John Berry

Students using posters as a means of communication and assessment

Poster sessions are widely used as a medium for the communication of results by professionals at conferences and by students to their peers. The authors have introduced poster sessions into undergraduate mathematical modelling courses. This has given our students an interesting and challenging task and it has caused us to devise a scheme for the assessment of posters.This paper surveys the use of poster sessions with undergraduates, outlines the rationale for using posters with mathematics students, describes our experiences and proposes criteria to use in the assessment of student posters.

A questionnaire to elicit the mathematical concept images of engineering students

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.

Developing Student‐centred Learning in Mathematics Through Co‐operation, Reflection and Discussion

Abstract 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 3 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 the 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.

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.

Observing student working styles when using graphic calculators to solve mathematics problems

Some research studies, many of which used quantitative methods, have suggested that graphics calculators can be used to effectively enhance the learning of mathematics. More recently research studies have started to explore students’ styles of working as they solve problems with technology. This paper describes the use of a software application that records the keystrokes made by students as they use calculators, in order to enable researchers to gain better insights into students’ working styles. The recordings obtained from this software can be replayed to observe how students have actually used their calculator in tackling a problem. The paper describes three pilot studies from quite different contexts, in which the software reveals how the calculators have been used by the students. In all of these studies the software provides insights into the working that would have been very difficult to obtain without the record of the keystrokes provided by the software.

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.

Student connections of linear algebra concepts: an analysis of concept maps

This article examines the connections of linear algebra concepts in a first course at the undergraduate level. The theoretical underpinnings of this study are grounded in the constructivist perspective (including social constructivism), Vernauds theory of conceptual fields and Pirie and Kierens model for the growth of mathematical understanding. In addition to the existing techniques for analysing concept maps, two new techniques are developed for analysing qualitative data based on student-constructed concept maps: (1) temporal clumping of concepts and (2) the use of adjacency matrices of an undirected graph representation of the concept map. Findings suggest that students may find it more difficult to make connections between concepts like eigenvalues and eigenvectors and concepts from other parts of the conceptual field such as basis and dimension. In fact, eigenvalues and eigenvectors seemed to be the most disconnected concepts within all of the students’ concept maps. In addition, the relationships between link types and certain clumps are suggested as well as directions for future study and curriculum design.