Proceedings of the Day Conference held at the University of Birmingham, March 1995
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University of Exeter
In the current post-Cockcroft era the learner of school mathematics engages with proof in an informal way. Through personal investigations and problem solving the learner is introduced to process skills such as conjecturing, generalising, and justifying. Recent research (Cae and Ruthven, 1994) reports that the proof-practices of advanced learners are predominantly empirical. These practices are nevertheless valuable: such proofs convince their [roducers and, under certain circumstances, empirical proof-practices may be precursors to deductive ones.
Centre for Mathematics Education, Open University
I describe my understanding of a teaching technique which I have labelled as “generic example” and the responses made to this description by a group of teachers. I consider some similarities and differences between my examples of the use of the technique and the teachers ‘examples.
King Alfred’s College (Winchester), Institute of Education, London
This paper describes a single experiment from early stages of work in progress. It examines one student’s work in depth following the analysis of a class set of solutions of first year teacher trainees and mathematics students for a well-known investigation.
School of Education, University of Southampton
This paper is concerned with planning as an activity at the core of mathematics educators’ work. Through analyses of reflective writings and course tasks, the dimensions of planning are considered in relation to discrete groups of mathematics teachers: trainees, mentors and MA students. The paper explores links between theory about and practice of planning and how we can understand the planning activities of practising teachers.
5 Gender, Courses and Curricula effects on Students’ Attitudes to Mathematical Modelling in 16-19 Mathematics Programmes
J. I. Kyeleve and J. S. Williams
School of Education, University of Manchester, Manchester
In 1993, Mathematical modelling was codified as a compulsory core component of all U.K “A’ level mathematics curricula. This study examines the attitudes (enjoyability, anxiety and confidence) of 269 students to mathematical modelling in 16-19 mathematics programmes. The students’ attitudes were found to be multi¬dimensional and varied significantly across the sub-scales. Gender and curricular factors and the effect of course combinations taken by the students showed mixed results.
6 Promoting Reflective Practice Amongst Mathematics Novice Teachers: Are the Perceived Benefits Related to Novices’ Learning Styles?
School of Education, University of Bath
Whilst the goal of developing critical reflective practitioners might be appropriate for all novice teachers Kolb’s work suggests that learning should be matched to learning style and this raises a question of whether the methods used, largely reflective writing, are appropriate for all novice teachers regardless of their learning style. Determining the extent to which novices’ learning styles affect the irifluence of tools used to promote reflective practice is neither simple to investigate nor easy to recognise. Two factors which merit consideration are the extent to which discussion of the ‘why’ and the ‘how’ of reflective practice are given adequate attention across the course components and, secondly, the extent to which the potential of reflective writing is not realised because the contextsfor the tasks and assignments do not connect meaningfully with novice teachers’ personal theories and experience.
University of Sheffield
Teachers have always gone beyond the textbook or scheme to design worksheets or other materials geared to the-needs of their children. However, until recently, the parallel activity in a computer environment was not possible. This paper describes some research with year 5 children (ages 9 to 10) in which the medium of Boxer ¬was used to introduce itself. Altogether, eight case-study children representing the full ability range were closely observed using three microworlds known as ‘First-‘, ‘Second-‘ and ‘Third-Boxer’. However, the microworlds were also being used simultaneously by the remainder of the year 5 class in so far as time, hardware and other classroom limitations allowed. The feedback from these two sets of users formed an integral component of the iterative design process.
Mathematics Education Research Centre, University Of Oxford
This presentation addresses one teacher’s method of teaching linear equations to a low ability group of pupils. It is a method that has them solving, with understanding, the most general forms of equations such as 3x-7=5x-29. The teacher treats the equations as ‘mathematics’, with no recourse to images from pseudo-real life, and he confronts the problems inherent in coming to a fuller understanding of the equals sign, by presenting the equation as a static entity rather than a dynamic instruction to perform some arithmetical action. Common methods of teaching the topic are summarised and the author claims that the notion of a “didactic cut”, identified by some researchers, is simply an artefact of certain teaching approaches. Its effects are not seen in this classroom.
This reports describes part of a pilot study investigating language use in the mathematics classroom. It focuses on the language used in a peer tutoring situation. I shall describe the theoretical background tothe study and illustrate the outcomes with a description and discussion of one incident.
South Bank University
This paper discusses the nature of the mathematical activity which may be expected to accompany the developing understanding of pattern – in particular an understanding that admits of abstraction of structure and thus classification, in this case, of frieze patterns. Some activities involving the use of COOri Geometre to explore pattern are described. These activities and a review of some of the pattern literature are used as a basis for discussion of the process of objectification which is held to characterise understanding in this context. The pedagogical implications of acknowledgment of a process/object distinction are illustrated through consideration of some work done by undergraduate students.
University of Bristol, School of Education
This group met for the fIrst time at Birmingham with a focus of introducing ourselves and the work we were currently undertaking to raise issues for consideration in future sessions. It seemed important to be aware that the membership of the group will not be stable. Those present may not be able to attend every BSRLM meeting and others may be interested in particular concerns of the group. Consequently, the planning for future meetings will take place at the end of each session and, presumably, if there is no common concern emerging, the life of the group will have ended.