ABSTRACT:
This project is an investigation of 12-16 year old pupils’ understanding of statistics and probability in the Kingdom of Bahrain.

Pupils were given seventeen items in problem solving format concerning several basic areas of statistics and probability, namely: uniform distribution, normal distribution, randomness, central measurements, sampling variation, sample distribution, two way tables, interpretation of graphical data, comparing probabilities, chance, correlation, correlation and causation. A reformulated Piagetian model was used to design tests involving these ideas. For each test item, pupils’ ways of reaching a solution were recorded in detailed individual protocols and their reasoning was matched directly or inferred against the Piagetian criteria and protocols described by Piaget (1958, 1975). The use of Piagetian model allowed test construction and scoring to be based on well established objective criteria rather than on a subjective perception of the logical structure of statistics and probability concepts.

A stratified random sample was obtained from middle and secondary schools. 100 pupils were interviewed individually during 80 minute periods on ordinary school days. Responses were grouped and categories were formed on the basis of these scores. The groups of answers were scrutinized in order to identify the differences between them in statistical and probability terms and to expose the distinctive features of comprehension of each concept. Three general score categories of concepts were identified in order to reveal understanding of statistics and probability.

Factor Analysis was carried out in order to determine internal consistency and to explore the structure of the relationships between the 17 items. Surprisingly the results highlighted that there are particular mathematical requirements for groups of task. These are more generalized statistical requirements permeating a number of tasks which also contribute to success in completing the cluster of tasks. These are relative quantity, descriptive representational graphing and the relationship between the incidence of abnormal and normal events.

The influence of a number of variables on these categories was also investigated. It was found that understanding was influenced by mathematical ability but not by gender and age.

The research also demonstrated that pupils revealed a positive attitude towards statistics in general; however the study did not demonstrate strong relationship between this attitude and their performance in the items.