Proceedings of the Day Conference held at the University of Birmingham, October 1995
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Richard Noss, Institute of Education, London
John Mason, Open University
Barbara Jaworski, University of Oxford
Critical responder: Steve Lerman, South Bank University
Chair: Laurinda Brown, University of Bristol
Richard Noss, John Mason and Barbara Jaworski were invited to address this issue in not more than fifteen minutes each with a brief to share their particular methodologies and give a sense of the range of problems which might be appropriate for the use of such methodologies. The discussion was then open for comments from the floor after which Steve Lerman gave a critical summary to close the session. What follows are the inputs from the panel in terms of what they chose to share by overhead transparency on the day and a post hoc reworked critical summary from Steve Lerman.
John Smeaton Community High School, Leeds
This paper examines the analysis of students’ understanding of algebraic expressions. Certain of the test items were written with the aim of allowing students to demonstrate a conceptual understanding of the use of a letter. They were also designed to allow students to show a conceptual understanding of an expression as a whole. These items have been piloted with 29 students and their responses are analysed. The extent to which conceptions can be ascertained from test items alone is discussed.
School of Education, University of Manchester
This paper reports the preliminary results of research into the nature of students’ intuitive models of motion of particles under the action of forces. Results from a small sample have indicated that a significant number of students have an intuitive model that is neither Newtonian or Aristotelian. This model is discontinuous: the nature of the motion changes as the force is increased. The data were collected by multichoice tests and by analysing verbal protocols, which were taken after the subject had sorted a number of cards depicting mass pulley systems into classes according to their motion.
Institute of Education, University of London
Recent developments in school mathematics involve school students in more extended writing than was the case in the past, but, although it is recognised that this is an area of difficulty for many students, little attention has been paid to how they might learn to produce more effective texts. Drawing on my research into the writing, reading and assessment of GCSE coursework texts, this paper considers issues related to the development of modes of writing likely to be judged to be appropriate, including the question of the role that may be played by explicit linguistic knowledge.
University of Sheffield
This paper gives an account of research aimed at elidting a group of year 6 children’s interpretations and representations of number. It raises questions concerning the usual school approaches to number and gives a briif summary of an alternative ‘operational’ approach adopted as a result of this study.
6 Gender effects in a small group mathematical problem solving environment of mature undergraduate students
University of Greenwich
In recent years the importance of mathematical investigations with the use of open ended problems as a means of developing mathematical processes has been an important factor in developing innovati ve undergraduate mathematical curricula. This study investigates the different perceptions of small groups of undergraduates undertaking such a programme of instruction and emphasizes that gender effects can impact on students undertaking such programmes, and should therefore be considered when implementing such a mathematical learning environment.
University of Bristol
At this meeting Liz Bills and Simon Goodchild, who are both nearing the end of work for PhDs, gave presentations relating to how their methodologies had developed over time. These inputs provoked a good discussion continuing the theme of the link between methodologies and methods in research. What follows are reports of their presentations.
University of Southampton
This report of a meeting of the geometry working grooup considers what it means to educate someone geometrically and what are useful contexts in which to consider geometry. An undergraduate unit on symmetry is described and this leads to the discussion of context. The relationship between geometry and algebra is briefly mentioned.
9 Geometrical Reasoning: a report on the working group at the ICMI Study Conference on “Perspectives on the Teaching of Geometry”
University of Southampton
The ICMI study conference on “Perspectives on the Teaching of Geometry for the 21st Century” took place recently in Italy. This paper reports on the discussion of one of the conference working groups which considered geometrical reasoning. Four main themes are covered: visual reasoning, geometrical reasoning in context, the meaning of proving in learning geometry, and assessing the range of reasoning ability in geometry. There was general agreement at the conference that more research is necessary in order to effectively address the wide range of issues that were discussed.
University of Sunderland
A succession of HMI/OFSTED reports over recent decades indicates that able children are often insufficiently challenged by the work that they are set. Why is this? Is it a problem of provision or a problem of identification or both? How discerning are we when it comes to recognising the mathematical characteristics of able children? The working group pursued a discussion and activity framework which was designed to explore these questions. Particular attention was given to problems of identification.