"PRINCIPLES OF LEARNING PROBABILITY AND STATISTICS"
ICOTS 2, 1986: Dr. David Green PRINCIPLES OF LEARNING PROBABILITY A N D STATISTICS Dr. David Green Loughborough University U. K. Our f i r s t session began with Ramesh Kapadia exploring t h e nature, philos- ophy, and pedagogy of probability which provided us w i t h a theoretical framework f o r our whole program. Any r i s k of t h i s session becoming dominated by abstractions was quickly dispelled as Hans Schupp spoke about teaching stochastics t o the middle years (grades 5-10), which is where t h e seeds must be sown. The f i r s t session concluded with Joan Garfield and Andrew Ahlgren reporting i n an entertaining and illuminating way on t h e i r review of research and their efforts t o undertake a major r e - search programme with college students. It is hoped t h a t t h e i r f u n d i n g requirements can be met! The second session began with Thomas Piazza perhaps upsetting t h e more conservative b y advocating the teaching of statistics t h r o u g h data analysis (on-the-job learning one could call i t ) . The iron curtain was rolled back as we welcomed Jordan Stoyanov from Bulgaria. He has over the past 15 years amassed a collection of more than 500 instances of t h e use of counter- examples f o r teaching purposes. He promised not t o reveal them all, how- ever! I closed this session b y reporting on my recent research on t h e understanding o f randomness involving 1600 English children aged 7-11 years. Maybe you will be interested t o follow u p t h i s work i n y o u r own country - it would be a nice collaborative venture. The last session had j u s t two papers. F i r s t Ruma Falk reported on s t u - dents' difficulties with conditional probabilities and then, with a related theme, Manfred Borovcnik introduced us t o the important intuition of r e - vising probabilities according t o new information, which neatly brought together theory (or theories!) and practical (psychological) issues so typical of work i n this area. Although it may be possible t o teach statistical rules, statistical education is primarily concerned with the f a r more d i f f i c u l t task of inculcating the ability t o make judgements about selection and interpretation. 1 believe t h a t no area o f education makes greater demands on both teacher and learner.