Search

We report on three approaches taken to incorporate collaborative activities into undergraduate mathematics classes. There is strong evidence from research in K-12 classrooms that these, and similar, approaches support a range of positive learning outcomes for students. Despite the potential benefits the cited studies have shown, research into the use of such methods at the tertiary level is limited. We describe the ways in which we have implemented research projects, collaborative tutorials, and team-based learning in a range of undergraduate mathematics classes in two countries. We present quantitative and qualitative evidence from these teaching experiences to support our claim that there is a definite mandate for significant opportunities within our courses for students to work cooperatively, talk together, and argue about mathematics.

In a 2-year project, we developed and trialled a mode of lecturing professional development amongst staff in our department of mathematics. Theoretically grounded in Schoenfeld's resources, orientations, and goals (ROG) model of teacher action, a group met regularly to discuss both the video excerpts of themselves lecturing along with written pre- and post-lecture statements of their "ROGs". We found evidence of improved teaching performance but more interestingly, identified key aspects of our practice and of undergraduate mathematics that received repeated attention and developed further theoretical insight into lecturer behaviour in mathematics. The trial has been successful enough to be expanded into further groups that now constitute a professional development culture within our department.

What is the evidence that teachers who return to learn more mathematics are better teachers? Over more than a decade we have been involved in six different projects giving teachers the opportunity to reengage with mathematics. We have returned to them to ask the teachers about the long-term impact and to give us examples. The result extends existing research to provide evidence for a broad range of positive effects. Furthermore, the strong positive affective responses imply that returning to mathematics is a welcomed and practical professional development strategy. (Contains 1 table.)

A group of mathematicians and mathematics educators are collaborating in the fine-grained examination of selected "slices" of video recordings of lectures, drawing on Schoenfeld's Resources, Orientations and Goals framework of teaching-in-context. In the larger project, we are exploring ways in which this model can be extended to examine university lecturing. During this process, we have identified a number of lecturer behaviours. This article describes one of these behaviours where, in what appears to be an internal dialogue, lecturing decisions are driven either by the mathematician, or the teacher, within the lecturer. We analyse two scenarios. In the first, the teacher prevails and in the second, the mathematician. We analyse these behaviours against the framework of the lecturers' Resources, Orientations and Goals that were either stated by the lecturer or inferred from lecturer practice or discussion and subsequently confirmed. The value of the approach used as a professional development model is also considered.

This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused on what he calls the "unspoken curriculum": mathematical thinking. We consider the ways in which the TBL model promoted and enabled this in the light of literature on mathematical thinking, sense-making and behaviours, and strongly suggest that this approach warrants more attention from the mathematics teaching community. We also discuss shifts in the mathematician's thinking about task construction as he refined the tasks to encourage students to think and behave like mathematicians.

Papers presented at earlier Delta conferences reported on the use of collaborative tutorials and peer-tutors in undergraduate mathematics courses at The University of Auckland. This paper reports on significant developments within the Department's programmes, including the extension of the collaborative small-class tutorials to cover all first-year undergraduate courses in the department. It provides evidence of the effectiveness of the tutorial programme, as gauged from a survey of students' perceptions. Many of the students enrolled in the "Tutoring in Mathematics" course that initially trains and provides the peer-group tutors continue on as tutors in other mathematics courses within the Department. Some subsequently enroll in the University's Graduate Diploma in Teaching (Secondary). The effects of the tutoring course on tutors continuing to tutor at higher levels, and their performances as novice teachers in the Diploma course are examined. (Contains 3 tables and 1 figure.)

Observes seven trainee mathematics teachers completing a one-year, post-graduate secondary teaching diploma as part of a larger research project. Researchers ranked the preservice teachers in terms of their future effectiveness using two methods of ranking. The correlations between the two rankings were high. (Contains 15 references.) (Author/ASK)

Background: Modelling the blood-CNS barriers of the brain and spinal cord in vitro continues to provide a considerable challenge for research studying the passage of large and small molecules in and out of the central nervous system, both within the context of basic biology and for pharmaceutical drug discovery. Although there has been considerable success over the previous two decades in establishing useful in vitro primary endothelial cell cultures from the blood-CNS barriers, no model fully mimics the high electrical resistance, low paracellular permeability and selective influx/efflux characteristics of the in vivo situation. Furthermore, such primary-derived cultures are typically labour-intensive and generate low yields of cells, limiting scope for experimental work. We thus aimed to establish protocols for the high yield isolation and culture of endothelial cells from both rat brain and spinal cord. Our aim was to optimise in vitro conditions for inducing phenotypic characteristics in these cells that were reminiscent of the in vivo situation, such that they developed into tight endothelial barriers suitable for performing investigative biology and permeability studies. Methods: Brain and spinal cord tissue was taken from the same rats and used to specifically isolate endothelial cells to reconstitute as in vitro blood-CNS barrier models. Isolated endothelial cells were cultured to expand the cellular yield and then passaged onto cell culture inserts for further investigation. Cell culture conditions were optimised using commercially available reagents and the resulting barrier-forming endothelial monolayers were characterised by functional permeability experiments and in vitro phenotyping by immunocytochemistry and western blotting. Results: Using a combination of modified handling techniques and cell culture conditions, we have established and optimised a protocol for the in vitro culture of brain and, for the first time in rat, spinal cord endothelial cells. High yields of both CNS endothelial cell types can be obtained, and these can be passaged onto large numbers of cell culture inserts for in vitro permeability studies. The passaged brain and spinal cord endothelial cells are pure and express endothelial markers, tight junction proteins and intracellular transport machinery. Further, both models exhibit tight, functional barrier characteristics that are discriminating against large and small molecules in permeability assays and show functional expression of the pharmaceutically important P-gp efflux transporter. Conclusions: Our techniques allow the provision of high yields of robust sister cultures of endothelial cells that accurately model the blood-CNS barriers in vitro. These models are ideally suited for use in studying the biology of the blood-brain barrier and blood-spinal cord barrier in vitro and for pre-clinical drug discovery. [ABSTRACT FROM AUTHOR]