrated students were better able to apply their understanding of mathematics in a real-life context. The performance on the final science exam was also improved for the integrated group. Improvement was not noted on the other measures, which included EQAO scores and laboratory practical tasks. These results raise the issue of the suitability of the instruments used to gauge both achievement and attitude. The accuracy and suitability of traditional measures of achievement are considered. It is argued that they should not necessarily be used as the measure of the value of integrated instruction in a science and mathematics classroom.

The interpretation of environmental sustainability (ES) by the IOC/Olympic Games 1994-2008

The purpose of this qualitative multi-case study was to examine the interpretation of environmental sustainability (ES) within the Olympic 11 Movement. Two research questions guided the inquiry - first, how has the concept of ES been defined by the International Olympic Committee (lOC), and second, how has the concept of ES been defined and enacted by the Organizing Committees ofthe Olympic Games (OCOGs)? During the past two decades, the International Olympic Committee (lOC) established several policies and programs related to ES. Its actions reflect a broader trend of environmentalism within economic and social spheres around the world (Milton-Smith, 2002). Despite the numerous initiatives, the Olympic Games continue to cause significant environmental damage. Frey, et al. (2007) argued that the Olympic Movement contradicts the fundamental premises of ES because the Games are hosted in a two week time period, are situated in a confined area, and accumulate operating and infrastructure costs in the billions of dollars. Further, Etzion (2007) stated "there is positive and significant correlation between firm siz~ and environmental performance" (p. 642) and in the context of the Olympics the sizeimpact relation is striking. Since 1972, the year the UN launched its international environmental awareness efforts, the Summer Olympics grew to 201 nations (39% increase), 10,500 athletes (32% increase), 28 sports (30% increase), and 302 events (43% increase) (Johnson, 2004; Girginov & Parry, 2005; Upegui, 2008). The proliferation of Games activities counters the ES principles that exist within many of the IOC declarations, policies and programs.

Organizational capacity and knowledge transfer : a qualitative case study of the 2007 Canada Winter Games host society

Understanding and managing the knowledge transfer process in sport organizations is an essential component to enhance organizational capacity. Very little research on either capacity or knowledge transfer within a sport organization exists. Consequently, the purpos e of this qualitative case study was to, examine the transfer of knowledge process within a major games host society. Specifically, two research goals guided the study: 1) To develop a model to explain a knowledge t r ans f e r process in a non-profit ma jor games hos t organization and 2) To examine the relevance of the model to a Canada Games Hos t Society. Data we r e collected from interviews with middle and senior level volunteers as well as senior s t a f f members (n= 27), document s and observations. The findings indicated three barriers to knowledge transfer: structural, systemic, and cultural. As a result of the findings a revised model for knowledge transfer wa s proposed that included modifications related to the direction of knowledge flow, timing of the knowledge transfer process, and group inter-relations. Implications identified the importance of intuition managers, time and organizational levels for successful knowledge transfer. Recommendations for future host societies and the Canada Games Council are presented.

A Temporal Analysis of Emotions in Girls' Secondary School Physical Education Games and Fitness Classes

Female enthusiasm towards engaging in physical education (PE) significantly decreases with age as it provides females with positive and negative emotional experiences. This study examined emotions within four grade nine female PE soccer and fitness classes (N = 67). Emotional patterns were studied over time and across two units of instruction and in relation to student grades. A mixed-method approach was utilized assessing the state emotions of shame, enjoyment, anxiety, and social physique anxiety (SPA). Results revealed unsatisfactory internal consistency for shame and thus it was removed. Statistical analysis revealed no significant changes in emotions over time, whereas qualitative analysis found that state emotions were inconsistent. Statistical analysis indicated that students in the fitness classes reported significantly higher levels of anxiety and SPA on the final class (p < .01). Qualitative analysis signaled different origins and themes of students‟ emotions. No predictive relationship between emotion and students‟ grade was found.

Teachers' professional learning within communities of mathematics-for-teaching practice

Ontario bansho is an emergent mathematics instructional strategy used by teachers working within communities of practice that has been deemed to have a transformational effect on teachers' professional learning of mathematics. This study sought to answer the following question: How does teachers' implementation of Ontario bansho within their communities of practice inform their professional learning process concerning mathematics-for-teaching? Two other key questions also guided the study: What processes support teachers' professional learning of content-for-teaching? What conditions support teachers' professional learning of content-for-teaching? The study followed an interpretive phenomenological approach to collect data using a purposive sampling of teachers as participants. The researcher conducted interviews and followed an interpretive approach to data analysis to investigate how teachers construct meaning and create interpretations through their social interactions. The study developed a model of professional learning made up of 3 processes, informing with resources, engaging with students, and visualizing and schematizing in which the participants engaged and 2 conditions, ownership and community that supported the 3 processes. The 3 processes occur in ways that are complex, recursive, nonpredictable, and contextual. This model provides a framework for facilitators and leaders to plan for effective, content-relevant professional learning by placing teachers, students, and their learning at the heart of professional learning.

Introduction to engineering : a case study of an interdisciplinary course in Mathematics, Science and Technology

This thesis research was a qualitative case study of a single class of Interdisciplinary Studies: Introduction to Engineering taught in a secondary school. The study endeavoured to explore students' experiences in and perceptions of the course, and to investigate the viability of engineering as an interdisciplinary theme at the secondary school level. Data were collected in the form of student questionnaires, the researcher's observations and reflections, and artefacts representative of students' work. Data analysis was performed by coding textual data and classifying text segments into common themes. The themes that emerged from the data were aligned with facets of interdisciplinary study, including making connections, project-based learning, and student engagement and affective outcomes. The findings of the study showed that students were positive about their experiences in the course, and enjoyed its project-driven nature. Content from mathematics, physics, and technological design was easily integrated under the umbrella of engineering. Students felt that the opportunity to develop problem solving and teamwork skills were two of the most important aspects of the course and could be relevant not only for engineering, but for other disciplines or their day-to-day lives after secondary school. The study concluded that engineering education in secondary school can be a worthwhile experience for a variety of students and not just those intending postsecondary study in engineering. This has implications for the inclusion of engineering in the secondary school curriculum and can inform the practice of curriculum planners at the school, school board, and provincial levels. Suggested directions for further research include classroom-based action research in the areas of technological education, engineering education in secondary school, and interdisciplinary education.