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.

The historical game-changes in the philosophy of devotion and caste as used and misused by the Bhagavad-gita

This thesis considers that the purport of the Bhagavadgita is to prioritize the philosophy of loving devotion to God (bhakti), not the propagation of color-coded-caste (varna system). The distinction between bhakti and caste becomes clear when one sees their effect on human life and on the society. Jnana and karma, two of the other polarities with which the Gita contends, finally support bhakti towards betterment, not deterioration, if done selflessly and with balance. Caste, however, is a totally different tension, which is always detrimental to the well-being of the person and the society. In the Gita, the devotees' mystical or emotional love of, God apprehends their ~ oneness with the Supreme God and with all beings, and transcends the pitiless segregation of the caste system, and opens the path of salvation to all irrespective of race, color, caste, class or gender in life. In spite of much opposition from orthodoxy, the bhakti movement spread allover India, and bhakti itself rose to the level of orthodoxy and has become the faith of millions of people especially of the south, and surprisingly, of even of those of the so called highest caste. And yet, caste still remains as an indelible mark of every Hindu, even after they change their religion. Although caste is less venomous now, it is still openly present in all walks of Indian life and shows up its ugly head at important moments such as marriage, elections for public office, admission to school or employment. True, bhakti is the antidote for. caste; but only real bhakti can remove caste completely, not mere lip-service to it. This thesis claims that bhakti is the deliberate major thrust of the teaching of the Gita while caste seems to be a contradiction of this thrust.

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.

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.

The association of faculty's teaching philosophy and teaching behaviour, and critical thinking and self- direction in learning

The intent in this study was to investigate in what ways teachers· beliefs about education and teaching are expressed in the specific teaching behaviours they employ, and whether teaching behaviours, as perceived by their students, are correlated with students· critical thinking and self-directed learning. To this end the relationships studied were: among faCUlty members· philosophy of teaching, locus of control orientation, psychological type, and observed teaching behaviour; and among students· psychological type, perceptions of teaching behaviour, self-directed learning readiness, and critical thinking. The overall purpose of the study was to investigate whether the implicit goals of higher education, critical thinking and self-direction, were actually accounted for in the university classroom. The research was set within the context of path-goal theory, adapted from the leadership literature. Within this framework, Mezirow·s work on transformative learning, including the influences of Habermas· writings, was integrated to develop a theoretical perspective upon which to base the research methodology. Both qualitative and quantitative methodologies were incorporated. Four faCUlty and a total of 142 students participated in the study. Philosophy of teaching was described through faCUlty interviews and completion of a repertory grid. Faculty completed a descriptive locus of control scale, and a psychological type test. Observations of their teaching behaviour were conducted. Students completed a Teaching Behaviour Assessment Scale, the Self-Directed Learning Readiness Scale, a psychological type test, and the Watson-Glaser Critical Thinking Appraisal. A small sample of students were interviewed. Follow-up discussions with faculty were used to validate the interview, observation, teaching behaviour, and repertory grid data. Results indicated that some discrepancies existed between faculty's espoused philosophy of teaching and their observed teaching behaviour. Instructors' teaching behaviour, however, was a function of their personal theory of practice. Relationships were found between perceived teaching behaviour and students· self-directed learning and critical thinking, but these varied across situations, as would be predicted from path-goal theory. Psychological type of students and instructor also accounted for some of the variability in the relationships studied. Student psychological type could be shown as a partial predictor of self-directed learning readiness. The results were discussed in terms of theory development and implications for further research and practice.

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.

Online problem-based learning : perceptions of nursing educators /

A qualitative study was conducted to detennine 5 nursing educators' perceptions about the online application of a problem-based learning strategy in undergraduate nursing education. The question asked in the study was: Can the essential elements of face-to-face problem-based learning be supported in an online format? The data for this study came from 2 individual tape-recorded interviews with each of the 5 participants over a 3-month period and from a researchjournaI. The educators felt that student-centered learning and critical thinking could be supported within an online format. However, they noted that challenges could exist in terms of developing tutor roles, fostering student self-direction, facilitating group process and connections, and incorporating a nursing philosophy of online learning. The importance of tailoring an online problem-based learning course to reflect educators' philosophies and values in nursing emerged as an important theme from the interview responses. Overall, the participants suggested that an ideal environment would blend both face-to-face and online elements and that fewer elements would be offered in the first 2 years of the nursing program. They described a hybrid model of problem-based learning in which the online component could be used to support face-to-face sessions.

Desire and the paths of recognation [sic] in Hegel's intersubjectivity

This thesis poses two fundamental issues regarding Hegel's philosophy of intersubjectivity. Firstly, it examines Kojeve's problematic interpretation of Hegelian intersubjectivity as being solely rooted in the dialectic of lordship and bondage. It is my contention that Kojeve conflates the concepts of recognition {Anerkennung) with that of desire (Begierde), thereby reducing Hegel's philosophy of intersubjectivity to a violent reduction of the other to the same. This is so despite the plenary of examples Hegel uses to define intersubjectivity as the mutual (reciprocal) recognition between the self and the other. Secondly, it examines Hegel's use of Sophocles' Antigone to demonstrate the notion of the individual par excellence. I contend that Hegel's use of Antigone opens a new methodological framework through which to view his philosophy of intersubjectivity. It is Antigone that demonstrates the upheaval of an economy of exchange between the self and the other, whereby the alterity of the other transcends the self Ultimately, Hegel's philosophy of intersubjectivity must be reexamined, not only to dismiss Kojeve's problematic interpretation, but also to pose the possibility that Hegel's philosophy of intersubjectivity can viably account for a philosophy of the other that has a voice in contemporary philosophical debate.

Gadamer's transformation of hermeneutics : from Dilthey to Heidegger

Abstract: The purpose of this paper is to show how Gadamer's hermeneutics synthesizes the insights of both Heidegger and Dilthey in order to introduce a new hermeneutics. Gadamer's hermeneutics is based not only on the priority of ontology, as Heidegger insists, and neither is it only a product of life which can be objectively understood through study and rigorous method, as Dilthey suggests. For Gadamer, hermeneutics is the bringing together of ontology in terms of history. By this synthesis Gadamer not only places himself within the context of a Lebensphilosophie, but also shows that it is within language that Being can be disclosed according to a lived context. Throughout this paper the philosophies ofDilthey and Heidegger are explicated within a historical context as to bring out how, and why, Gadamer sees the need to surpass these philosophies. Through Gadamer's philosophy of play and the game, language, the dialogical model, application, and the fusion of horizons we can see how Gadamer's critique and questioning of these two philosophy leads to his new hermeneutics. Special attention is paid to the role in which these two contrasting philosophies were used to complement each other in the product of Gadamer' s philosophical hermeneutics as it is presented in his major work Truth andMethod. For Gadamer, the task of understanding is never complete. Therefore, his hermeneutics remains a dynamic structure with which we can always question the past and our traditions. This paper seeks to show his philosophical movements within these questions

An analysis of Ibn al-'Arabi's al-Insan al-Kamil, the Perfect Individual, with a brief comparison to the thought of Sir Muhammad Iqbal

This thesis analyzes four philosophical questions surrounding Ibn al-'Arabi's concept of the al-iman al-kamil, the Perfect Individual. The Introduction provides a definition of Sufism, and it situates Ibn al-'Arabi's thought within the broader context of the philosophy of perfection. Chapter One discusses the transformative knowledge of the Perfect Individual. It analyzes the relationship between reason, revelation, and intuition, and the different roles they play within Islam, Islamic philosophy, and Sufism. Chapter Two discusses the ontological and metaphysical importance of the Perfect Individual, exploring the importance of perfection within existence by looking at the relationship the Perfect Individual has with God and the world, the eternal and non-eternal. In Chapter Three the physical manifestations of the Perfect Individual and their relationship to the Prophet Muhammad are analyzed. It explores the Perfect Individual's roles as Prophet, Saint, and Seal. The final chapter compares Ibn al-'Arabi's Perfect Individual to Sir Muhammad Iqbal's in order to analyze the different ways perfect action can be conceptualized. It analyzes the relationship between freedom and action.

Kierkegaardian intersubjectivity and the question of ethics and responsibility

Kierkegaardian Intersubjectivity and the Question of Ethics and Responsibility By Kevin Krumrei. Kierkegaard's contributions to philosophy are generally admitted and recognized as valuable in the history of Western philosophy, both as one of the great anti-Hegelians, as the founder (arguably) of existentialism, and as a religious thinker. However valid this may be, there is similarly a generally admitted critique of Kierkegaard in the Western tradition, that Kierkegaard's philosophy of the development of the self leads the individual into an isolated encounter with God, to the abandonment of the social context. In other words, a Kierkegaardian theory of intersubjectivity is a contradiction in terms. This is voiced eloquently by Emmanuel Levinas, among others. However, Levinas' own intersubjective ethics bears a striking resemblance to Kierkegaard's, with respect to the description and formulation of the basic problem for ethics: the problem of aesthetic egoism. Further, both Kierkegaard and Levinas follow similar paths in responding to the problem, from Kierkegaard's reduplication in Works of Love, to Levinas' notion of substitution in Otherwise than Being. In this comparison, it becomes evident that Levinas' reading of Kierkegaard is mistaken, for Kierkegaard's intersubjective ethics postulates, in fact, the inseparability and necessity of the self s responsible relation to others in the self s relation to God, found in the command, "you shall love your neighbour as yourself."

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.