A case study of one teacher's professional development journey
In 2007 Caroline Ainsworth, became interested in the use of Cuisenaire rods as a tool for teaching and learning mathematics. This led her to the work of Caleb Gattegno and Madeleine Goutard which she began to read extensively and which informed a series of investigations into her own teaching, her children’s learning and the nature of mathematics.
As such this is a rich and complex example of professional development which explores the interrelation between theory and practice.
This unique and innovative collection of materials comprises the following elements:
an article written by Caroline about her work and ideas
a filmed discussion between Pete Griffin (NCETM SW regional coordinator) and Caroline
samples of Caroline’s children’s mathematical writing
a collection of videos filmed by Caroline of children in her school working on mathematics.
This resource is not intended to serve as an instruction manual. It is simply a story of one teacher’s professional development which we hope will inspire and stimulate you to engage in your own research and professional development.
Although a suggested order has been offered these materials are flexible and can be used in a variety of ways and in (almost) any order. In the end the usefulness of these materials will rest in the extent to which they prompt your own investigations.
(While watching some of the video clips and working with some of the related written material you might find it useful to have a set of Cuisenaire rods to hand).
Foreword by Caroline Ainsworth:
My aim in producing these materials has been to try to capture my research process in all its complexity, rather than present polished findings. In order to do this effectively I felt that I needed to focus on something specific that I was trying to find out more about - something which seems to be important, but I don't yet fully understand.
I have settled on the teaching of fractions, with which I have already had some success, enough to become aware of just how much more the children are capable of. Therefore, the materials which you will find here (including video clips of children of various ages in my school working on mathematics) act as a diary indicating a cycle of:
reading the theory and reflecting:
translating my understanding into teaching;
studying the children’s responses;
returning to the theory
and so on.
Having been working in this way now for over year, this will be a snapshot of the process rather than showing the whole of it from the beginning. This will make it harder for you, the viewer, but that might be a good thing!
Rather than aiming to show a finished product or conclusion, it is this research cycle which I am trying to capture.
My research is in pursuit of understanding and replicating the fluent, complex expressions Goutard's children wrote at such a young age (see below) which included astonishing mastery of fractions.
(Taken from M. Goutard. "Mathematics and Children", Educational Explorers Company, Reading, 1964.)
Already, the work my children are producing in their ‘free writing’ shows similarities with Goutard’s children’s work, (mine at a later age – mainly due to my lack of ambition with my teaching!) but I need now to analyse their writing more systematically, looking for specific features, in order to understand it better.