Tall, David and Rashidi Razali , Mohamad. (1993) Diagnosing students' difficulties in learning mathematics. International Journal of Mathematical Education in Science and Technology, Vol.24 (No.2). pp. 209-222. ISSN 0020-739X

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Abstract

This study considers the results of a diagnostic test of student difficulty and contrasts the difference in performance between the lower attaining quartile and the higher quartile. It illustrates a difference in qualitative thinking between those who succeed and those who fail in mathematics, illustrating a theory that those who fail are performing a more difficult type of mathematics (coordinating procedures) than those who succeed (manipulating concepts). Students who have to coordinate or reverse processes in time will encounter far greater difficulty than those who can manipulate symbols in a flexible way. The consequences of such a dichotomy and implications for remediation are then considered.

Item Type:	Journal Article
Subjects:	L Education > LB Theory and practice of education Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Institute of Education
Library of Congress Subject Headings (LCSH):	Mathematics -- Study and teaching, Mathematical ability
Journal or Publication Title:	International Journal of Mathematical Education in Science and Technology
Publisher:	Taylor & Francis Ltd.
ISSN:	0020-739X
Date:	1993
Volume:	Vol.24
Number:	No.2
Page Range:	pp. 209-222
Identification Number:	10.1080/0020739930240206
Status:	Peer Reviewed
Access rights to Published version:	Open Access
References:	Bartlett F. C. , 1958: Thinking, George Allen ~ Unwin, London. Bell F. H. , 1978: Teaching and Learning Mathematics (in Secondary schools), Wm.C.Brown Co. Pub., USA. Chiarugi I., Fracassina, G. & Furinghetti F., 1990, “Learning difficulties behind the notion of absolute value”, Proceedings of PME 13, Mexico, III 231-238. Ekenstam A. Af & Greger K. , 1983: “Some aspects of children’s ability to solve mathematical problems”, Educational Studies in Mathematics 14, 369-384. Freudenthal., H., 1983: The Didactical Phenomenology of Mathematics Structures, Dordrecht, Holland; Boston, Reidel. Gagné R. M., 1970: The Conditions of Learning, Holt Rinehart and Winston Inc., New York, 2nd. edition. Gray E. & Tall D. O. , 1991: “Duality, Ambiguity and Flexibility in Successful Mathematical Thinking”, Proceedings of PME14, Assisi, II, 72–79. Greer B. ,1987: “Nonconservation of multiplication and division involving decimals”, Journal for Research in Mathematics Education 18 37-45. Laporan Jawatankuasa Kabinet Mengkaji Perlaksanaan Dasar Pelajaran,1979, pp. 18-20 (in Malay). Laporan Jawatankuasa Mengkaji Taraf Pelajaran di Sekolah-Sekolah, 1982, p.18 (in Malay). Markovits Z., Eylon B. & Bruckheimer M., 1988: “Difficulties Students have with the Function Concept”, The Ideas of Algebra, K-12, N.C.T.M. 1988 Yearbook, 43-60. Newell A. & Simon H.A.,1972: Human Problem Solving, Prentice Hall, N.J., USA. Steen L.A.,1989: “Mathematics for a new century”, The Australian Mathematics. Teacher, 45 19-23. Tall, D. O. & Bakar, M. N., 1993: “Students’ Mental Prototypes for Functions and Graphs”, International Journal of Mathematics Education in Science and Technology, 23 1, 39–50. Tall D. O. & Thomas M. O. J. ,1991: “Encouraging Versatile Thinking in Algebra Using the Computer”, Educational Studies in Mathematics, 22 2, 125–147. Thurston, W. P., 1990: “Mathematical Education”, Notices of the American Mathematical Society 37 7, 844-850. Vinner S.,1983: “Concept definition, concept image and the notion of function”, The International Journal of Mathematical Education in Science and Technology, 14, 293- 305.
URI:	http://wrap.warwick.ac.uk/id/eprint/512

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