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Xerox University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 75-11,398 MITCHELMQRE, Michael Charles, 1940- THE PERCEPTUAL DEVELOPMENT OF JAMAICAN STUDENTS, WITH SPECIAL REFERENCE TO VISUALIZATION AND DRAWING OF THREE-DIMENSIONAL GEOMETRICAL FIGURES AND THE EFFECTS OF SPATIAL TRAINING. The Ohio State University, Ph.D., 1974 Education, psychology Xerox University Microfilms, Ann Arbor, Michigan 48io6 0 1975 MICHAEL CHARLES MITCHELMQRE ALL RIGHTS RESERVED THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. THE PERCEPTUAL DEVELOPMENT OF JAMAICAN STUDENTS, WITH SPECIAL REFERENCE TO VISUALIZATION AND DRAWING OF THREE-DIMENSIONAL GEOMETRICAL FIGURES AND THE EFFECTS OF SPATIAL TRAINING DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Michael Charles Mitchelmore, M.A., Cert, Ed. ***** The Ohio State University 1974 Reading Committee: Approved by F. Joe Crosswhite Fred L. Damarin, Jr. Dean H. Owen Adviser Richard J. Shumway îollege of Education ACKNOWLEDGEMENTS This study, although executed in one country (Jamaica), was planned in a second (the United States), supported by funds from a third (the United Kingdom), and based on ideas conceived in a fourth (Ghana). It therefore owes its suc­ cessful completion to an international band of colleagues, advisers, encouragers, supporters and cooperators. I should like first to thank all those school and college principals, teachers and students in Jamaica who so willingly gave me their time and interest. The eager cooper­ ation of the eight schools involved in the pilot-testing and the forty schools involved in the developmental and Grade Nine surveys turned a lengthy task into a most enjoyable one, I am particularly grateful to the staff of Mico College for making me feel so much a part of their institution— especial­ ly to the principal. Dr. Errol Miller, whose early interest made a Jamaican study feasible and who gave his continual support to the spatial training experiment; to the head of the mathematics department, Mr. A. Hibbert, who undertook all the administrative details of the experiment; and to all the other mathematics tutors of the college. ii In the planning of the tv: i surveys, I received what I now regard as typically Jamaican cooperation from officials of the Examinations Section of the Ministry of Education, the Overseas Examinations Centre, and the Department of Town Planning, who not only granted me access to confidential and unpublished data but also gave me considerable help in inter­ preting it for my peculiar purposes. Members of the School of Education in the University of the West Indies at Mona were also most helpful. I am grateful to Dr. L. H. E. Reid for accepting me as an Occasional Student and to Dr. A. S. Phillips for providing me with a letter of introduction authorizing me Lo conduct research in the schools. My deepest gratitude goes to Mr. Ian Isaacs for sharing with me not only his life-long knowledge of Jamaica and its schools and his more recent experiences in educational re­ search, but also (with his wife Pat) the hospitality and friendship of his home. It was because of my previous association with Mr. Isaacs as adapter of the Caribbean edition of the Join Schools Project mathematics series that I was invited to Jamaica in 1972, and I shall always be thankful to him for encouraging me to return. For their instruction, assistance and comradeship during my years at OSU, I am deeply grateful to all the iii members of the Faculty of Science and Mathematics Education; especially to the chairman, Robert Howe; my adviser, Joe Crosswhite; Richard Shumway, who was also on my reading committee; Jon Higgins, who served on my advisory committee; and Alan Osborne and Harold Trimble. I also thank James Duncan of Curriculum and Foundations for serving on my advisory committee. This study would not have been possible without the exceptional flexibility of my adviser. In mathematics education research, studies of the visualization aspect of geometry are rare, of drawing even more so, and cross- cultural studies unheard of; yet "Papa Jre" gave me nothing but encouragement as my planned study grew and took its final shape. I am also very grateful to the two psychologists on my committee for contributing from their specialities; Fred Damarin in testing and measurement and Dean Owen in per­ ception. This dissertation was written and typed while I was still in Jamaica, and I am indebted to my committee for making time to see me on my one trip to Columbus, for reviewing draft chapters by mail at short notice, and for completing in my absence many of the formal arrangements for graduation which are normally the candidate's responsibility. My headaches iv at this stage were greatly alleviated by the known relia­ bility of my typist, Jane Burrows, who deserves my sincere thanks for working so speedily and accurately. I would like to take this opportunity to thank the psychologists and educators all over the world who have taken time to correspond with me about their work, sent reprints, and commented on my research proposals. I am especially grateful to John Berry, Alan Bishop, John Dawson, Jan Deregowski, Hall Duncan, John Eliot, I. Macfarlane Smith, and Philip Vernon. Their willingness to help the distant, unknown neophyte was a fine example to follow should I ever attain their stature. It was an Educational Development Award from the Ministry of Overseas Development, London, which allowed me to spend the year in Jamaica which was needed to carry out the present study. Without that substantial support, only a shorter and more poorly planned spatial training experi­ ment would have been possible. A further grant, from the Society for the Psychological Study of Social Issues, covered the cost of test papers and other equipment. Mico College kindly bore the cost of producing the workcards and other materials used in the spatial training experiment (no small contribution) and the School of Education at the V University also helped with the duplication of test papers. For all this financial assistance, I am most grateful. I must also thank Educational Testing Service and Longman Group Ltd. for allowing me to reproduce material for which they hold the copyright, the American Institutes for Research for sending me background material on their I-D test series, and the Australian Council for Educational Research for per­ mission to use the Pacific Design Construction Test. My thinking on the aims of mathematics education in developing countries took shape during my early years of teaching in Ghana. Conversations on geometry with other mathematics teachers, especially Hugh Benzie, John Fletcher, Neil Harding, Marion Harbourn, and Kenneth Snell, were part of my education. Our conclusions were put into print in the Joint Schools Project mathematics series, and all those associated with that project will long be remembered for their kindness and friendship. I am particularly grateful to Dr. Mary Hartley, who gave the project life and resus­ citated it at several critical moments, and to Brian Raynor, my co-editor for ten years, who has frequently taught me how to turn unworkable ideals into teachable practice. My wife June and daughters Margaret, Sylvia and Catherine have accompanied and supported me in all four vi countries. Actually, they seemed rather to enjoy it, and thrived wherever we pitched. For this study, they acted as guinea pigs during test development and collated thousands of test papers. My wife also went through the entire manuscript with a fine toothcomb, as a result of which many muddled thoughts and sentences were clarified. I am very grateful for all their help. Vll VITA July 25, 1940 . Born at Dartmouth, England 196 1 ............... B.A., University of Cambridge, England 196 2 ............... Certificate in Education, University of Bristol, England 1962-66 ..........