An investigation into the statistical understanding of 12-18 year olds.

The aim of this project was to develop a model for the structure of the development of statistical thinking in students of secondary school age, i.e. 12-18. Previous research has tended to concentrate on individual problems and no large scale research has been carried out in this area. The aim was therefore to produce a model which encompassed all areas of Statistics and showed the building up of concepts. The basis of the model was a hierarchical structure based on Gagne's Cumulative Learning Theory, with due allowances made for subsequent criticisms of the rigidity of such a model. Models were proposed in five areas considered to involve the main principles of elementary statistics. Superimposed on to these maps of conceptual development was a 3-stage structure corresponding to classical Piagetian stages. Prior to testing a detailed survey was made of available techniques for examining the validity of such models. In particular the Inclusion Analysis technique devised by Clarke & White was carefully examined noting cases where it was inappropiate or invalid.After some initial testing and expert analysis the initial models were modified. The strength of the restructured models was examined by presenting detailed written tests to over 200 students in the age range under investigation. Using Clarke & White Inclusion Tests the strength of links between the concepts was tested and some justification given to the ordering of concepts in the hierarchy and adjustments made where necessary. The validity of grouping skills into 3 stages was tested and an attempt made to correspond these to age using correlation techniques.Although, from the data collected the full detail of the model could not be entirely supported, there was evidence to justify the main framework and certain key linkages to produce a final model. This enabled a detailed analysis of the National Curriculum and its United States counterpart to take place in terms of age-related content and structure. Suggestions were also presented to writers and curriculum designers in the light of research findings.