What is Normal Anyway? Therapy for Epistemological Anxiety

This paper presents two case studies of learners attempting to make sense of the concept of normal distribution — in particular, why physical phenomena such as height fall into normal distributions. The notion of epistemological anxiety is advanced as being the source of the difficulties learners have in making sense of normal distributions. The framework of Connected Mathematics is used to analyze the learners' coming to understanding of normal distributions and as a source of therapeutic intervention for the epistemological anxiety. As both a symbolizing medium and an aid to analysis, one learner is provided with an object-based parallel modeling language (OBPML) with which the learner can formulate computational hypotheses about the local probability rules that lead to the emergence of a global distribution. Through the investigation, supported by the OBPML, the learner makes connections between the micro-rules of probability and the resultant (macro-) statistical distributions. Conclusions are then drawn about the features of a Connected Mathematics learning environment that enable confrontation with epistemological anxiety and the features of modeling languages that enable learners to conduct a successful probability investigation.This revised version was published online in September 2005 with corrections to the Cover Date.