Ted Graham

Can we Speak of Alternative Frameworks and Conceptual Change in Mechanics

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.

A hierarchical model of the development of student understanding of momentum

This paper describes the results of an investigation into student understanding of momentum including a model of the development of student understanding. This model is based on the results of a large scale survey which are analysed to form a set of hierarchies. The procedure used to form the model is described briefly and is followed by a detailed discussion of the model itself.

Using concept questions in teaching mechanics

It has for some time been recognized that many sixth form students have great difficulty assimilating the fundamental concepts in mechanics, instead developing their own alternative conceptions. This paper first summarizes the current state of sixth form students understanding of mechanics, as revealed by recent research, describing a framework into which students approaches to problems fit. It then moves on to describe how simple ‘concept problems’ can be used to challenge students alternative conceptions and improve understanding of mechanics. These problems require a qualitative approach that promotes student discussion and highlights the deficiencies of students alternative conceptions, leading to a need for the students to revise their original ideas.

Students’ intuitive understanding of gravity

Research has suggested that there are weaknesses in students understanding of gravity and that these persist even after students have completed courses in mechanics. This paper examines the responses given to two simple questions by sixth‐form mathematics students before they start a mechanics course. The results indicate that intuitively students use four main types of argument. The universal argument is used by students with a sound understanding of gravity, but who only form a small part of the sample. A fair number of students use mass dependent arguments, expecting heavier objects to fall more quickly than lighter ones. An earth dominated argument is used by some students who give correct responses in earth bound situations. The fourth weightlessness argument is used by students who have a weak understanding of gravity, and in particular expect all objects not on the earth to be weightless. The paper concludes that there is a need for teachers to examine and challenge their students’ intuitive ideas ...

Are ‘misconceptions’ or alternative frameworks of force and motion spontaneous or formed prior to instruction?

It has often been assumed that misconceptions of force and motion are part of an alternative framework and that conceptual change takes place when that framework is challenged and replaced with the Newtonian framework. There have also been variations of this theme, such as this structure is not coherent and conceptual change does not involve the replacement of concepts, conceptions or ideas but consists of the development of scientific ideas that can exist alongside ideas of the everyday. This article argues that misconceptions (or preconceptions, intuitive ideas, synthetic models, p-prims etc.) may not be formed until the learner considers force and motion within the learning situation and reports on a classroom observation (that is replicated with similar results) that suggest misconceptions arise, not because of prior experience, but spontaneously in the attempt at making sense of the terms of the discourse. The implications are that misconceptions may not be preformed, that research ought to consider the possible spontaneity in the students’ reasoning and then, if possible, attempt to discern any preformed elements or antecedents, and that we ought to reconsider what is meant by ‘conceptual change’. The classroom observation also suggests gravity as a particular stumbling-block for students. The implications for further research are discussed.

Using Computer Software in the Teaching of Mechanics

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.

Identifying stumbling blocks in the development of student understanding of moments of forces

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 suggests 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 lin...

MISCONCEPTIONS OF FORCE: SPONTANEOUS REASONING OR WELL-FORMED IDEAS PRIOR TO INSTRUCTION?

Throughout its forty year history, the conceptual change literature assumed student misconceptions of force are formed prior to instruction. We argue that it may well be the case that misconceptions are not formed until the student considers force and motion in a scientific context for the first time. This has obvious implications for research methods. We are in the early stages of developing a research method for investigating conceptual change in mechanics. To illustrate this method, we have taken examples from one-to-one Socratic tutoring. We conclude by outlining the next step of the research, which is to build a model that will enable the Socratic method to reveal the characteristics of misconceptions.

Developing an approach to the introduction of rigid body dynamics

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 the 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.

A hierarchical model of the development of student understanding of force

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 understanding 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 applications of Newtons laws.