Mathematics and language

This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes that we view mathematics as a system of conventions and norms that is designed to help us make sense of the world and reason efficiently. Like any designed system, it can perform well or poorly, and the philosophy of mathematics has a role to play in helping us understand the general principles by which it serves its purposes well

Chapter 5: Evaluation

The OTiS (Online Teaching in Scotland) programme, run by the now defunct Scotcit programme, ran an International e-Workshop on Developing Online Tutoring Skills which was held between 8–12 May 2000. It was organised by Heriot–Watt University, Edinburgh and The Robert Gordon University, Aberdeen, UK. Out of this workshop came the seminal Online Tutoring E-Book, a generic primer on e-learning pedagogy and methodology, full of practical implementation guidelines. Although the Scotcit programme ended some years ago, the E-Book has been copied to the SONET site as a series of PDF files, which are now available via the ALT Open Access Repository. The editor, Carol Higgison, is currently working in e-learning at the University of Bradford (see her staff profile) and is the Chair of the Association for Learning Technology (ALT)

Experiences with HPTN 067/ADAPT Study-Provided Open-Label PrEP Among Women in Cape Town: Facilitators and Barriers Within a Mutuality Framework.

Placebo-controlled trials of pre-exposure prophylaxis (PrEP) have reported challenges with study-product uptake and use, with the greatest challenges reported in studies with young women in sub-Saharan Africa. We conducted a qualitative sub-study to explore experiences with open-label PrEP among young women in Cape Town, South Africa participating in HTPN 067/Alternative Dosing to Augment Pre-Exposure Prophylaxis Pill Taking (ADAPT). HPTN 067/ADAPT provided open label oral FTC/TDF PrEP to young women in Cape Town, South Africa who were randomized to daily and non-daily PrEP regimens. Following completion of study participation, women were invited into a qualitative sub-study including focus groups and in-depth interviews. Interviews and groups followed a semi-structured guide, were recorded, transcribed, and translated to English from isiXhosa, and coded using framework analysis. Sixty of the 179 women enrolled in HPTN 067/ADAPT participated in either a focus group (six groups for a total of 42 participants) or an in-depth interview (n = 18). This sample of mostly young, unmarried women identified facilitators of and barriers to PrEP use, as well as factors influencing study participation. Cross-cutting themes characterizing discourse suggested that women placed high value on contributing to the well-being of one's community (Ubuntu), experienced a degree of skepticism towards PrEP and the study more generally, and reported a wide range of approaches towards PrEP (ranging from active avoidance to high levels of persistence and adherence). A Mutuality Framework is proposed that identifies four dynamics (distrust, uncertainty, alignment, and mutuality) that represent distinct interactions between self, community and study and serve to contextualize women's experiences. Implications for better understanding PrEP use, and non-use, and intervention opportunities are discussed. In this sample of women, PrEP use in the context of an open-label research trial was heavily influenced by underlying beliefs about safety, reciprocity of contributions to community, and trust in transparency and integrity of the research. Greater attention to factors positioning women in the different dynamics of the proposed Mutuality Framework could direct intervention approaches in clinical trials, as well as open-label PrEP scale-up

After the Social Meaning Turn : Implications for Research Design and Methods of Proof in Contemporary Criminal Law Policy Analysis

The social norm movement in criminal justice has received a lot of attention in academic and public policy circles. This essay critically examines social norm writings and explores some of the implications for methods of proof and research design in the social sciences. In the process, the essay offers an alternative theoretical approach. This alternative focuses on the multiple ways in which the social meaning of practices (such as juvenile gun possession, gang membership, or disorderly conduct) and the social meaning of policing techniques (such as juvenile snitching policies, youth curfews, or order-maintenance policing) may shape us as contemporary subjects of society. This alternative theoretical approach has its own important implications for methods of proof and research design, and the essay develops these implications into a four-prong research agenda

Being in a seclusion room: the forensic inpatients’ perspective.

Objective: The aim of this thesis portfolio is to explore and understand the patient experience of seclusion. Methods: A qualitative systematic review was undertaken of research exploring the experience of seclusion. Thematic synthesis was used to develop analytical themes to explore the inpatient experience of seclusion. Alongside this a qualitative research project was undertaken using Interpretative Phenomenological Analysis to explore forensic psychiatric inpatients’ experience of being in a seclusion room. Results: The systematic review found eight studies which met inclusion criteria and all were of high methodological quality. The thematic synthesis identified four analytical themes: feeling vulnerable, feeling neglected and abused, disconnecting and seclusion is dangerous to mental health. The empirical research project identified four superordinate themes: intense fear, not getting the care I needed, I am being abused and power struggle. Conclusion: This thesis portfolio has highlighted the emotional and interpersonal challenges associated with the experience of seclusion. It draws attention to the relevance of the seclusion room in the overall experience and how a forensic population may have a power struggle dynamic within their experience. It provides direction for future research and emphasises the importance of improving seclusion practices by making changes to staff-patient interaction to reflect the emotional needs of the patients

The use of reflective journal in a postgraduate research methodology course: student experiences

This paper examines the research skill development of an intact group of postgraduate (Master of Arts) students in a research methodology course. Data were collected from the students' weekly introspective reflective journals over one semester and a semi-structured interview at the end of the course. Results from the students' reflections revealed the initial high anxiety among novice researchers who had to juggle between learning new concepts and applying the knowledge in practice. Those who looked at the rewards instead of the challenges found their learning processes more meaningful although they also struggled in completing tasks and writing assignments. The students' esearch skill development culminated in a sense of achievement and satisfaction. The findings from the study contribute to the awareness of the difficulties, the strategies used and the worthwhile learning experiences of novice researchers in acquiring and developing research skills. Suggestions for pedagogy are identified for the use of reflections in the classroom

Third-graders' problem solving performance and teachers' actions

Peer reviewe

Exploring lesson study as a form of professional development for enriching teacher knowledge and classroom practices

This study tracked the development of teacher knowledge through a professional development experience called lesson study. Lesson study is a Japanese professional development process in which a group of teachers develop a series of lessons using the following stages: planning lessons, teaching/observing the lessons, reflecting on lessons taught as well as sharing and discussing the lessons with their colleagues (Lewis, 2002). The aim of this study was to explore how the lesson study process influenced teacher knowledge of mathematics content and pedagogical content. Study participants were four secondary mathematics teachers from a rural high school in the Northeast. All participants were certified in teaching secondary mathematics and varied in their educational background and teaching experience. These four teachers and the researcher created a Mathematics Lesson Study Group at the high school level. Throughout the 2004-2005 school year, this group met to plan three different mathematics lessons. After planning each lesson, one teacher from the group taught the lesson to his/her class of students while the other teachers observed. Following the teaching/observing stage of the lesson development, the teachers had a debriefing meeting to reflect on how the lesson went and to propose possible revisions. Each stage of the lesson study process - planning, teaching/observing, and debriefing was examined carefully in order to determine how the various aspects of that stage contributed to the development of the teachers\u27 mathematics content and pedagogical content knowledge. This information was gathered from videotapes and teachers\u27 notes taken at all meetings, journal reflections following the meetings, initial and final interviews, and classroom observations. All data was analyzed qualitatively. Results indicate that the teachers\u27 mathematics content knowledge in the form of substantive and syntactic knowledge was influenced throughout all stages of the lesson study process. In addition, during each of the stages of lesson study the teachers\u27 pedagogical content knowledge evolved in the areas of prior knowledge connections, anticipating student misconceptions, questioning, choosing example problems, assessing student understanding during the lesson, and curriculum knowledge. Lastly, the results support how important the components of planning and reflection, within the lesson study model, are to the enrichment of teachers\u27 knowledge and classroom practices

Civil Procedure—Reflections on the Comparison of Systems

The James McCormick Mitchell Lecture, delivered at the University of Buffalo School of Law, November 15, 1960