Teaching, Learning and Mathematics: Challenging Beliefs
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Loose leaf sheets wrapped and ready to slot into a ring binder.
This is the third collection of articles from the journals of ATM to be published in the successful Teaching, Learning and Mathematics series. The articles will challenge beliefs you hold about mathematics and help you think through your views of what makes for effective teaching and learning.
Challenging Beliefs in Mathematics
Teaching trainees come with beliefs about what constitutes effective mathematics teaching. We present a series of articles designed to challenge existing views.
Working in the Classroom
Stories about classroom experiences - ranging from exploring Vedic squares and working with Logo in a primary classroom to working personally with aspects of number theory.
Using Information Technology
We focus attention on issues related to the use of Information Technology in schools.
International Comparisons
The various international surveys which have been undertaken over the last few years are forcing us as mathematics educators to consider and to reflect practice on practices from within our own culture.
ISBN 1 898611 03 3
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Challenging Beliefs in Mathematics
Teaching Trainees come into teacher training with beliefs about what constitutes effective mathematics teaching. In this section we present a series of articles designed to raise awareness and challenge existing views. We invite trainees and mentors to engage in a re-examination of the fundamental issues discussed.
Jack Price’s remarks to the National Council of Teachers of Mathematics offers a clear message of entitlement and asks teachers to take up the challenge of ‘building bridges of mathematical understanding for all children’. This theme of inclusivity rather than elitism is fundamental to the transition that needs to be made by many successful mathematicians who wish to become successful mathematics teachers. Tony Cotton asks us to examine our view of leaming together with our personal view of justice to seek a way of addressing a series of dilemmas which face teachers in the quest for a curriculum based on the principle of equality. Barbara Jaworski acknowledges the movement towards regarding the teacher as a researcher, able to reflect critically on events in the classroom. In asking teachers to engage with analysis, she encourages intellectual honesty through an ‘overt spirit of enquiry and critique’.
Cate Payne, Val Bates and Will Turner were all PGCE trainees when they wrote their article describing how they set themselves the aim of overcoming other PGCE students' fear of mathematics. In describing how they approached this target they engage with the principles of good practice in relation to teaching mathematics in school. David Wells and Gill Hatch debate the nature of the ‘investigations movement. David suggests that the original ATM goal of ‘pupils doing research type activity at their own level has failed’, and he questions the use of ‘investigations’ over recent years. Gill offers a more positive view of the changes which have occurred and describes how limited over-structured `investigations’ can be better replaced by ‘investigative work related to the content of the curriculum’. This debate fuels the challenge to re-examine our views of the nature of mathematics.
If only teaching were solely a matter of giving clear explanations to a class! Tony Brown emphasises that this apparently simple task is fraught with difficulty. He describes activities which involved the giving and receiving of verbal instructions and the differing responses of the receivers. How do learners think they learn mathematics? Alan Bell describes two class activities devised to promote reflection and awareness of learning. How do we encourage teachers to reflect upon their teaching ? Melissa Rodd offers three themes or ‘tensions’ that can structure discussion about teaching mathematics in such a way as to focus on the mathematics in mathematics teaching rather than generic concerns. Jenny Taylor reminds us all that as class teachers we need to be sensitive to children’s anxieties and to try to ensure that the atmosphere in which children learn is one of encouragement. In reflecting upon teaching mathematics such an aim is fundamental.
Working in the Classroom
Inevitably this section contains a pot-pourri of stories which teachers have told about their classroom experiences - ranging from the primary classroom through to Higher Education. The stories told range from exploring Vedic squares and working with Logo in a primary classroom to working personally with aspects of number theory. In her story, Nicola Woolf talks about how her 20 day WEE course enabled her to work on her own mathematics and thereby help her to develop the mathematics that she was able to introduce in her classroom. Shapes is the theme of David Newcombe’s article which shares ways of exploring shapes using matchsticks. We then move to the secondary sector and explore with Bernard Murphy a number based -lesson which he worked on with a year 7 class. It provides an imaginative way of exploring standard form. The next two articles by Basil Reid and Pat Stafford show how assessment can become an integral part of a lesson and how appropriate activities help us to find out what pupils know. The final article takes us back to a personal mathematics experience where Barbara Wolstenholme shares her experience of working on some Number Theory. All the stories encourage the reader to think about aspects of the learning of mathematics and to consider how teachers facilitate good learning opportunities for the pupils.
Using Information Technology
The use of Information Technology in schools is something which continues to produce much thought and discussion. The articles in this section help to focus attention on issues related to this aspect of learning. The areas covered by this set of articles are: Dynamic Geometry, Using the Graphic Calculator, and Spreadsheets. The first two articles share ideas about how to get started in an environment such as Cabri, Geometer Sketchpad or Geometry Inventor and then how to use the environment to explore Rangoli Patterns. In the next article Henryk Kakol from Poland shows how the graphic calculator can provide a different way of approaching what is traditionally called “hard maths&rdsquo;. The emphasis is on the power of visualising. The final two articles show how a spreadsheet can be used to explore aspects of ‘A’ level mathematics - Calculus and Numerical Analysis. Again the power of visualising approaches to solving problems is important.
International Comparisons
The last section invites the reader to think more globally about mathematics education, by focusing on experiences from other countries. The various international surveys which have been undertaken over the last few years are forcing us as mathematics educators to consider practice in other countries and to reflect on those practices from within our own culture. Sue Hams gives us a flavour of some of the questions that were used in the TIMMS study and which has led to some questioning of our practice in England. Tony Harries and Paul Andrews focus on practice in Hungarian schools - one on primary and one on secondary. In both cases the reader is encouraged to ask searching questions about his/her own practice and to consider some of the principles on which practice is based in the countries concerned. From Hungary we move to Russia to share Anne Watson’s experiences in St Petersburg and to be challenged by her observations. Finally we move to Japan and reflect with Geoffrey Howson on a number of episodes from his visit there.These are a challenging set of articles which help the reader to move from a somewhat parochial position to one in which she/he can share in and reflect on experiences of other professionals in other cultures.
