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.

Investigating Formative Assessment: Exploring the Impact on the Self-Efficacy and Motivation of Mathematics Students

This is a study of the implementation and impact of formative assessment strategies on the motivation and self-efficacy of secondary school mathematics students. An explanatory sequential mixed methods design was implemented where quantitative and qualitative data were collected and analyzed sequentially in 2 different phases. The first phase involved quantitative data from student questionnaires and the second phase involved qualitative data from individual student and teacher interviews. The findings of the study suggest that formative assessment is implemented in practice in diverse ways and is a process where the strategies are interconnected. Teachers experience difficulty in incorporating peer and self-assessment and perceive a need for exemplars. Key factors described as influencing implementation include teaching philosophies, interpretation of ministry documents, teachers’ experiences, leadership in administration and department, teacher collaboration, misconceptions of teachers, and student understanding of formative assessment. Findings suggest that overall, formative assessment positively impacts student motivation and self-efficacy, because feedback is provided which offers encouragement and recognition by highlighting the progress that has been made and what steps need to be taken to improve. However, students are impacted differently with some considerations including how students perceive mistakes and if they fear judgement. Additionally, the impact of formative assessment is influenced by the connection between self-efficacy and motivation, namely how well a student is doing is a source of both concepts.

Attitudes toward Konglish of South Korean teachers of English in the Province of Jeollanamdo /

This study examined the attitudes of South Korean teachers of English in Jeollanamdo toward Konglish, particularly in relation to English education. The literature search shows that Konglish is a typical local variety, evolved from the borrowing and redefining of English words that became part of everyday South Korean speech. Konglish is not unique in this regard. Japlish in Japan and Chinglish in China developed for similar reasons and display the distinctive characteristics of those languages. However, Konglish is usually defined as poor and incorrect. Teachers in the study expressed embarrassment, shyness, guilt, and anger about Konglish. On the other hand, they also valued it as something uniquely theirs. Teachers believed that students should not be taught that Konglish is bad English. However, students should be taught that it is poor or incorrect. With few exceptions, they correct Konglish in their classes. Teachers exhibited considerable inner conflict. They defined Konglish as valid when used in Korea with Koreans. However, some preferred that their students not use it, even with their friends. This may cause students to judge Konglish as unacceptable or inferior. The teachers believed that students should learn to distinguish between Konglish and "Standard English," and that they should learn about the contexts in which each is appropriate or preferred. The conclusion, therefore, is that South Korean teachers see the value of teaching about varieties of English. The recommendations are that intelligibility, broader communication skills, and information about International English be included in the curriculum in South Korea.

Retired Women Teachers of Ontario—St. Catharines branch fonds, 1970-2013.

The Retired Women Teachers of Ontario (RWTO) was founded in Toronto by a small group of retired women teachers known as the Rendezvous Club. This group brought together several branches in 1956 to form the Ontario Association of Superannuated Teachers (OAWST), which was changed to the RWTO in 1999. The group was initially formed in order to provide retired women teachers with the same pension that was received by their male colleagues. The group came to the realization that they would have a better chance of success if they had a larger group of supporters. As a result, new branches were formed throughout Ontario. In 1967, the government concurred that the pension should be raised, and the minimum pension level was increased to $1200 a year. The following year the Retired Teachers of Ontario was formed, representing both male and female retired teachers. This new group was now responsible for communicating and negotiating with the government concerning pension matters. However, the RWTO continued to exist with a focus on the special interests and well-being of retired women teachers. There are currently 53 branches throughout Ontario.

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.

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.

A conceptual analysis of research literature on teachers' ideology and literacy practices: extending the dialogue through a secondary analysis of high school English as an additional language contexts /

This thesis provides a conceptual analysis of research literature on teachers' ideology and literacy practices as well as a secondary analysis of three empirical studies and the ways in which the ideologies of the English as an Additional Language (EAL) (Street, 2005) teachers in these contexts impact the teaching of literacy in empowering/disabling ways. Several major theoretical components of Cummins (1996, 2000), Gee (1996, 2004) and Street (1995, 2001) are examined and integrated into a conceptual triad consisting of three main areas: power and ideology, validation of students ' cultural and linguistic backgrounds, and teaching that empowers. This triad provides the framework for the secondary analysis of three empirical studies on the ideologies of secondary EAL teachers. Implications of the findings from the conceptual and secondary analyses are examined in light of the research community and secondary school teachers of EAL.

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.

Thinking skills in the language arts : an application of cognitive schema theory to the narrative writing process /

A cognitively based instructional program for narrative writing was developed. The effects of using cognitively based schematic planning organizers at the pre-writing stage were evaluated using subjects from the Primary, Junior and Intermediate divisions. Results indicate that the use of organizers based on problem solving significantly improved the organization and the overall quality of narrative writing for students in grades 3, 6 and 7. The magnitude of the improvement of the treatment group over the control group performance in Organization ranged from 10.7% to 22.9%. Statistical and observational data indicate many implications for further research into the cognitive basis for writing and reading; for the improvement and evaluation of school writing programs; for the design of school curricula; and for the inservice education for teachers of writing.

"Where is the value in education for me?": experiences and perspectives of Ontario secondary students at risk of non-completion of their Ontario Secondary School Diploma /

This study examined students considered at risk of non-completion of their Ontario Secondary School Diploma and aimed to offer insight into the questions, "What factors currently lead to school disconnect" and "How can these factors be addressed?" Eight students currently enrolled in an alternative learning environment participated in the study. Each was asked to take part in two, digitally recorded interviews that were subsequently transcribed by the researcher. The data were then coded and analysed according to specific themes: obstacles, empowerment, goals, views about success, opinions of school, and power of the teacher. From these themes, three broad focus areas emerged that were used to keep the data analysis focused: worldview, school effects, and self-image. Variances between the data collected and ideas presented in the current literature were highlighted as a reminder that when dealing with a human population, we cannot rely on textbook definitions and theory alone.

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.

The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.

Response curves of deterministic and probabilistic cellular automata in one and two dimensions

One of the most important problems in the theory of cellular automata (CA) is determining the proportion of cells in a specific state after a given number of time iterations. We approach this problem using patterns in preimage sets - that is, the set of blocks which iterate to the desired output. This allows us to construct a response curve - a relationship between the proportion of cells in state 1 after niterations as a function of the initial proportion. We derive response curve formulae for many two-dimensional deterministic CA rules with L-neighbourhood. For all remaining rules, we find experimental response curves. We also use preimage sets to classify surjective rules. In the last part of the thesis, we consider a special class of one-dimensional probabilistic CA rules. We find response surface formula for these rules and experimental response surfaces for all remaining rules.

TA tales : [re]storying the teaching and learning experiences of university teaching assistants

This inquiry examines reported critical incidents that shaped the lived experience of 5 university TAs as they negotiated multiple roles and relationships within the teaching and learning context. Questions and ensuing conversations explore the ways in which these critical incidents in teaching contributed to the TAs' understanding of themselves as teachers, of teaching and learning tensions in higher education, and of the institutional contexts in which they work. The inquiry also explores the ways in which narrative, particularly creative fiction, can represent the stories TAs tell of their experiences.

Acyclic 5-Choosability of Planar Graphs Without Adjacent Short Cycles

The conjecture claiming that every planar graph is acyclic 5-choosable[Borodin et al., 2002] has been verified for several restricted classes of planargraphs. Recently, O. V. Borodin and A. O. Ivanova, [Journal of Graph Theory,68(2), October 2011, 169-176], have shown that a planar graph is acyclically 5-choosable if it does not contain an i-cycle adjacent to a j-cycle, where 3<=j<=5 if i=3 and 4<=j<=6 if i=4. We improve the above mentioned result and prove that every planar graph without an i-cycle adjacent to a j-cycle with3<=j<=5 if i=3 and 4<=j<=5 if i=4 is acyclically 5-choosable.