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.

A Minor Change?: A Case Study of Carleton Place's Integration of Minor Variance Procedures into Ontario's Development Permit System

The Development Permit System has been introduce with minimal directives for establishing a decision making process. This is in opposition to the long established process for minor variances and suggests that the Development Permit System does not necessarily incorporate all of Ontario’s fundamental planning principles. From this concept, the study aimed to identify how minor variances are incorporated into the Development Permit System. In order to examine this topic, the research was based around the following research questions: • How are ‘minor variance’ applications processed within the DPS? • To what extent do the four tests of a minor variance influence the outcomes of lower level applications in the DPS approval process? A case study approach was used for this research. The single-case design employed both qualitative and quantitative research methods including a review of academic literature, court cases, and official documents, as well as a content analysis of Class 1, 1A, and 2 Development Permit application files from the Town of Carleton Place that were decided between 2011 and 2015. Upon the completion of the content analysis, it was found that minor variance issues were most commonly assigned to Class 1 applications. Planning staff generally met approval timelines and embraced their delegated approval authority, readily attaching conditions to applications in order to mitigate off-site impacts. While staff met the regulatory requirements of the DPS, ‘minor variance’ applications were largely decided on impact alone, demonstrating that the principles established by the four tests, the defining quality of the minor variance approval process, had not transferred to the Development Permit System. Alternatively, there was some evidence that the development community has not fully adjusted to the requirements of the new approvals process, as some applications were supported using a rationale containing the four tests. Subsequently, a set of four recommendations were offered which reflect the main themes established by the findings. The first two recommendations are directed towards the Province, the third to municipalities and the fourth to developers and planning consultants: 1) Amend Ontario Regulation 608/06 so that provisions under Section 4(3)(e) fall under Section 4(2). 2) Change the rhetoric from “combining elements of minor variances” to “replacing minor variances”. 3) Establish clear evaluation criteria. 4) Understand the evaluative criteria of the municipality in which you are working.

A Quantitative Investigation of Selected Reactions in the Fibrinolytic Cascade

Previous work has shown that thrombin activatable fibrinolysis inhibitor (TAFI) was unable to prolong lysis of purified clots in the presence of Lys-plasminogen (Lys-Pg), indicating a possible mechanism for fibrinolysis to circumvent prolongation mediated by activated TAFI (TAFIa). Therefore, the effects of TAFIa on Lys-Pg activation and Lys-plasmin (Lys-Pn) inhibition by antiplasmin (AP) were quantitatively investigated using a fluorescently labeled recombinant Pg mutant which does not produce active Pn. High molecular weight fibrin degradation products (HMW-FDPs), a soluble fibrin surrogate that models Pn modified fibrin, treated with TAFIa decreased the catalytic efficiency (kcat/Km) of 5IAF-Glu-Pg cleavage by 417-fold and of 5IAF-Lys-Pg cleavage by 55-fold. A previously devised intact clot system was used to measure the apparent second order rate constant (k2) for Pn inhibition by AP over time. While TAFIa was able to abolish the protection associated with Pn modified fibrin in clots formed with Glu-Pg, it was not able to abolish the protection in clots formed with Lys-Pg. However, TAFIa was still able to prolong the lysis of clots formed with Lys-Pg. TAFIa prolongs clot lysis by removing the positive feedback loop for Pn generation. The effect of TAFIa modification of the HMW-FDPs on the rate of tissue type plasminogen activator (tPA) inhibition by plasminogen activator inhibitor type 1 (PAI-1) was investigated using a previously devised end point assay. HMW-FDPs decreased the k2 for tPA inhibition rate by 3-fold. Thus, HMW-FDPs protect tPA from PAI-1. TAFIa treatment of the HMW-FDPs resulted in no change in protection. Vitronectin also did not appreciably affect tPA inhibition by PAI-1. Pg, in conjunction with HMW-FDPs, decreased the k2 for tPA inhibition by 30-fold. Hence, Pg, when bound to HMW-FDPs, protects tPA by an additional 10-fold. TAFIa treatment of the HMW-FDPs completely removed this additional protection provided by Pg. In conclusion, an additional mechanism was identified whereby TAFIa can prolong clot lysis by increasing the rate of tPA inhibition by PAI-1 by eliminating the protective effects of Pn-modified fibrin and Pg. Because TAFIa can suppress Lys-Pg activation but cannot attenuate Lys-Pn inhibition by AP, the Glu- to Lys-Pg/Pn conversion is able to act as a fibrinolytic switch to ultimately lyse the clot.

A Quantitative and Mechanistic Assessment of Activated Thrombin-Activatable Fibrinolysis Inhibitor and its Role in Pathological Bleeding and Thrombosis

The coagulation and fibrinolytic systems are linked by the thrombin-thrombomodulin complex which regulates each system through activation of protein C and TAFI, respectively. We have used novel assays and techniques to study the enzymology and biochemistry of TAFI and TAFIa, to measure TAFI activation in hemophilia A and protein C deficiency and to determine if enhancing TAFI activation can improve hemostasis in hemophilic plasma and whole blood. We show that TAFIa not TAFI attenuates fibrinolysis in vitro and this is supported by a relatively high catalytic efficiency (16.41μM-1s-1) of plasminogen binding site removal from fibrin degradation products (FDPs) by TAFIa. Since the catalytic efficiency of TAFIa in removing these sites is ~60-fold higher than that for inflammatory mediators such as bradykinin it is likely that FDPs are a physiological substrate of TAFIa. The high catalytic efficiency is primarily a result of a low Km which can be explained by a novel mechanism where TAFIa forms a binary complex with plasminogen and is recruited to the surface of FDPs. The low Km also suggests that TAFIa would effectively cleave lysines from FDPs during the early stages of fibrinolysis (i.e. at low concentrations of FDPs). Since individuals with hemophilia suffer from premature fibrinolysis as a result of insufficient TAFI activation we quantified TAFI activation in whole blood from hemophilic subjects. Both the rate of activation and the area under the TAFI activation time course (termed TAFIa potential) was determined to be reduced in hemophilia A and the TAFIa potential was significantly and inversely correlated with the clinical bleeding iii phenotype. Using a novel therapeutic strategy, we used soluble thrombomodulin to increase TAFI activation which improved the clot lysis time in factor VIII deficient human plasma and hemophilic dog plasma as well as hemophilic dog blood. Finally, we briefly show in a biochemical case study that TAFI activation is enhanced in protein C deficiency and when afflicted individuals are placed on Warfarin anticoagulant therapy, TAFI activation is reduced. Since TAFIa stabilizes blood clots, this suggests that reducing TAFI activation or inhibiting TAFIa may help restore blood flow in vessels with pathological thrombosis.