Mathematics Teaching 186 - March 2004
Mathematics Teaching is the journal of the Association of Teachers of Mathematics. It is a professional journal sent to all members of the Association. It is not a refereed journal. Submissions are reviewed by the editorial team. Many articles have additional information or associated files placed on the journal website.
Ginsburg suggests that, although mathematics is big, children's minds are bigger. He argues that young children posses greater competence and interest in mathematics than we ordinarily recognise and we should aim to develop a curriculum for them in which they are challenged to understand big mathematical ideas and have opportunities to achieve the fulfilment and enjoyment of their intellectual interests.
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If you are a teacher in a challenging environment you may well find that you become the focus of well-meaning support from various agencies in order to raise the attainment of your pupils. You start to feel that there is an assumption that your teaching is somehow deficient; it's your fault that the children are not reaching the national average and teachers in higher attaining schools are somehow better.
Photographs from the book Crop Circles – The Hidden Form by Nick Kollerstrom.
As a teacher I need to ask myself whether the representations I am giving children are within their scope of understanding and ensure that the children are allowed enough time to reflect and absorb or internalise the image for themselves. As I have reflected on these experiences, this is the question I have constantly returned to, 'What does it say to you?' I must continually ask that question of myself as I approach new representations, and must ask it of the children I am working with. I must also encourage children to ask it of each other.
Sarah is a Y7 pupil in the lower of two broad sets. Before taking over the class, I observed them working through practice exercises on converting units of measure. These involved multiplying and dividing by 10, 100 and 1000. Sarah's work was beautifully laid out, with over twenty questions completed each lesson and almost all answers correct. For two lessons she worked steadily and seemed to enjoy completing them. In the third lesson she began to chat about unrelated things and completed five questions. As the questions were of the same level and style it seems possible that she had become bored...
As a consultant I am never quite sure what I will have to face when I arrive in the classroom. I have been told the Y7 class I am to work with is full range mixed ability and it is a wet Friday afternoon, that situation beloved of all teachers. When teaching I try to provide images and activities that will help with the understanding of the concept being taught. I have thought long about how I am going to link the teaching of fractions into their existing experiences and have chosen to use the counting stick as an image that is both familiar and from past experience, useful.
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The attainment target 'using and applying' has become a catchall phrase for anything to do with thinking in mathematics classrooms. Whether you associate it with problem solving, investigations, logical reasoning or standard heuristics, teachers are required to integrate Ma 1 into their 'everyday' practice.
I investigated two particular teaching styles: that recommended by the numeracy strategy framework ('framework teaching') and what has become known as 'progressive' teaching. It is the findings of this study that I would like to share with you. Whilst this research is limited in its scope, it seems that progressive teaching methods do have considerable potential. It requires substantial planning and care must be taken to ensure that all pupils, particularly girls, are fully involved.
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Recently I was looking for some materials to support a group of trainee teachers in developing mental calculation methods at their own level...
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Geoff found it fascinating that Fermat was, 'well-known for offering mathematical results without stating their proofs. He published nothing, so his mathematical ideas are known only through his letters, notes written in the margins of his mathematical books and his private papers'. Clearly finding the results was of greater importance to him than proving them.
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As a result of our recent collaboration in preparing a new ATM publication on polyhedra, we thought the notion of 'prime' polyhedra was an interesting one for the classroom. The correct technical term for this notion is 'elementary' but as it has similarities with the concept of prime numbers; 'prime' may be a more helpful description to start with. By considering only those convex polyhedra whose faces are regular polygons, we can arrive at an interesting set of families.
It was almost exactly a year ago when I last contributed to Reflections and attempted to make MT readers more aware of the educational debate that was raging in the north of Ireland. What to do about the eleven plus was the question, which resulted in much debate, consultation, the setting up of a review body and eventually a working party to consider all of the results. Good old fashioned political stuff, really.
News and things...
Invariance is an important idea in mathematics. When I explore a new mathematical problem I pay attention to what stays the same and what changes. And if too much is changing the problem is more intractable. As in mathematics, so in life. As I write this we are preparing to move from Leicestershire to Shropshire. In addition, two new grandchildren have been born in the last couple of weeks and my son's baby daughter had to spend several days in hospital because she was not feeding properly. And my step-daughter will die of cancer in the next day or two...
Crop Circles – The Hidden Form; Teaching and Learning Algebra; Decoding Mathematics; Mathematics Teaching Practice: A Guide for University and College Lecturers; Engineering Mathematics through Applications; Classroom Activities from the Numeracy Posters – An A4 Photocopiable Masters Pack; Times Tables Tactics Investigating multiplication facts; Making Sense of Statistics: A non-mathematical approach.