Perspectives of Teachers Regarding the Integration of Mathematics and Science at the Secondary School Level

The integration of mathematics and science in secondary schools in the 21st century continues to be an important topic of practice and research. The purpose of my research study, which builds on studies by Frykholm and Glasson (2005) and Berlin and White (2010), is to explore the potential constraints and benefits of integrating mathematics and science in Ontario secondary schools based on the perspectives of in-service and pre-service teachers with various math and/or science backgrounds. A qualitative and quantitative research design with an exploratory approach was used. The qualitative data was collected from a sample of 12 in-service teachers with various math and/or science backgrounds recruited from two school boards in Eastern Ontario. The quantitative and some qualitative data was collected from a sample of 81 pre-service teachers from the Queen’s University Bachelor of Education (B.Ed) program. Semi-structured interviews were conducted with the in-service teachers while a survey and a focus group was conducted with the pre-service teachers. Once the data was collected, the qualitative data were abductively analyzed. For the quantitative data, descriptive and inferential statistics (one-way ANOVAs and Pearson Chi Square analyses) were calculated to examine perspectives of teachers regardless of teaching background and to compare groups of teachers based on teaching background. The findings of this study suggest that in-service and pre-service teachers have a positive attitude towards the integration of math and science and view it as valuable to student learning and success. The pre-service teachers viewed the integration as easy and did not express concerns to this integration. On the other hand, the in-service teachers highlighted concerns and challenges such as resources, scheduling, and time constraints. My results illustrate when teachers perceive it is valuable to integrate math and science and which aspects of the classroom benefit best from the integration. Furthermore, the results highlight barriers and possible solutions to better the integration of math and science. In addition to the benefits and constraints of integration, my results illustrate why some teachers may opt out of integrating math and science and the different strategies teachers have incorporated to integrate math and science in their classroom.

Experience, Education and Subjectivity: A Comparison of John Dewey's and Maurice Merleau-Ponty's Conceptions of Experience and Their Implications for Education

This thesis compares John Dewey’s philosophy of experience and Maurice Merleau-Ponty’s phenomenology, and illustrates how Merleau-Ponty’s phenomenology can strengthen and further Dewey’s philosophy of education. I begin by drawing the connection between Dewey’s philosophy of experience and his philosophy of education, and illustrate how Dewey’s understanding of growth, and thinking in education, is rooted in and informed by his detailed philosophy of experience. From there, I give an interpretation of Merleau-Ponty’s phenomenology with a focus on his descriptions of subjectivity that he presents in the Phenomenology of Perception. Following this, I outline some of the implications Merleau-Ponty’s phenomenology has on our understanding of rationality, expression and existence. In the final chapter, I make the comparison between Dewey’s philosophy of experience and Merleau-Ponty’s phenomenology. After demonstrating how these two philosophies are not only similar but also complementary, I then look to Merleau-Ponty’s phenomenology to provide insight into and to advance Dewey’s philosophy of education. I will illustrate how Merleau-Ponty’s understanding of subjectivity helps to support, and reinforce the rationale behind Dewey’s inquiry-based approach to education. Furthermore, I will show how Merleau-Ponty’s phenomenology and its implications for rationality, expression and existence support Dewey’s democratic ideal and add a hermeneutical element to Dewey’s philosophy of education.

THE EFFECT OF PURPOSEFUL MATHEMATICS DISCOURSE IN THE CLASSROOM ON STUDENTS’ MATHEMATICS LANGUAGE IN THE CONTEXT OF PROBLEM SOLVING

This study examines how one secondary school teacher’s use of purposeful oral mathematics language impacted her students’ language use and overall communication in written solutions while working with word problems in a grade nine academic mathematics class. Mathematics is often described as a distinct language. As with all languages, students must develop a sense for oral language before developing social practices such as listening, respecting others ideas, and writing. Effective writing is often seen by students that have strong oral language skills. Classroom observations, teacher and student interviews, and collected student work served as evidence to demonstrate the nature of both the teacher’s and the students’ use of oral mathematical language in the classroom, as well as the effect the discourse and language use had on students’ individual written solutions while working on word problems. Inductive coding for themes revealed that the teacher’s purposeful use of oral mathematical language had a positive impact on students’ written solutions. The teacher’s development of a mathematical discourse community created a space for the students to explore mathematical language and concepts that facilitated a deeper level of conceptual understanding of the learned material. The teacher’s oral language appeared to transfer into students written work albeit not with the same complexity of use of the teacher’s oral expression of the mathematical register. Students that learn mathematical language and concepts better appear to have a growth mindset, feel they have ownership over their learning, use reorganizational strategies, and help develop a discourse community.

Livelihood Strategies of Dock Workers in Durban, c. 1900-1959

This dissertation examines the livelihood strategies of African dock workers in Durban, South Africa, between the Anglo-Boer War and the 1959 strikes. These labourers did not conform to common conceptions of radical dock workers or conservative African migrant workers. While Marxist scholars have been correct to stress the working class consciousness of Durban’s dock workers, this consciousness was also more ambiguous. These workers and their leaders displayed a peculiar mix of concern for workers’ issues and defences of the rights and interests of African traders. Many of Durban’s dock workers were not only wage labourers. In fact, only a minority had wages as their only source of income. The Reserve economy played a role in sustaining the consumption levels of their households and, more importantly, more than half of the former dock workers interviewed for this research engaged in some form of commercial enterprise, often based on the pilferage and sale of cargoes. Some also teamed up with township women who sold pilfered goods while the men were at work. This combination of commercial strategies and wage labour has often been overlooked in the literature. By looking at these livelihood strategies, this dissertation considers how rural and urban economies interacted in households’ strategies and reinterprets the reproduction of labour and the household in order to move beyond dichotomies of proletarian versus rural consciousness. The dock workers’ households were neither proletarian households that were forced to reside in the countryside because of apartheid, nor traditional rural homesteads with a missing migrant member. The households were reproduced in three geographically separate spheres of production and consumption, none of which could reproduce the household on its own. These spheres were dependent on each other, but also separate, as physical distance gave the different household members some autonomy. Such multi-nodal households not only bridged the rural and the urban, but equally straddled the formal/informal divide. For many, their employment on the docks made their commercial enterprises possible, which allowed them to retire early from urban wage labour. Consequently, the interests of wage labourers could not be divorced from those of African small-scale entrepreneurs.

Preservice Elementary Teachers’ Beliefs toward Mathematics and Mathematics Teaching

As they began their one-year teacher education program 138 elementary school teacher candidates completed a questionnaire designed to measure their beliefs concerning the nature of mathematics, measured on a scale from absolutist to fallibilist, and their beliefs concerning effective mathematics instruction, measured on a scale from traditional to constructivist. Interviews were conducted with volunteer questionnaire participants, with selection based on the questionnaire results and using two sets of criteria. Study 1. involved 8 teacher candidates showing distinct absolutist or fallibilist views of mathematics and individual interviews explored participants' beliefs concerning the use of information and communication technology, particularly interactive whiteboards (IWB), in the teaching and learning of mathematics. Participants with absolutist beliefs about the nature of mathematics tended to focus on the IWB as a presentation tool, while those with fallibilist beliefs appreciated the use of the IWB to support student exploration. Study 2. involved 8 teacher candidates with apparently misaligning absolutist beliefs concerning the nature of mathematics and constructivist beliefs concerning teaching. Interviews exploring participants' favoured instructional approaches, particularly those involving the use of manipulatives, showed that constructivist views involved essentially surface beliefs and that in fact manipulatives would be employed to support traditional direct instruction.