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.

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.

Preliminary epidemiological study of latent tuberculosis in Mexican agricultural workers in the Niagara region, Canada

It is well documented that the majority of Tuberculosis (TB) cases diagnosed in Canada are related to foreign-bom persons from TB high-burden countries. The Canadian seasonal agricultural workers program (SAWP) operating with Mexico allows migrant workers to enter the country with a temporary work permit for up to 8 months. Preiimnigration screening of these workers by both clinical examination and chest X-ray (CXR) reduces the risk of introducing cases of active pulmonary TB to Canada, but screening for latent TB (LTBI) is not routinely done. Studies carried out in industrialized nations with high immigration from TBendemic countries provide data of lifetime LTBI reactivation of around 10% but little is known about reactivation rates within TB-endemic countries where new infections (or reinfections) may be impossible to distinguish from reactivation. Migrant populations like the SAWP workers who spend considerable amounts of time in both Canada and TBendemic rural areas in Mexico are a unique population in terms of TB epidemiology. However, to our knowledge no studies have been undertaken to explore either the existence of LTBI among Mexican workers, the probability of reactivation or the workers' exposure to TB cases while back in their communities before returning the following season. Being aware of their LTBI status may help workers to exercise healthy behaviours to avoid TB reactivation and therefore continue to access the SAWP. In order to assess the prevalence of LTBI and associated risk factors among Mexican migrant workers a preliminary cross sectional study was designed to involve a convenience sample of the Niagara Region's Mexican workers in 2007. Research ethics clearance was granted by Brock University. Individual questionnaires were administered to collect socio-demographic and TB-related epidemiological data as well as TB knowledge and awareness levels. Cellular immunity to M tuberculosis was assessed by both an Interferon-y release assay (lGRA), QuantiFERON -TB Gold In-Tube (QFf™) and by the tuberculin skin test (TSn using Mantoux. A total of 82 Mexican workers (out of 125 invited) completed the study. Most participants were male (80%) and their age ranged from 22 to 65 years (mean 38.5). The prevalence of LTBI was 34% using TST and 18% using QFTTM. As previously reported, TST (using ~lOmm cut-off) showed a sensitivity of 93.3% and a specificity of 79.1 %. These findings at the moment cannot predict the probability of progression to active TB; only longitudinal cohort studies of this population can ascertain this outcome. However, based on recent publications, lORA positive individuals may have up to 14% probability of reactivation within the next two years. Although according to the SA WP guidelines, all workers undergo TB screening before entering or re-entering Canada, CXR examination requirements showed to be inconsistent for this population: whereas 100% of the workers coming to Canada for the first time reported having the procedure done, only 31 % of returning participants reported having had a CXR in the past year. None of the participants reported ever having a CXR compatible with TB which was consistent with the fact that none had ever been diagnosed with active pulmonary TB and with only 3.6% reporting close contact with a person with active TB in their lifetime. Although Mexico reports that 99% of popUlation is fully immunized against TB within the first year of age, only 85.3% of participants reported receiving BOC vaccine in childhood. Conversely, even when TST is not part of the routine TB screening in endemic countries, a suqDrisingly high 25.6% reported receiving a TST in the past. In regards to TB knowledge and awareness, 74% of the studied population had previous knowledge about (active) TB, 42% correctly identified active TB symptomatology, 4.8% identified the correct route of transmission, 4.8% knew about the existence of LTBI, 3.6% knew that latent TB could reactivate and 48% recognized TB as treatable and curable. Of all variables explored as potential risk factors for LTBI, age was the only one which showed statistical significance. Significant associations could not be proven for other known variables (such as sex, TB contact, history of TB) probably because of the small sample size and the homogeneity of the sample. Screening for LTBI by TST (high sensitivity) followed by confirmation with QFT''"'^ (high specificity) suggests to be a good strategy especially for immigrants from TB high-burden countries. After educational sessions, workers positive for LTBI gained greater knowledge about the signs and symptoms of TB reactivation as well as the risk factors commonly associated with reactivation. Additionally, they were more likely to attend their annual health check up and request a CXR exam to monitor for TB reactivation.

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.

A survey of attitudes of agricultural society leaders toward leadership development education

It was the purpose of this study to investigate attitudes toward leadership development education of one client group served by the ontario Ministry of Agriculture and Food. The survey, answered by 175 participants, attempted to answer the following questions: (a) What is a common definition of leadership?, (b) What leadership concepts are important to leadership development education? and, (c) What are client attitudes toward leadership development education? A descriptive research approach was used and the data were analyzed according to a model developed by Colaizzi. Concept maps were developed under the broad areas of: (a) Developing leader qualities; (b) Past experiences that developed leadership skills that worked on the jOb; (c) Leadership skills developed from present day positions; and (d) How leadership skills may be developed in future situations. A description of the dynamics of leadership development was written and the essential dynamics of leadership skill development in one volunteer organization was described. This study supports the linkages perspective of leadership within voluntary organizations developed by Vandenberg, Thullen and Fear (1987). The linkages perspective consists of three major components: perception, property and process. As a perception, leadership is the set of beliefs each group member holds regarding the behaviours and qualities characteristic of effective leaders. As a property, leadership represents the qualities attributed by group members to persons perceived as effectively (or potentially) influencing the goal achievement process. As a process, leadership involves the use of non-coercive influence to facilitate group accomplishment of valued goals. Leadership concepts important for development in a leadership development education program related to personal, organizational and societal development. The top five concepts in terms of rank order are communicating effectively, forming and working with groups, working creatively (tie), developing followers, managing meetings, directing projects or activities, understanding financial matters, managing negotiations (tie), developing resources and understanding and developing oneself (tie). Several recommendations are relevant for extension personnel as educators. Theoretical concepts on leadership need to be shared to extension practitioners involved in leadership development. currently used teaching materials for leadership development should be evaluated to see if they include concepts from preferrred theoretical leadership perceptions.

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.

Vitamin D status and latent tuberculosis infection : a preliminary study in a group of healthy Mexican agricultural workers

Vitamin D metabolites are important in the regulation of bone and calcium homeostasis, but also have a more ubiquitous role in the regulation of cell differentiation and immune function. Severely low circulating 25-dihydroxyvitamin D [25(OH)D] concentrations have been associated with the onset of active tuberculosis (TB) in immigrant populations, although the association with latent TB infection (LTBI) has not received much attention. A previous study identified the prevalence of LTBI among a sample of Mexican migrant workers enrolled in Canada's Seasonal Agricultural Workers Program (SA WP) in the Niagara Region of Ontario. The aim of the present study was to determine the vitamin D status of the same sample, and identify if a relationship existed with LTBI. Studies of vitamin D deficiency and active TB are most commonly carried out among immigrant populations to non-endemic regions, in which reactivation of LTBI has occurred. Currently, there is limited knowledge of the association between vitamin D deficiency and LTBI. Entry into Canada ensured that these individuals did not have active TB, and L TBI status was established previously by an interferon-gamma release assay (IGRA) (QuantiFERON-TB Gold In-Tube®, Cellestis Ltd., Australia). Awareness of vitamin D status may enable individuals at risk of deficiency to improve their nutritional health, and those with LTBI to be aware of this risk factor for disease. Prevalence of vitamin D insufficiency among the Mexican migrant workers was determined from serum samples collected in the summer of 2007 as part of the cross sectional LTBI study. Samples were measured for concentrations of the main circulating vitamin D metabolite, 25(OH)D, with a widely used 1251 250HD RIA (DiaSorin Inc.®, Stillwater, MN), and were categorized as deficient «37.5 nmoI/L), insufficient (>37.5 nmollL, < 80 nmol/L) or sufficient (2::80 nmoI/L). Fisher's exact tests and t tests were used to determine if vitamin D status (sufficiency or insufficiency) or 25(OH)D concentrations significantly differed by sex or age categories. Predictors of vitamin D insufficiency and 25(OH)D concentrations were taken from questionnaires carried out during the previous study, and analyzed in the present study using multiple regression prediction models. Fisher's exact test and t test was used to determine if vitamin D status or 25(OH)D concentration differed by LTBI status. Strength of the relationship between interferongamma (IFN-y) concentration (released by peripheral T cells in response to TB antigens) and 25(OH)D concentration was analyzed using a Spearman correlation. Out of 87 participants included in the study (78% male; mean age 38 years), 14 were identified as LTBI positive but none had any signs or symptoms of TB reactivation. Only 30% of the participants were vitamin D sufficient, whereas 68% were insufficient and 2% were deficient. Significant independent predictors of lower 25(OH)D concentrations were sex, number of years enrolled in the SA WP and length of stay in Canada. No significant differences were found between 25(OH)D concentrations and LTBI status. There was a significant moderate correlation between IFN-y and 25(OH)D concentrations ofLTBI-positive individuals. The majority of participants presented with Vitamin D insufficiency but none were severely deficient, indicating that 25(OH)D concentrations do not decrease dramatically in populations who temporarily reside in Canada but go back to their countries of origin during the Canadian winter. This study did not find a statistical relationship between low levels of vitamin D and LTBI which suggests that in the presence of overall good health, lower than ideal levels of 2S(OH)D, may still be exerting a protective immunological effect against LTBI reactivation. The challenge remains to determine a critical 2S(OH)D concentration at which reactivation is more likely to occur.

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.

Competing and Conflicting Land Uses at the Rural-Urban Interface: Understanding the Impacts of Residential Development on Agricultural Landscapes

Rural communities are currently undergoing rapid restructuring as globalization impacts the future viability of many small towns. Agricultural regions throughout Canada, in particular, Niagara-on-the-Lake, are forced to adapt to changes within the industry. In addition to these challenges, sprawling residential developments from nearby urban centres are changing the dynamic of this town, resulting in conflicts between the residential and agricultural land uses. This thesis explores these conflicts from the perspective of the residents and the farmers. It was found that the initial sources of conflict related to noise-generating farm activities are no longer a concern, while the use of pesticide have become a source of contention among the residents. The farmers, alternately, were found to be proactive and strived to limit the potential for conflict with adjacent residents. Lastly, it was determined that planning legislation aggravates land use conflicts within Niagara-on-the-Lake and need to better address these land use conflicts.

Using Effective Teaching Strategies and Personality Type to Enhance the Mathematics Classroom: A Handbook for Intermediate Math Teachers

This project addressed the need for more insightful, current, and applicable resources for intermediate math teachers in Canadian classrooms. A need for a handbook in this division seemed warranted by a lack of government resource support. Throughout an extensive review of the literature, themes and topics for the handbook emerged. The handbook was designed to not only provide educators with examples of effective teaching strategies within the mathematics classroom but to also inform them about the ways in which their personal characteristics and personality type could affect their students and their own pedagogical practices. Three teaching professionals who had each taught in an intermediate math class within the past year evaluated the handbook. The feedback received from these educators was directly applied to the first draft of the handbook in order to make it more accessible and applicable to other math teachers. Although the handbook was written with teachers in mind, the language and format used throughout the manual also make it accessible to parents, tutors, preservice education students, and educational administrators. Essentially, any individual who is hoping to inspire and educate intermediate math students could make use of the content within the handbook.