Everyone is Special
“There is no such thing as the average child, don’t presume to cater for it.”
Key Stage suitability • Explanation
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- KS1
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This book offers a wide range of activities from a popular session at Conference 2002 by Mike Ollerton.
“There is no such thing as the average child, don’t presume to cater for it.” - Jan Mark (TES 28.7.95)
My intention in documenting the ideas used in the workshop is for readers to find something of value for use in mathematics classrooms. This publication is neither a scheme nor a systematic collection of ideas. I offer no ‘levels’ nor suggest how any ideas might map against National Curriculum statements or to the Mathematics Strategy; such decisions underpin teachers’ professional judgements.
Ideas can be adapted for use across all abilities in the 7-16 age group.
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ISBN 1 898611 19 X
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A driving force for much of the work I did as a mathematics teacher and continue to do as an initial teacher educator and through continuing professional development, is teaching mathematics in mixed-ability groups. This, however, is not the flavour of the month, nor has been for several decades. Setting by notions of measured ‘ability’ is the most common form of grouping in mathematics classrooms, particularly in secondary schools and more so since the introduction of national testing and league tables. Although I often feel to be somewhat at odds with the current orthodoxy of teaching in setted groups, it was my intention, through the workshop that inspired this book, to open up discussion that it is not only feasible to teach in mixed-ability groups but it is beneficial to students’ mathematical development. There are also issues of social justice and equity however, as it is popular to say nowadays “I won’t go there”.
One of the more challenging aspects of planning to run sessions at an ATM conference is recognising that there will be some delegates who will have a vast amount of teaching experience and that anything I have to offer, based upon my teaching is likely to be ‘old hat’.
It is likely also that there will be other delegates such as trainee or new teachers who will not have had lengthy classroom experience; all in all a highly mixed-experience group. It is therefore with a mix of anticipation and trepidation that I seek to use ideas for the classroom that will cater for this mix of people and offer everyone something to work on, something to be challenged by.
With this in mind I decided to plan a double session Maths is Special for the 2002 conference at Edge Hill College, Ormskirk along ‘traditional’ ATM workshop lines. This, in my understanding, entailed setting out the room with a wide range of problems and ideas, each one explained on separate pieces of cards. Next to each idea I left some equipment which I thought might prove useful in trying to work on the problem. From the outset I made no pretence that the ideas were new or of my own invention, indeed, several can be found by leafing through the pages of ATM publications Points of Departure (volumes 1 to 4). What was important, however, was that at some point in my teaching I had used every idea, very many times with people, some as old as 7 and a half and others as young as 90!
The session was described as follows in the conference handbook:
Everyone is Special
These sessions will be about working in mathematics classrooms where students have not been categorised, or ‘set’ by notions of ability’. The intention is to consider a variety of accessible-to-all starting points and possible extension tasks that could be offered to different students according to how they respond to a starter task. Through exploration of yaj-iozts ideas tive can discuss the possibilities, challenges and witi’ards of teaching in non-setted mathematics groups.
A driving force for much of the work I did as a mathematics teacher and continue to do as an initial teacher educator and through continuing professional development, is teaching mathematics in mixed-ability groups. This, however, is not the flavour of the month, nor has been for several decades. Setting by notions of measured ‘ability’ is the most common form of grouping in mathematics classrooms, particularly in secondary schools and more so since the introduction of national testing and league tables. Although I often feel to be somewhat at odds with the current orthodoxy of teaching in setted groups, it was my intention, through this workshop, to open up discussion that it is not only feasible to teach in mixed-ability groups but it is beneficial to students’ mathematical development. There are also issues of social justice and equity however, as it is popular to say nowadays “I won’t go there”.
At the heart of the workshop was the issue of access, where problems could be worked on by students in all-ability groups, thus negating the need to separate them by some notion of ability.
The approach of finding accessible starting points with planned extensions tasks for more confident mathematicians is, I believe, underpinned by the following quote: “Mathematical content needs to be differentiated to match the abilities of the pupils, but according to the principle quoted from the Cockcroft report, this is achieved at each stage by extensions rather than deletions.” (p 26) DES (1985). Mathematics from 5 to 16. HMI Series Curriculum Matters 3 London: HMSO.
The workshop therefore was intended to provide problem-solving situations and rich starting points that are accessible and could be developed to different depths with different students.
Each idea/problem in this publication is intended to fit this kind of framework. My intention in documenting the ideas used in the workshop is for readers to find something of value for use in mathematics classrooms. This publication is neither a scheme nor a systematic collection of ideas. I offer no ‘levels’ nor suggest how any ideas might map against National Curriculum statements or to the Mathematics Strategy; such decisions underpin teachers’ professional judgements.
At the end of the workshop several delegates asked if they could access the ideas written on the cards. This publication is an attempt to keep a promise I made.
Mike Ollerton
Contents
Using Geo-Strips
Mixed Trains (Cuisenaire Rods)
Partitions (another problem with Cuisenaire)
Centres of triangles
Four-in-a-square
1,2,3,...
The 1 to 5 problem
Pentagon Triangles
Fraction to decimal grid
Tweaking Pascal
Averaging
Cylinders
Folding a strip of paper
Divideandadddivideandadd...
Fractions and decimals
Connect 4
IRATS
Co-ordinates and transformations
Diagonals
30°, 60°, 90° triangular grid
Flipping triangles
Wholesome triangles
Setting up and solving simultaneous equations 8-dot circles
