Students' approaches to mathematical tasks using software as a black-box, glass-box or open-box

Three mathematical software modes are investigated in this thesis: black-box software showing no mathematical steps; glass-box software showing the intermediate mathematical steps; and open-box software showing and allowing interaction at the intermediate mathematical steps. The glass-box and open-box software modes are often recommended over the black-box software to help understanding but there is limited research comparing all three. This research investigated students' performance and their approaches to solving three mathematical task types when assigned to the software boxes. Three approaches that students may undertake when solving the tasks were investigated: students' processing levels, their software exploration and their self-explanations. The effect of mathematics confidence on students' approaches and performance was also considered. Thirty-eight students were randomly assigned to one of the software boxes in an experimental design where all audio and video data were collected via a web-conference remote observation method. The students were asked to think-aloud whilst they solved three task types. The three task types were classified based on the level of conceptual and procedural knowledge needed for solving: mechanical tasks required procedural knowledge, interpretive tasks required conceptual knowledge; and constructive tasks used both conceptual and procedural knowledge. The results indicated that the relationship between students' approaches and performance varied with the software box. Students using the black-box software explored more for the constructive tasks than the students in the glass-box and open-box software. These black-box software students also performed better on the constructive tasks, particularly those with higher mathematics confidence. The open-box software appeared to encourage more mathematical explanations whilst the glass-box software encouraged more real-life explanations. Mathematically confident students were best able to appropriate the black-box software for their conceptual understanding. The glass-box software or open-box software appeared to be useful for helping students with procedural understanding and familiarity with mathematical terms

Postgraduate blogs: beyond the ordinary research journal

The study described in this paper investigated ways in which keeping a research journal as a blog rather than as a paper document influenced the postgraduate student research experience. Four blogs (three individual and one collaborative blog) initiated by three research students were used as the corpus of data. The three individual blogs acted as alternatives to the traditional research journal. The analysis indicated that blogs can promote a community where students are encouraged to reflect and share ideas, skills and research life idiosyncrasies. Blogs also acted as memory repositories and encouraged collaboration amongst the research students

Shifting themes, shifting roles: the development of research blogs

The study described in this paper investigated the use of research blogs by postgraduate students over a four-year period. An initial, one-year, pilot focused on the research blogs of three first-year doctoral students (Ferguson, Clough, & Hosein, 2007). Analysis indicated that blogs were used to promote a community where students were encouraged to reflect and share ideas, skills and stories of research life. The blogs also acted as memory repositories and encouraged collaboration. The main study followed the students’ blogs for another three years, as they completed their doctorates and took jobs as early-career researchers. It investigated changes in the use and content of research blogs during this period. All three students continued to make use of their blogs for reflection over this period, and the blogs’ use as a memory repository became increasingly important, especially during the period of writing up research. Once the students had made the transition to early-career researcher, the nature of their blog use changed and began to fragment. This was due, in part, to issues of confidentiality, and data protection associated with their employment. While they continued to use their original research blogs to promote community and collaboration, the constraints of their work meant that new posts were often posted in closed blogs, or were marked as protected. At the same time, they were required or encouraged to make use of project-related blogs as part of a planned communication strategy by their employers. The findings of this longitudinal study clarify the changing expectations and needs of learners, employers and society in relation to researchers’ blogs, and identify skills, awareness and knowledge needed to support the use of blogging by research students

The teaching of linear programming in different disciplines and in different countries

This paper discusses an online survey of linear programming (LP) lecturers in four countries in various disciplines. The study uses Biglan’s [1, 2] classification of disciplines to show that courses in hard-pure and hard-applied subjects were more likely to teach theoretical aspects of linear programming whilst the hard-applied and soft-applied subjects looked more at the application. Further, the soft-applied disciplines were more likely to utilize software during the teaching of the topic. Also, US lecturers were more likely to teach theoretical aspects of LP whilst the UK lecturers were more likely to use common software such as spreadsheets rather than dedicated LP or maths software

Learning and living technologies: a longitudinal study of first-year students' expectations and experiences in the use of ICT

This paper presents results from a longitudinal study on first-year students' expectations and actual reported use of information and communication technologies (ICT) at university. The study was interested in firstly, knowing if students from the Net Generation (? 25 years) would appropriate more ICT time for both social life and leisure, and study purposes than older students, as this forms the basis for many Net Generation and Digital Natives claims about young people use of technology. Secondly, the impact of university type (place-based or distance-learning) on ICT use was explored. Data were analysed from two surveys that were part of the Economic Social Research Council (ESRC) funded project: The Net Generation Encountering eLearning at University. The first survey which asked for expected ICT time was sent at the beginning of the academic year. The second survey was sent towards the end of the academic year and asked for the actual time spent on using ICTs. Students studying 14 different courses in five different universities (four place-based and one distance-learning) in England took part in the study. The results showed that students underestimated their total ICT time (combined time for social life and leisure, and study purposes) by at least 1 hour per day. The Net Generation students were found to spend more time per day using ICT for social life and leisure purposes than the non-Net Generation students (2.2 vs 1.7 hrs). In contrast, the non-Net Generation students spent more ICT time on study than the Net Generation students (2.3 vs 1.9 hrs. It appears that younger generation students used ICT for social life and leisure more frequently and older students were more likely to use it for study. University mode of study also influenced how students appropriated their ICT time. Place-based university students spent at least one hour more per day on ICT than distance-learning university students. The results found differences across the two age groups were more noticeable at the place-based university than at the distance-learning university

Students’ Reflective Essays as insights into Student Centred-Pedagogies within the Undergraduate Research Methods Curriculum

In higher education, despite the emphasis on student-centred pedagogical approaches, undergraduate research methods pedagogy remains surprisingly teacher-directed although undergraduate research itself is student-centred. Consequently, research methods students may believe becoming a researcher is about learning information rather than a continuous developmental process. To combat this idea, a reflective student-centred pedagogical approach is evaluated for encouraging students’ development as researchers. In this study, undergraduate research methods students piloted a research method and produced a reflective essay on their research experience which were qualitatively analysed. Analysis indicated that students demonstrated an awareness of both their research skills such as choosing an appropriate research instrument and their researcher identity such as their metacognition of their competence. Pedagogical approaches which encourages ‘reflection on action’ in the research curriculum therefore helps students to articulate their researcher identity and build their research skills confidence and should be actively promoted

Complex Transitions of Early Career Academics (ECA): A Mixed Method Study of With Whom ECA Develop and Maintain New Networks

The purpose of this article is to explore how Early Career Academics (ECAs) cope with their complex and multiple transitions when starting their new role. By focussing on the participants’ lived experiences in a professional development (PD) training programme to discuss and share practice, we explored how ECAs developed and maintained social network relations. Using social network analysis (SNA) with web crawling of public websites, data was analysed for 114 participants to determine with whom they shared practice outside PD (i.e., external connectors), the seniority of these connectors, and similarity to their job area. The results highlight that ECA networks were hierarchically flat, whereby their sharing practice network of 238 external connectors composed of their (spousal) partner and (male) colleagues at the same hierarchical level. The persons whom ECAs were least likely to discuss their practice with were people in senior management roles. The results of this study highlight that the creation of a community of practice for discussing and sharing of practice from PD programmes appear to be insular. Activities within the organisation and the formation of learning communities from PD may become lost as most of the sharing of practice/support comes from participants’ partners. Organisations may have to create spaces for sharing practice beyond the PD classroom to further organisational learning

An Illustration of Students’ Engagement with Mathematical Software using Remote Observation

Students using three types of spreadsheet calculators for understanding expected value were observed remotely. This remote observation involves the use of webcams and application sharing for observing students learning mathematics. The study illustrates how remote observation can be used for collecting mathematical education data and raises questions about the extent to which such a method can be used in future experiments