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.

Variation in offspring size towards the high elevational range edge of a montane annual

Understanding the ecological determinants of species’ distribution is a fundamental goal of ecology, and is increasingly important with changing limits to species’ range. Species often reach distributional limits on gradients of resource availability, but the extent to which offspring provisioning varies towards range limits is poorly understood. Selection is generally expected to favour higher provisioning of individual offspring in environments with short growing seasons and limited moisture, nutrients, or hosts for parasitism. However, individual provisioning may decline if parent size is limited by resources. This thesis focuses on three major questions: 1) does seed size vary over an elevational gradient? 2) does this variation respond adaptively towards the range limit? and 3) is potential elevational variation environmentally or genetically controlled? I tested variation in seed investment towards the upper elevational limit of the hemiparasitic annual herb Rhinanthus minor, sampled across an elevational range of 1,000m in the Rocky Mountains of Alberta, Canada. I also used a reciprocal transplant experiment to address the heritability of seed mass. Seed mass increased marginally towards higher elevations, while seed number and plant size declined. There was a strong elevational increase in seed mass scaled by overall plant size. Therefore, investment in individual seeds was higher towards the upper range edge, indicating potential adaptation of the reproductive strategy to allow for establishment in marginal environments. Genetic, environmental, and genotype-by-environment interactions were observed in transplanted populations, but the relative proportions of these effects on seed size were unclear.