Report on Innovation Working Group : The Mathematics Education into the 21st Century Project. Dresden, Saxony

This document reports on the Innovations Working Group that met at the 10th International Conference “Models in Developing Mathematics Education” from the 11-17th September 2009 in Dresden, Saxony. It briefly describes the over arching and consistent themes that emerged from the numerous papers presented. The authors and titles of each of the papers presented will be listed in Table 2.

Students as decoders of graphics in mathematics

This paper reports on students’ ability to decode mathematical graphics. The findings were: (a) some items showed an insignificant improvement over time; (b) success involves identifying critical perceptual elements in the graphic and incorporating these elements into a solution strategy; and (c) the optimal strategy capitalises on how information is encoded in the graphic. Implications include a need for teachers to be proactive in supporting students’ to develop their graphical knowledge and an awareness that knowledge varies substantially across students.

Students' perceptions of the relevance of mathematics in engineering

In this paper, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society (Kirschenman and Brenner 2010)d. Qualitative and quantitative data on students' views of the relevance of their mathematics study to their engineering studies and future careers in engineering was collected. The students described using a range of mathematics techniques (mathematics skills developed, mathematics concepts applied to engineering and skills developed relevant for engineering) for various usages (as a subject of study, a tool for other subjects or a tool for real world problems). We found a number of themes relating to the design of mathematics engineering curriculum emerged from the data. These included the relevance of mathematics within different engineering majors, the relevance of mathematics to future studies, the relevance of learning mathematical rigour, and the effectiveness of problem solving tasks in conveying the relevance of mathematics more effectively than other forms of assessment. We make recommendations for the design of engineering mathematics curriculum based on our findings.

Malcolm Shepherd Knowles : A History of His Thought

This book traces the evolution of thinking of the American adult educator, Malcolm Knowles, and maps the development of his conceptual framework over the period 1950 to 1995. It constructs an overall narrative history of Knowles’ thought, and shows how andragogy provided him with both a label and a unifying theme for his practical-theoretical framework aimed at producing self-directed lifelong learners. Knowles died in 1997 and left a large legacy of books and journal articles. The book examines the writings that constitute Knowles' principal works. It identifies the major elements of his thought, shows the interrelationships between ideas and indicates the major phases through which his thinking passed. Importantly, the book establishes that Knowles’ theorising was traceable and that he possessed a clear and coherent conceptual framework.

Recognising Torres Strait Islander women’s knowledges in their children’s mathematics education

This paper discusses women’s involvement in their children’s mathematics education. It does, where possible, focus Torres Strait Islander women who share the aspirations of Aborginal communities around Australia. That is, they are keen for their children to receive an education that provides them with opportunities for their present and future lives. They are also keen to have their cultures’ child learning practices recognised and respected within mainstream education. This recognition has some way to go with the language of instruction in schools written to English conventions, decontextualised and disconnected to the students’ culture, Community and home language.

Teacher change and professional development in mathematics education

It is generally agreed that if authentic teacher change is to occur then the tacit knowledge about how and why they act in certain ways in the classroom be accessed and reflected upon. While critical reflection can and often is an individual experience there is evidence to suggest that teachers are more likely to engage in the process when it is approached in a collegial manner; that is, when other teachers are involved in and engaged with the same process. Teachers do not enact their profession in isolation but rather exist within a wider community of teachers. An outside facilitator can also play an active and important role in achieving lasting teacher change. According to Stein and Brown (1997) “an important ingredient in socially based learning is that graduations of expertise and experience exist when teachers collaborate with each other or outside experts” (p. 155). To assist in the effective professional development of teachers, outside facilitators, when used, need to provide “a dynamic energy producing interactive experience in which participants examine and explore the complex components of teaching” (Bolster, 1995, p. 193). They also need to establish rapport with the participating teachers that is built on trust and competence (Hyde, Ormiston, & Hyde, 1994). For this to occur, professional development involving teachers and outside facilitators or researchers should not be a one-off event but an ongoing process of engagement that enables both the energy and trust required to develop. Successful professional development activities are therefore collaborative, relevant and provide individual, specialised attention to the teachers concerned. The project reported here aimed to provide professional development to two Year 3 teachers to enhance their teaching of a new mathematics content area, mental computation. This was achieved through the teachers collaborating with a researcher to design an instructional program for mental computation that drew on theory and research in the field.

Making sense of mass education

Making Sense of Mass Education provides a comprehensive analysis of the field of mass education. The book presents new assessment of traditional issues associated with education – class, race, gender, discrimination and equity –to dispel myths and assumptions about the classroom. It examines the complex relationship between the media, popular culture and schooling, and places the expectations surrounding the modern teacher within ethical, legal and historical contexts. The book blurs some of the disciplinary boundaries within the field of education, drawing upon sociology, cultural studies, history, philosophy, ethics and jurisprudence to provide stronger analyses. The book reframes the sociology of education as a complex mosaic of cultural practices, forces and innovations. Engaging and contemporary, it is an invaluable resource for teacher education students, and anyone interested in a better understanding of mass education.

A history of heart interventions moderates the relationship between psychological variables and the presence of chest pain in older women with self-reported coronary heart disease

Objectives: This study examines the hypothesis that a past history of heart interventions will moderate the relationship between psychosocial factors (stressful life events, social support, perceived stress, having a current partner, having a past diagnosis of depression or anxiety over the past 3 years, time pressure, education level, and the mental health index) and the presence of chest pain in a sample of older women. Design: Longitudinal survey over a 3-year period. Methods: The sample was taken from a prospective cohort study of 10,432 women initially aged between 70 and 75 years, who were surveyed in 1996 and then again in 1999. Two groups of women were identified: those reporting to have heart disease but no past history of heart interventions (i.e., coronary artery bypass graft/angioplasty) and those reporting to have heart disease with a past history of heart interventions. Results: Binary logistic regression analysis was used to show that for the women with self-reported coronary heart disease but without a past history of heart intervention, feelings of time pressure as well as the number of stressful life events experienced in the 12 months prior to 1996 were independent risk factors for the presence of chest pain, even after accounting for a range of traditional risk factors. In comparison, for the women with self-reported coronary heart disease who did report a past history of heart interventions, a diagnosis of depression in the previous 3 years was the significant independent risk factor for chest pain even after accounting for traditional risk factors. Conclusion: The results indicate that it is important to consider a history of heart interventions as a moderator of the associations between psychosocial variables and the frequency of chest pain in older women. Statement of Contribution: What is already known on this subject? Psychological factors have been shown to be independent predictors of a range of health outcomes in individuals with coronary heart disease, including the presence of chest pain. Most research has been conducted with men or with small samples of women; however, the evidence does suggest that these relationships exist in women as well as in men. What does this study add? Most studies have looked at overall relationships between psychological variables and health outcomes. The few studies that have looked at moderators have mainly examined gender as a moderator. To our knowledge, this is the first published study to examine a history of heart interventions as a moderator of the relationship between psychological variables and the presence of chest pain.

Theories of learning mathematics

According to Karl Popper, widely regarded as one of the greatest philosophers of science in the 20th century, falsifiability is the primary characteristic that distinguishes scientific theories from ideologies – or dogma. For example, for people who argue that schools should treat creationism as a scientific theory, comparable to modern theories of evolution, advocates of creationism would need to become engaged in the generation of falsifiable hypothesis, and would need to abandon the practice of discouraging questioning and inquiry. Ironically, scientific theories themselves are accepted or rejected based on a principle that might be called survival of the fittest. So, for healthy theories on development to occur, four Darwinian functions should function: (a) variation – avoid orthodoxy and encourage divergent thinking, (b) selection – submit all assumptions and innovations to rigorous testing, (c) diffusion – encourage the shareability of new and/or viable ways of thinking, and (d) accumulation – encourage the reuseability of viable aspects of productive innovations.

Assessing the potential of mathematics textbooks to promote deep learning

Curriculum documents for mathematics emphasise the importance of promoting depth of knowledge rather than shallow coverage of the curriculum. In this paper, we report on a study that explored the analysis of junior secondary mathematics textbooks to assess their potential to assist in teaching and learning aimed at building and applying deep mathematical knowledge. The method of analysis involved the establishment of a set of specific curriculum goals and associated indicators, based on research into the teaching and learning of a particular field within the mathematics curriculum, namely proportion and proportional reasoning. Topic selection was due to its pervasive nature throughout the school mathematics curriculum at this level. As a result of this study, it was found that the five textbook series examined provided limited support for the development of multiplicative structures required for proportional reasoning, and hence would not serve well the development of deep learning of mathematics. The study demonstrated a method that could be applied to the analysis of junior secondary mathematics in many parts of the world.

Background to the development of a curriculum for the history of “cyber” and “communications” security

For any discipline to be regarded as a professional undertaking by which its members may be treated as true “professionals” in a specific area, practitioners must clearly understand that discipline’s history as well as the place and significance of that history in current practice as well as its relevance to available technologies and artefacts at the time. This is common for many professional disciplines such as medicine, pharmacy, engineering, law and so on but not yet, this paper submits, in information technology. Based on twenty five elapsed years of experience in developing and delivering Cybersecurity courses at undergraduate and postgraduate levels, this paper proposes a rationale and set of differing perspectives for the planning and development of curricula relevant to the delivery of appropriate courses in the history of cybersecurity or information assurance to information and communications technology (ICT) students and thus to potential information technology professionals.