Proceedings of the Day Conference held at the Institute of Education, London, December 1994
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The area of teachers as researchers is one which has been given quite a lot of attention, as has the relationship between teachers and researchers, which is not always a comfortable one. Partly as a result of spending a year working on a research project in which I took both roles, I am interested in exploring the interactions between the role of teacher and the role of researcher in a very personal way. My interest is in trying to look at my own actions and reactions within both roles, and seeing how one can inform the other. As my daughter attends the school in which the project is running, I now find it impossible to ignore the role of parent (and particularly that of parent-as-teacher) in this context. What follows is in the nature of an exploratory discussion, rather than any well formed theory or argument. Interspersed in this paper are a number of ‘fragments’: short pieces of writing (printed in italics) recording incidents, conversations, reflects which have informed my thinking on this topic, but which I have not yet worked on in detail.
Though experts perform algebraic manipulation using symbol-moving rules, they are also aware of underlying principles, which provide additional guidance and safeguard against error. This study examines these connections in some students at an intermediate stage. Twenty year-lO students in a boys’ private school in Melbourne were interviewed individually while they worked on algebraic tasks. The tasks included solving very simple linear equations and simplifying expressions. Informal terminology (e.g., “You move the 2 over there and put it on top”) was used successfully by some students, but for many others it was associated with making mistakes. Students often appeared to be guided by memory of actions they might carry out rather than by general principles. They showed difficulties in understanding the ways in which numbers can be used for checking algebraic work and the purposes of basic algebraic tasks such as simplifying and solving.
The study of ‘A’ level maths is full of “forms”. My work with A level students has convinced me that these forms are very important in shaping their thinking and problem-solving strategies. I will offer you accounts of two incidents which have occurred in the course of my teaching in the last year. In each case the validity of what I have to say rests with the reader through an appeal to their experience.
“One way of representing the present condition of our educational system is as follows: it is as if we are driving a multi million dollar sports car, screaming, ”faster, faster!” while peering fixedly in the rear view mirror. It is an awkward way to tell where we are much less to tell where we are going, and it has been sheer dumb luck that we have not smashed ourselves to bits – so far. We have paid almost exclusive attention to the car, equipping it with all sorts of fantastic gadgets and an engine which propels it at ever increasing speeds, but we seem to have forgotten where we wanted to go in it. Obviously we are in for a helluva jolt. The question is not whether but when.” (Postman and Weingarter 1969, p 12-13)
This paragraph is one of the earliest memories I have of reading in preparation for my own PGCE course. I feels that the metaphor holds for much of my experience since then. I seemed to rapidly forget my reasons for entering the profession, which where for me to do with personal political ideas of social justice, as the everyday life of the classroom took over. I use the paragraph as an opening to this paper as my present work aims to return to these commitments. I also use the paragraph as a metaphor for much of our educational life post National Curriculum.
The main aim of the study is to investigate the developing understanding of algebraic concepts of a group of low attaining pupils as they work within a Logo environment.
Speaking from the point of view of an art educator (in this instance) I see an expansion of attempts to link art and mathematics and am increasingly concerned with the answers to two questions: Is it Art? and Is it Mathematics?
This paper outlines the way in which the NCC multimedia package ‘W orId of Number’ was used as the focus for a group activity with a Year 9 mathematics class. The classroom research was carried out in a South Yorkshire comprehensive school during the Spring Term of 1994. The class was engaged in work which involved graphs of relationships and close attention was paid to relationships between distance, speed and time in a variety of contexts.
Barbara Jaworski and Clare Lee
The purpose of this project is to investigate the development of mathematics teaching which occurs when mathematics teachers undertake research or enquiry as part of their practice of teaching.
9 Using a Vygotskian theoretical perspective to facilitate prospective secondary mathematics teachers’ professional development
What follows is a study related to my attempts to create a Vygostkian-based learning environment aimed at promoting both academic and professional development of prospective secondary mathematics teachers. It took place within the context of a two semesters Mathematics Methods course which I was in charge of, at the Department of Pure Mathematics of the Science Faculty, Oporto University, Portugal.
In investigating the ways in which teachers assess pupils’ texts, eleven experienced teachers were asked to read and assess three piece of student’s coursework on tasks set by LEAG (LEAG, 1991). Six of the teachers read work on the ‘Inner Triangle’ task (investigating the relationship between the dimensions and the area of trapezia drawn on isometric paper) while the rest read work on the ‘Topples’ task (investigating the point at which piles of Cuisenaire rods starting with a small rod and adding successively larger rods will topple over). All of the children’s texts on both tasks contained diagrams of one sort or another. It is the ways in which teachers read these diagrams and the values that they placed on them that I intend to address in this paper.
The ‘mathematics mentor’ is the school teacher tutor for student teachers within school-based Initial Teacher Education (ITE). My anecdotal and recorded observations of mentor-student interaction indicated that discussing points of mathematics and mathematical pedagogy were rare, (whereas discussion of general issues, like classroom management, were frequent). Student teachers need to learn strategies for teaching mathematics in particular, as well as children in general. As the students are based in school, the mentors have a key role in developing this learning; what then, is the nature of the mentors’ knowledge and how might they express this knowledge?
If you look through a current primary Mathematics textbook you can see illustrations every where. Counting only the drawings, at least you can find one in each page and a half, all of different sizes, colours, styles. Furthermore, if we look at the role each illustration plays in the textbook lesson we can see that it varies from illustration to illustration. So, if we consider only the drawings or photographs we may think that the effort (economically and intellectually) the authors, designers and publishers put to the illustrations is considerable. So, what is the purpose of including so many illustrations? Why do they designate a considerable amount of money to include illustrations?
There is little doubt that different cultural traditions result in significant variations in artistic output. Whilst they may vary over time they also contain some lasting resonances. English folk song and choir technique differ from the German choral, Italian ‘bel canto’ and the French ‘impressionist’ traditions. Of course, for the western world there is some doubt as to how long this will survive the influence and pressure of television, with its ability to present the same images to everyone. I have very definite preferences in what I watch and like. They can of course be changed, and my tastes in time-wasting have certainly been adapted and redeveloped as I have grown older, but they remain largely a reflection of the social milieu in which I move. I belong now to a subculture of serious viewers, opera goers and ‘intellectuals’ who analyse and discuss theatre. That is not my original cultural setting of soap operas, quiz shows and tabloid newspapers.