Teaching and Learning Research Papers Pre 2001

Please click on the links below to read the abstracts of the papers, alternatively you may wish to scroll through them.

J. MacBean, E. Graham and C. Sangwin, 2001, Group Work Reluctance in Maths Education, MSOR Connections, Vol. 1, No. 3, 24-25.
This provides an interim report on a research project to investigate undergraduate students views of the use of group work as part of their studies. The project aims to identify student views and to make recommendations on the use of group work.

Judith MacBean, Ted Graham and Chris Sangwin, 2001, Guidelines for Introducing Group Work in Undergraduate Mathematics, published by the LTSN Maths, Stats & OR Network.
These guidelines result from a research study that was undertaken by three differing higher education institutions in the UK. First year undergraduate students were surveyed and interviewed to find the extent to which students worked in groups and their attitudes to this.

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Graham E., Rowlands S., Jennings S. and English J., 1999. Towards Whole-class Interactive Teaching. J Teaching Mathematics & its Applications, Vol. 18 No 2, pp 50-60
This paper considers an approach to addressing the decline in the level of achievement of British pupils in mathematics. It looks in detail at the differences between the teaching methods of Britain and Hungary, as research studies have indicated the high level of achievement of Hungarian pupils in mathematics. The paper outlines three theoretical perspectives (radical constructivism, social constructivism, and Vygotsky’s zone of proximal development) that are helpful in considering the important differences. The major differences are considered under four categories: expectation and consistency, assessment, continuity and differentiated teaching. The paper proposes the method of whole-class interactive teaching as a way forward that would improve pupils’ achievement, and gives practical suggestions for developing such a teaching strategy.

Graham E., Sharp J. and Maull W., 1999. Bridge Building; a Practical Mathematics Task. Mathematics in School, Vol. 28 No 2 pp 2-5
The bridge building task is one that we have now used a number of times in different situations as part of the Centre for Teaching Mathematics’ Enrichment Programme. It has always proved both popular and challenging for students from year 8 to year 12. The actual task was inspired by the Dartford Bridge built in the early 1990’s to provide an improved link across the River Thames. The practical task was an attempt to allow children to reproduce some aspects of the design of this type of bridge in a simple way. The students are required to build a model of this type of bridge using retort stands, cardboard bridge sections and thin elastic. A considerable amount of mathematics is used to determine the lengths of elastic prior to stretching. The elastic is then cut and the bridge assembled to test. This article describes the stages that are involved in this task and concludes with some comments about how students approach and solve the problem.

Graham E, 1997, The ways in which different students respond to the same mathematical modelling problem, J. Teaching Mathematics and its Applications, 16, 19-22.
This paper reports on the responses that were obtained when the same mathematical problem was presented to approximately 300 students, with generally similar backgrounds and mathematical experiences. The students were instructed to work in pairs and given a limited time in which to find a solution to the problem. The results obtained show the variety of approaches taken and have been sorted into a number of categories. It also shows a tendency to consistently underestimate the solution to the problem (of estimating the amount of shortening that takes place when a knot is tied in a length of rope).

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Berry J. and Sharp J., 1999, Developing Student-centred Learning in Mathematics through Co-operation, Reflection and Discussion Teaching in Higher Education, Vol. 4 No 1, 27- 41
This paper describes a student-centred learning model for university level mathematics modules through whole class interaction that involves co-operation, reflection and discussion. The module delivery style has been developed during the past three years and for one module in 1996/97 we carried out a small research project investigating students pre- and post-module concepts of learning.

We found that at the start of the module most of the students had a passive transmission model of learning in which the lecturer was a key player. The post-module feedback was positive with students identifying the advantages of co-operation and discussion as important parts of the learning process.


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Maull W. and Berry J., 2000, An Investigation of Student Working Styles in a Mathematical Modelling Activity. Journal of Teaching Mathematics and Its Applications, 31 No 6, 899-917
Four groups of mathematics undergraduates were observed carrying out a mathematical modelling exercise of a familiar physical process (cooling of a cup of hot water). We found that students neither took time to reflect upon the physical process not to reflect on the appropriateness of the model they produced. They also appeared to be much more prone to take an empirical approach to modelling. We recommend that classroom instruction should promote this reflection, to encourage a theoretical approach, that data logging equipment should not be available at the outset and that students should be encouraged to discuss and explore the physical situation.

Berry J., Johnson P., Maull W. and Monaghan J., 1999, Routine Questions and Examination Performance. In: Ed: O Zaslavsky, Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education (PME23), 2, 105 – 112, 1999. Technion, Haifa, Israel
This study concerns student performance in pre-university examination questions. In general, do lower attaining students in mathematics examinations generally gain their marks on routine parts of questions? This is an important issue because routine questions could be awarded fewer marks if algebraic calculators are allowed in examinations. Students' scripts in a recent mathematics examination were examined in an attempt to evaluate this question. The results are not conclusive but indicate that a problem of this type does exist, though the nature and location of the problem is not as straightforward as expected.

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