Proofs and refutations in the undergraduate mathematics classroom

In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics. In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional approaches that support the learning of mathematics through the process of guided reinvention.     

Students' mental models of the environment

What are students' mental models of the environment? In what ways, if any, do students' mental models vary by grade level or community setting? These two questions guided the research reported in this article. The Environments Task was administered to students from 25 different teacher‐classrooms. The student responses were first inductively analyzed in order to identify students' mental models of the environment. The second phase of analysis involved the statistical testing of the identified mental models. From this analysis four mental models emerged: Model 1, the environment as a place where animals/plants live—a natural place; Model 2, the environment as a place that supports life; Model 3, the environment as a place impacted or modified by human activity; and Model 4, the environment as a place where animals, plants, and humans live. The dominant mental model was Mental Model 1. Yet, a greater frequency of urban students than suburban and rural students held Mental Model 3. The implications to environmental science education are explored. © 2007 Wiley Periodicals, Inc. J Res Sci Teach 44: 327–348, 2007     

What Mathematics Education May Prepare Students for the Society of the Future?

This paper attempts to engage the field in a discussion about what mathematics is needed for students to engage in society, especially with an increase in technology and digitalization. In this respect, mathematics holds a special place in STEM as machines do most of the calculations that students are taught in K-12. We raise questions about what mathematical proficiency means in today’s world and what shifts need to be made in both content and pedagogy to prepare students for 21st Century Skills and mathematical reasoning.     

Snakes or Ladders? Evaluating a LibGuides Pilot at UCD Library

Online subject guides are commonly used by libraries to provide information support to students. LibGuides (a cloud-based commercial product launched in 2007) represents one of the latest incarnations of the traditional subject guide or portal, and are widely used across American academic libraries. In Ireland however, library subject guides of entirely local design and hosted on a local web server still dominate.This paper outlines the project management process involved in implementing a LibGuides pilot at University College Dublin Library, including the planning, design and implementation of a new range of subject-related guides. The pilot nature of the project necessitated a strong focus on evaluation, particularly in assessing the effectiveness and suitability of LibGuides as a platform for delivering information literacy support, both from an administrative and end-user perspective. A two-stranded approach was used in this review process, incorporating quantitative web statistics and analytics alongside qualitative feedback from students, academic staff and Library staff.Feedback that was gathered suggested that the LibGuides subject guides were generally viewed very positively by both staff and students. Notwithstanding this, awareness (as indicated through usage statistics) remained moderate during the pilot, pointing to the importance of the visibility, positioning and promotion of guides.     

The Development of Research Skills in Young Adults with Intellectual Disability in Participatory Research

There is limited information about specific research constructs developed by adults with intellectual disability in undertaking research despite increasing involvement in research with rather than on these individuals. Participatory research was used with three young adults with intellectual disability to collaboratively develop a training programme and investigate the skills used and developed when undertaking the research project. Three research domains—Knowledge, Conceptual understandings and Skills, were identified, within which 18 subsets were categorised. Development in all domains and subsets occurred for all young adults, with variations in gains across subsets and participants. These young adults attained research knowledge, understanding and skills that enabled them to become collaborative researchers within this project.     

More than just charts and graphs: What to teach in a data visualization course

Based on our experience developing and delivering a highly successful data visualization course within a Master of Science in Business Analytics program, we present a taxonomy for data visualization courses and recommend content and pedagogical features for each type of data visualization course therein. We also discuss the interdependence between data visualization and business communication as a critical consideration in course design.     

Supervision provided to Indigenous Australian doctoral students: a black and white issue

The number of Indigenous Australians completing doctoral qualifications is disparately below their non-Indigenous contemporaries. Whilst there has been a steady increase in Indigenous completions in recent years, significant work remains to redress the imbalance. Supervision has been identified as a primary influencer of the likely success of Indigenous doctoral students, yet very little research has been undertaken in this area. This paper examines the experiences of 11 Indigenous Australians who hold a doctoral qualification. It also provides the experiences of five non-Indigenous supervisors who were an integral part of the supervision team of one of the successful doctoral graduates. A best-practice framework for supervision is offered as a guide for how supervisors, universities and national bodies can contribute to building the number of doctoral qualified Indigenous Australians.     

Patterns,drivers and challenges pertaining to postgraduate taught study: an international comparative analysis

The global growth in postgraduate (PG) study since the mid-1990s has been attributed to the expansion in Masters by Coursework participation (Bekhradnia, B. (2005). Postgraduate education in the UK: Trends and challenges higher education policy institute. Paper presented at a conference The future of postgraduate education supporting the students of today and tomorrow, London, 17 March). However, unlike at undergraduate level, research into understanding PG growth has been under-researched. This paper aims to contribute to the knowledge gap by identifying and comparing the growth in PG study in Australia, Canada, the USA and the UK. It explores the possible drivers behind the growth and concludes by highlighting potential challenges facing the future of PG study across the sector.     

Course of depression and anxiety symptoms during the transition to parenthood for female adolescents with histories of victimization

The aim of the current study was to increase understanding of how victimization history impacts the longitudinal course of depression and anxiety in a sample of 55 adolescents emerging into parenthood. Adolescents were interviewed about their victimization experiences during their second trimester of pregnancy, and interviews were subsequently classified according the Maltreatment Classification Scale (Barnett, Manly, & Cicchetti, 1993). Adolescents reported on their symptoms of depression and anxiety prenatally and 6 and 12 months postpartum. Growth curve modeling revealed that, on average, there was a steady linear decline in depression and anxiety symptoms across the transition to parenthood, with a rate of change of 25% and 20%, respectively, from the prenatal assessment to 12 months postpartum. Sexual abuse history attenuated the likelihood of a decrease in depressive symptoms over time. Neglect history was associated with higher prenatal levels of anxiety, as well as a steeper decline in anxiety symptoms over time. Future research is needed to determine the role of poly-victimization in predicting the onset and change of depression and anxiety symptoms. Findings from the current study have the potential to aid in the design of preventative and intervention efforts to reduce risks of mental health difficulties in adolescent parents.