Conceptual Understanding Pre 2001

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

Graham E. and Rowlands S., 2000, Using computer software in the teaching of mechanics. International Journal of Mathematics Education in Science and Technology, Vol. 31 No 4, pp 479-493
The paper looks at ways of using computer software in the teaching of mechanics. The various reasons for using software are discussed to justify the use of software. A number of examples are then considered to show how different types of software can be used. Examples shown are taken from very specific types of software, more general simulation software and mathematical software. The paper discusses using software to explore mechanics, to challenge ‘misconceptions’, to make links between mathematical representations and motion and to solve non-standard problems. The paper also stresses the need for structured approaches to the use of software.

Rowlands S., Graham E. and Berry J., 1999, Can we speak of alternative frameworks and conceptual change in mechanics? Science and Education, 8, pp 241 – 271
This paper discusses the various conflicting trends in mechanics education that have appeared over the past two decades, and proposes the theory of schemata as a means to resolve the conflict that exists within the literature. The conflict has two causes: the prevailing relativism that exists within science education, and the mistaken view that student alternative ideas are concepts that are well defined. We argue that student alternative ideas can be best understood in terms of schema theory, and that schema theory can offer support to the Vygotskian idea of the teacher facilitating the construction of the Newtonian system within the students zone of proximal development. Within the context of schema theory we propose the category of idealised abstraction that has as its starting point the logical structure of Newtonian mechanics rather than the cognitive state of uninstructed students.

Rowlands S., Graham E. and Berry J., 1998, Identifying Stumbling blocks in the Development of Student Understanding of Moments of Forces International Journal of Mathematics Education in Science and Technology Vol. 29 No 4, pp 511-531
Student intuitive ideas in mechanics, especially concerning the relationship between force and motion, have been the subject of much research. Many students find aspects of the topic of moments of forces to be stumbling blocks, yet there has been little or no research in this area. This paper reports on a small-scale investigation of student understanding of moments of forces to provide some indication as to the nature of intuitive ideas in this area, and to provide some suggestions as to the appropriate teaching strategy. The results of the investigation suggest three stumbling blocks in the conceptual understanding of moments of forces. The first stumbling block seems to contain problems where the forces applied are still acting vertically, but the points of application of the forces are not at the same horizontal level. The second stumbling block seems to either contain problems where the forces applied are vertical but there is no obvious sense of symmetry, or problems that represent a conceptual link between moments and rotation. The third stumbling block contains questions whereby the student has to recognise the line of action of the appropriate force and take note of the point of application of the force.

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Graham E and Peek A. 1997, Developing an approach to the introduction of rigid body dynamics, International Journal of Mathematics Education in Science and Technology, 28, 3, 373-380
This paper first explores student understanding of some aspects of rigid body motion and in particular tries to expose intuitive ways of thinking. It illustrates that developing an understanding of rigid body motion is not easy, and that misconceptions that students have with particle mechanics can be carried forward to cause further problems with rigid body motion. The paper goes on to describe some introductory activities that the authors believe would help students approaching rigid body dynamics for the first time.

Graham E. and Berry J., 1997, A hierarchical model of the development of student understanding of force, International Journal of Mathematics Education in Science and Technology, Vol. 28 No. 6, pp 839-853
This paper describes how the authors have applied an approach that they had previously used with momentum to form a set of hierarchies that model students’ development of the concept of force. The approach used is set out and the results obtained described. There is a clear link between the development of understand and the force in the direction of motion’ misconception or preconception. The model shows that as students move from a view dominated by this misconception or preconception to a Newtonian view, they pass through a number of intermediate stages. It also shows how many students have not reached the higher levels of understanding, before they go on to consider application of Newton’s laws.

Maull W. and Berry J., 2000, A Questionnaire to elicit the mathematical concept images of engineering students. International Journal of Mathematics Education in Science and Technology, Vol. 31 No 6, pp 899-917
As part of a study into the mathematical understanding of engineering students, a questionnaire has been developed which seeks to elicit from students their concept images attached to key mathematical concepts. The questionnaire seeks to address both the level of understanding of the students and the mode in which the students hold the concept image. The instrument has been used on over 200 students in the schools of mathematics and engineering at the University of Plymouth, and while the details may not be exactly suited to other groups, it is suggested that the method may be helpful to other researchers in the field. Initial results suggest that engineering and mathematics students do have different concept images, and in particular that engineering students gradually adopt mathematical ideas into their engineering knowledge in a way which makes sense of them.

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Berry J., 2000, Developing the mathematical feel; the 2000 Presidential Address of The Mathematical Association. The Mathematical Gazette, Vol. 84 No 501, pp 386-404
I came to the Mathematical Association through our local Branch and being involved in the Plymouth Annual Conference. After three years as Chair of Branches Committee I thought that it was time to settle back to the lazy golfing life of the SouthWest! Thus it came as a surprise and an honour to be invited to be President of our Association. I believe that one of the important features of the Mathematical Association is the Branch structure and I am saddened to see the decline in active Branches (including the West Devon and Cornwall Branch). Thus one of my wishes as your President was to visit as many Branches as possible to support and thank the active members who keep their Branch alive. Now I realise the reality of the travelling salesman problem and the challenge of travelling from Plymouth to the far flung corners of the UK (and Ireland) by public transport. But it has been possible and I have enjoyed visits to Dublin, Belfast, Exeter, Liverpool, Cheltenham, Leeds, Cardiff, London, Norwich, Sheffield and Hull as well resurrecting our local Branch in the Southwest. I had the pleasure of visiting Glasgow two years ago and I look forward to Newcastle in May. With the travelling salesman problem in mind I have chosen mathematical modelling as a theme to run through the talk. One of my aims is to illustrate some of the mathematics that I enjoy and to suggest that one of the important, and often neglected, aspects of mathematics is its application to real world problems. Not far away though is my belief in the power of technology to develop mathematical understanding and as a tool in the problem solving process. The twin themes of modelling and the appropriate use technology provide the main aim of the talk, which is to discuss the importance of our students developing a feel for mathematics. By feel I mean that sort of inside gut sense of understanding that we have as mathematicians.

Townend M. S. and Berry J., 1999, Experiences and Observations on the Introduction of Concept Questions into a Mechanics Module. J Teaching Mathematics & its Applications, Vol. 18 No 1, pp 20 - 29
In this paper we reflect on the introduction of concept questions into examination papers in mechanics. The research shows that student attainment on the concept type questions compares favourably with their performance on more traditional questions.

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