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 effects of teaching a mathematics problem solving strategy on the problem solving ability of grade nine students

Forty grade 9 students were selected from a small rural board in southern Ontario. The students were in two classes and were treated as two groups. The treatment group received instruction in the Logical Numerical Problem Solving Strategy every day for 37 minutes over a 6 week period. The control group received instruction in problem solving without this strategy over the same time period. Then the control group received the treat~ent and the treatment group received the instruction without the strategy. Quite a large variance was found in the problem solving ability of students in grade 9. It was also found that the growth of the problem solving ability achievement of students could be measured using growth strands based upon the results of the pilot study. The analysis of the results of the study using t-tests and a MANOVA demonstrated that the teaching of the strategy did not significaritly (at p s 0.05) increase the problem solving achievement of the students. However, there was an encouraging trend seen in the data.

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.

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.

Introduction to engineering : a case study of an interdisciplinary course in Mathematics, Science and Technology

This thesis research was a qualitative case study of a single class of Interdisciplinary Studies: Introduction to Engineering taught in a secondary school. The study endeavoured to explore students' experiences in and perceptions of the course, and to investigate the viability of engineering as an interdisciplinary theme at the secondary school level. Data were collected in the form of student questionnaires, the researcher's observations and reflections, and artefacts representative of students' work. Data analysis was performed by coding textual data and classifying text segments into common themes. The themes that emerged from the data were aligned with facets of interdisciplinary study, including making connections, project-based learning, and student engagement and affective outcomes. The findings of the study showed that students were positive about their experiences in the course, and enjoyed its project-driven nature. Content from mathematics, physics, and technological design was easily integrated under the umbrella of engineering. Students felt that the opportunity to develop problem solving and teamwork skills were two of the most important aspects of the course and could be relevant not only for engineering, but for other disciplines or their day-to-day lives after secondary school. The study concluded that engineering education in secondary school can be a worthwhile experience for a variety of students and not just those intending postsecondary study in engineering. This has implications for the inclusion of engineering in the secondary school curriculum and can inform the practice of curriculum planners at the school, school board, and provincial levels. Suggested directions for further research include classroom-based action research in the areas of technological education, engineering education in secondary school, and interdisciplinary education.

Using Effective Teaching Strategies and Personality Type to Enhance the Mathematics Classroom: A Handbook for Intermediate Math Teachers

This project addressed the need for more insightful, current, and applicable resources for intermediate math teachers in Canadian classrooms. A need for a handbook in this division seemed warranted by a lack of government resource support. Throughout an extensive review of the literature, themes and topics for the handbook emerged. The handbook was designed to not only provide educators with examples of effective teaching strategies within the mathematics classroom but to also inform them about the ways in which their personal characteristics and personality type could affect their students and their own pedagogical practices. Three teaching professionals who had each taught in an intermediate math class within the past year evaluated the handbook. The feedback received from these educators was directly applied to the first draft of the handbook in order to make it more accessible and applicable to other math teachers. Although the handbook was written with teachers in mind, the language and format used throughout the manual also make it accessible to parents, tutors, preservice education students, and educational administrators. Essentially, any individual who is hoping to inspire and educate intermediate math students could make use of the content within the handbook.

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.

Some Applications of Markov Additive Processes as Models in Insurance and Financial Mathematics

Cette thèse est principalement constituée de trois articles traitant des processus markoviens additifs, des processus de Lévy et d'applications en finance et en assurance. Le premier chapitre est une introduction aux processus markoviens additifs (PMA), et une présentation du problème de ruine et de notions fondamentales des mathématiques financières. Le deuxième chapitre est essentiellement l'article "Lévy Systems and the Time Value of Ruin for Markov Additive Processes" écrit en collaboration avec Manuel Morales et publié dans la revue European Actuarial Journal. Cet article étudie le problème de ruine pour un processus de risque markovien additif. Une identification de systèmes de Lévy est obtenue et utilisée pour donner une expression de l'espérance de la fonction de pénalité actualisée lorsque le PMA est un processus de Lévy avec changement de régimes. Celle-ci est une généralisation des résultats existant dans la littérature pour les processus de risque de Lévy et les processus de risque markoviens additifs avec sauts "phase-type". Le troisième chapitre contient l'article "On a Generalization of the Expected Discounted Penalty Function to Include Deficits at and Beyond Ruin" qui est soumis pour publication. Cet article présente une extension de l'espérance de la fonction de pénalité actualisée pour un processus subordinateur de risque perturbé par un mouvement brownien. Cette extension contient une série de fonctions escomptée éspérée des minima successives dus aux sauts du processus de risque après la ruine. Celle-ci a des applications importantes en gestion de risque et est utilisée pour déterminer la valeur espérée du capital d'injection actualisé. Finallement, le quatrième chapitre contient l'article "The Minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model" écrit en collaboration avec Romuald Hervé Momeya et publié dans la revue Asia-Pacific Financial Market. Cet article présente de nouveaux résultats en lien avec le problème de l'incomplétude dans un marché financier où le processus de prix de l'actif risqué est décrit par un modèle exponentiel markovien additif. Ces résultats consistent à charactériser la mesure martingale satisfaisant le critère de l'entropie. Cette mesure est utilisée pour calculer le prix d'une option, ainsi que des portefeuilles de couverture dans un modèle exponentiel de Lévy avec changement de régimes.

Embracing the Crisis in the Foundations of Mathematics

The crisis in the foundations of mathematics is a conceptual crisis. I suggest that we embrace the crisis and adopt a pluralist position towards foundations. There are many foundations in mathematics. However, ‘many foundations’ (for one building) is an oxymoron. Therefore, we shift vocabulary to say that mathematics, as one discipline, is composed of many different theories. This entails that there are no absolute mathematical truths, only truths within a theory. There is no unified, consistent ontology, only ontology within a theory.

Indian Mathematics Related to Architecture and Other Areas With Special Reference to Kerala

Department of Mathematics, Cochin University of Science and Technology

Some aspects of history of Indian mathematics in 18th and early 19th century

This thesis is an attempt to throw light on the works of some Indian Mathematicians who wrote in Arabic or persian In the Introductory Chapter on outline of general history of Mathematics during the eighteenth Bnd nineteenth century has been sketched. During that period there were two streams of Mathematical activity. On one side many eminent scholers, who wrote in Sanskrit, .he l d the field as before without being much influenced by other sources. On the other side there were scholars whose writings were based on Arabic and Persian text but who occasionally drew upon other sources also.

Aspekte der linearen Minimax-Schätzung

Es werde das lineare Regressionsmodell y = X b + e mit den ueblichen Bedingungen betrachtet. Weiter werde angenommen, dass der Parametervektor aus einem Ellipsoid stammt. Ein optimaler Schaetzer fuer den Parametervektor ist durch den Minimax-Schaetzer gegeben. Nach der entscheidungstheoretischen Formulierung des Minimax-Schaetzproblems werden mit dem Bayesschen Ansatz, Spektralen Methoden und der Darstellung von Hoffmann und Laeuter Wege zur Bestimmung des Minimax- Schaetzers dargestellt und in Beziehung gebracht. Eine Betrachtung von Modellen mit drei Einflussgroeßen und gemeinsamen Eigenvektor fuehrt zu einer Strukturierung des Problems nach der Vielfachheit des maximalen Eigenwerts. Die Bestimmung des Minimax-Schaetzers in einem noch nicht geloesten Fall kann auf die Bestimmung einer Nullstelle einer nichtlinearen reellwertigen Funktion gefuehrt werden. Es wird ein Beispiel gefunden, in dem die Nullstelle nicht durch Radikale angegeben werden kann. Durch das Intervallschachtelungs-Prinzip oder Newton-Verfahren ist die numerische Bestimmung der Nullstelle moeglich. Durch Entwicklung einer Fixpunktgleichung aus der Darstellung von Hoffmann und Laeuter war es in einer Simulation moeglich die angestrebten Loesungen zu finden.

Error estimates for approximate approximations on compact intervals

The aim of this paper is the investigation of the error which results from the method of approximate approximations applied to functions defined on compact in- tervals, only. This method, which is based on an approximate partition of unity, was introduced by V. Mazya in 1991 and has mainly been used for functions defied on the whole space up to now. For the treatment of differential equations and boundary integral equations, however, an efficient approximation procedure on compact intervals is needed. In the present paper we apply the method of approximate approximations to functions which are defined on compact intervals. In contrast to the whole space case here a truncation error has to be controlled in addition. For the resulting total error pointwise estimates and L1-estimates are given, where all the constants are determined explicitly.

Visualisierungsverfahren zur Interaktion mit objekt-relationalen Datenbanken

In der vorliegenden Arbeit 1 wird ein neues, erweiter- und konfigurierbares Visualisierungsverfahren zur Interaktion mit komplex strukturierten Datenobjekten vorgestellt. Die Erweiterbarkeit bezieht sich dabei auf die vom Verfahren einsetzbaren Techniken der Visualisierung (Visualisierungsfunktionen) und auf die in das Verfahren integrierte Interaktion. Die mit dem Verfahren generierbaren Repräsentationen sind besonders zum Browsen in den Objekten und zum Editieren der Objekte geeignet, die typischerweise in objekt-relationalen Datenbanken gespeichert werden. Die generierten Repräsentationen können modulartig in vorhandene graphische Benutzerschnittstellen integriert werden oder als vollständige graphische Benutzerschnittstelle einer Anwendung eingesetzt werden. Modularität und Orthogonalität, also die sinnvolle Aufteilung in Funktionseinheiten und die Möglichkeit, Methoden einer Komponente auf andere Komponenten anzuwenden, werden als Mittel eingesetzt, mit weniger Komponenten mehr Funktionalität zu erreichen. Für den Teilaspekt der Benutzerschnittstelle wurde dies durch Visualisierungsvorschriften für Datenobjekte (Relationen, Tabellen) vorgeschlagen, indem ein Baum aus der Strukturdefinition (Schema) abgeleitet und als persistentes (Meta-) Datenobjekt in der Datenbank gespeichert wird. Sie werden kurz "Visualisierungen" genannt. Wie gezeigt werden kann, sind sechs Meta-Objekte die notwendige und hinreichende Anzahl und Ausprägung von Schemata und Visualisierungen zur Definition und visuellen Repräsentation beliebiger Anwendungs-Objekte (Schemata und durch sie definierte Tabellen), inklusive ihrer eigenen Schemata und Visualisierungen. Der Einsatz der Selbstreferenzierung mit Meta-Objekten hat zu mehr Sicherheit und Kompaktheit ohne nenneswerte Laufzeiteinbußen geführt.