Students’ understanding of the function-derivative relationship when learning economic concepts

The aim of this study is to characterise students’ understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding of these economic concepts is linked to students’ capacity to perform conversions and treatments between the algebraic and graphic registers of the function-derivative relationship when extracting the economic meaning of concavity/convexity in graphs of functions using the second derivative.

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.

State goals for learning and sample learning objectives.

"Grades 3,6, 8, 10, 12."

Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing

Thesis (Ph.D.)--University of Washington, 2016-08

Pre-Service Teachers’ Mathematics Language and Reflection in the Context of an Early Childhood Mathematics Methods Course

Thesis (Ph.D.)--University of Washington, 2016-06

Learning difficulties in numeracy in Australia

In this article, we provide an understanding of the term numeracy as it is used in Australia and a description of numeracy education in this country. In particular, we discuss the role of outcomes-based curriculum frameworks and outline the dominant teaching approaches. The focus is on students with learning difficulties and how they are identified and supported in schools. We create two vignettes based on real students with difficulties in numeracy, which highlight two of the most common problems. We report on the prevalence of learning difficulties in numeracy in Australia and describe some of the initiatives related to the assessment and enhancement of learning in numeracy that are being undertaken in various states in Australia. Finally, we identify some of the future challenges facing the Australian education system in this area. These challenges relate to teacher knowledge, mandated assessment, and the role of parents. We conclude the article by calling for the evaluation of current assessment and intervention initiatives as well as the development of a national program to support the goal of numeracy for all students.

Improving learning in undergraduate control engineering courses using context-based learning models

Control Engineering is an essential part of university electrical engineering education. Normally, a control course requires considerable mathematical as well as engineering knowledge and is consequently regarded as a difficult course by many undergraduate students. From the academic point of view, how to help the students to improve their learning of the control engineering knowledge is therefore an important task which requires careful planning and innovative teaching methods. Traditionally, the didactic teaching approach has been used to teach the students the concepts needed to solve control problems. This approach is commonly adopted in many mathematics intensive courses; however it generally lacks reflection from the students to improve their learning. This paper addresses the practice of action learning and context-based learning models in teaching university control courses. This context-based approach has been practised in teaching several control engineering courses in a university with promising results, particularly in view of student learning performances.

Building partnerships with families and communities to support children's numeracy learning

The importance of building home, school and community partnerships is increasingly acknowledged since family and community involvement in education is thought to be associated with children’s success at school. This paper reports on aspects of an Australian Government commissioned research project that analysed educational partnerships aiming to enhance children’s numeracy education. Snapshots of two school case studies are presented to highlight features of effective partnerships and the kinds of numeracy learning they supported.

The engineering link project: Learning about engineering by becoming an engineer

There has been a greater emphasis over the past few years of encouraging high school students to take up engineering as a career. This is due to a greater need for engineers in society, particularly in areas that are suffering a skills shortage. Both the engineering profession and universities across Australia have moved to address this shortage, with a proliferation of engineering outreach activities and programs the result. The Engineering Link Group (TELG) began the Engineering Link Project (ELP) over a decade ago with a focus on helping motivated high school students make an informed choice about engineering as a career. It also aimed at encouraging more high school students to study maths and science at high school. From the start the ELP was designed so that the students became engineers, rather than just hear from or watch engineers. Real working engineers pose problems to groups of students for them solve over the course of a day. In this way, students experience what it is like to be an engineer. It has been found that the project does help high school students make more informed career choices about engineering. The project also gave the students real life and practical reasons for studying sciences and mathematics at high school. © 2005, Australasian Association for Engineering Education

A sociocultural analysis of learning to teach

This paper addresses the question of how teachers learn from experience during their pre-service course and early years of teaching. It outlines a theoretical framework that may help us better understand how teachers' professional identities emerge in practice. The framework adapts Vygotsky's Zone of Proximal Development, and Valsiner's Zone of Free Movement and Zone of Promoted Action, to the field of teacher education. The framework is used to analyse the pre-service and initial professional experiences of a novice secondary mathematics teacher in integrating computer and graphics calculator technologies into his classroom practice. (Contains 1 figure.) [For complete proceedings, see ED496848.]

An online community of practice for pre-service and beginning teachers of secondary mathematics

The aim of this study was to investigate how a community of practice focused on learning to teach secondary mathematics was created and sustained by pre-service and beginning teachers. Bulletin board discussions of one pre-service cohort are analysed in terms of Wenger’s (1998) three defining features of a community of practice: mutual engagement, joint enterprise, and a shared repertoire. The study shows that the emergent design of the community contributed to its sustainability in allowing the pre-service teachers to define their own professional goals and values. Sustainability was also related to how the participants expanded, transformed, and maintained the community during the pre-service program and after graduation.

Understanding technology integration in secondary mathematics: Theorising the role of the teacher

Previous research on computers and graphics calculators in mathematics education has examined effects on curriculum content and students’ mathematical achievement and attitudes while less attention has been given to the relationship between technology use and issues of pedagogy, in particular the impact on teachers’ professional learning in specific classroom and school environments. This observation is critical in the current context of educational policy making, where it is assumed – often incorrectly – that supplying schools with hardware and software will increase teachers’ use of technology and encourage more innovative teaching approaches. This paper reports on a research program that aimed to develop better understanding of how and under what conditions Australian secondary school mathematics teachers learn to effectively integrate technology into their practice. The research adapted Valsiner’s concepts of the Zone of Proximal Development, Zone of Free Movement and Zone of Promoted Action to devise a theoretical framework for analysing relationships between factors influencing teachers’ use of technology in mathematics classrooms. This paper illustrates how the framework may be used by analysing case studies of a novice teacher and an experienced teacher in different school settings.