An approach to learning mathematics through knowledge engineering

Journal of Computer Assisted Learning

Volumn 15, Issue 4, 1999, Pages 291-301

  Kadijevich, Djordje ^a  

^a MATHEMATICAL INSTITUTE   (Serbia)

Author keywords

Expert systems; Knowledge engineering; Learning; Logic programming; Mathematics education; Problem solving; PROLOG; Social constructivism

Indexed keywords

EID: 0033236246     PISSN: 02664909     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-2729.1999.00104.x     Document Type: Article

References (58)

1. Abidin, B. & Hartley, J.R. (1998) Developing mathematical problem solving skills. Journal of Computer Assisted Learning, 14, 4, 278-291.
2. Bagui, S. (1998) Reasons for Increased Learning Using Multimedia. Journal of Educational Multimedia and Hypermedia, 7, 1, 3-18.
3. Boden, M. (1989) Artificial Intelligence in Psychology. MIT Press, Cambridge.
4. Byrnes, J.P. & Wasik, B.A. (1991) Role of Conceptual Knowledge in Mathematical Procedural Learning. Developmental Psychology, 27, 5, 777-787.
5. Clement, J. (1983) Use of analogies and spatial transformations by experts solving mathematical problems. In Proceedings of the fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA). Vol. 2 (eds. J.C. Bergeron & N. Herscovics) pp. 101-111. International Group for the Psychology of Mathematics Education, North American Chapter.
6. Confrey, J. (1991) Learning To Listen: A Student's Understanding of Powers of Ten. In Radical Constructivism in Mathematics Education (ed. E. von Glasersfeld) pp. 111-138. Kluwer, Dordrecht.
7. Confrey J. & Costa S. (1996) A Critique of the Selection of 'Mathematical Objects' as Central Metaphor for Advanced Mathematical Thinking. International Journal of Computers for Mathematical Learning, 2, 1, 139-168.
8. Cope, P. (1989) Teaching PROLOG programming in the secondary school. Journal of Computer Assisted Learning, 5, 4, 223-230.
9. Crowe, D. & Zand, H. (1997) Novices entering mathematics - I. The impact of new technology. Computers & Education, 28, 1, 43-54.
10. Cumming, G. (1998) Artificial intelligence in education: an exploration. Journal of Computer Assisted Learning, 14, 4, 251-259.
11. Davydov, V.V. (1986) Problems of Developmental Teaching (in Russian). Pedagogika, Moscow.
12. Davydov, V.V. (1995) The influence of L.S. Vygotsky on education theory, research and practice. Educational Researcher, 24, 3, 12-21.
13. Ernest, P. (1991) The Philosophy of Mathematics Education. Falmer, Basingstoke.
14. Ernest, P. (1994a) Varieties of constructivism: their metaphors, epistemologies and pedagogical implications. Hiroshima Journal of Mathematics Education, 2, 1-14.
15. Ernest, P. (ed) (1994b) Constructing mathematical knowledge: Epistemology and mathematics education. Falmer Press, London.
16. Ernest, P. (1998) Social constructivism as a philosophy of mathematics. State University of New York Press, Albany.
17. Fischbein, E. (1990) Introduction. In Mathematics and Cognition: A Research Synthesis by the International Group for the Psychology of Mathematics (eds. P. Nesher & J. Kilpatrick) pp. 1-13. Cambridge University Press, Cambridge.
18. Gagné, R.M. (1977) The Conditions of Learning (3rd edition). Holt, Rinehart and Winston, New York.
19. Galle, P. & Kovács, L.B. (1992) The logic of worms: a study in architectural knowledge representation. Environment and Planning B: Planning and Design, 19, 5-31.
20. Grabinger, R.S. (1996) Rich environments for active learning. In Handbook of research for educational communications and technology (ed. D.H. Jonassen) pp. 665-692. Macmillan, New York.
21. Haapasalo, L. (1993) Systematic Constructivism in Mathematical Concept Building. In Constructivist and Curricular Issues in the School Mathematics Education. Mathematics Education Research in Finland (Yearbook 1992-1993) (eds. P. Kupari & L. Haapasalo). University of Jyväskylä & The Finnish Association of Mathematics and Science Education Research, Jyväskylä.
22. Haapasalo, L. & Kadijevich, Dj. (1999) Two types of mathematical knowledge and their relation. Submitted to Journal für Mathematik-Didaktik (the first revision).
23. Hiebert, J. & Carpenter, T.P. (1992) Learning and Teaching with Understanding. In Handbook of Research on Mathematics Teaching and Learning (ed. D.A.Grouws) pp. 65-97. Macmillan, New York.
24. Hofstadter, D.R. (1980) Gödel, Echer, Bach: An Eternal Golden Braid. Penguin, London.
25. Hölzl, R. (1996) How Does 'Dragging' Affect the Learning of Geometry? International Journal of Computers for Mathematical Learning, 1, 2, 169-187.
26. Hoyles, C. & Noss, R. (eds.) (1992) Learning Mathematics and Logo. MIT Press, Cambridge, MA.
27. Ivic, I. (1989) Profiles of Educators: Lev Vygotsky. Prospects (UNESCO), 19, 3, 427-436.
28. Jensen, H.S. (1988) Logic Systems as Knowledge Tools in Education. In Artificial Intelligence Tools in Education (eds. P. Ercoli & R. Lewis) pp. 221-226. North Holland, Amsterdam.
29. Jonassen, D.H. (1996) Computers in the classroom: Mindtools for critical thinking. Prentice-Hall, Englewood Cliffs, NJ.
30. Kadijevich, Dj. (1993) Learning, Problem Solving and Mathematics Education (report 93/3). Department of Computer Science, University of Copenhagen.
31. Kadijevich, Dj. (1998) Can Mathematics Students Be Successful Knowledge Engineers? Journal of Interactive Learning Research, 9, 3/4, 235-248.
32. Kadijevich, Dj. (2000) The LISD Approach, Facta Universitatis (Series: Philosophy and Sociology), 2, 7, 347-355. Internet: http://ni.ac.yu/Facta/pas/pas.html
33. Kaput, J. (1992) Technology and Mathematics Education. In Handbook of Research on Mathematics Teaching and Learning (ed. D.A. Grouws) pp. 515-556. Macmillan, New York.
34. Kaput, J.J. & Thompson, P.W. (1994) Technology in Mathematics Education Research: The First 25 Years in the JRME. Journal for Research in Mathematics Education, 25, 6, 667-684.
35. Keitel, C. & Ruthven, K. (eds) (1993) Learning from Computers: Mathematics Education and Technology. Springer-Verlag, Berlin.
36. Kovács, L.B. (1991) Knowledge-based floor plan design by space partitioning: A logic programming approach. Artificial Intelligence in Engineering, 6, 4, 162-185.
37. Leith, P. (1990) Formalism in AI and Computer Science. Ellis Horwood, New York.
38. Lippert, R. (1990) Teaching Problem Solving in Mathematics and Science with Expert Systems. Journal of Artificial Intelligence in Education, 1, 3, 27-40.
39. Marro Clement, P., Perret-Clermont, A.-N., Grossen, M. & Trognon, A. (1998) Le partenaire comme enseignant ou comme interlocuteur: une analyse expérimentale et interlocutoire. Cahiers de Psychologie, 34. Séminaire de Psychologie, Neuchâtel.
40. Nesher, P. (1986) Are Mathematical Understanding and Algorithmic Performance Related? For the Learning of Mathematics, 6, 3, 2-9.
41. Pain, H., Brna, P. & du Boulay, B. (eds.) (1991) Teaching, Learning and Using Prolog (special issue). Instructional Science, 20, 2/3.
42. Pólya, G. (1990) How To Solve It (2nd edition). Penguin, London.
43. Ruthven, K. (ed.) (1989) Informational Technology and Mathematics Education (special issue). Educational Studies in Mathematics, 20, 3.
44. Schoenfeld, A.H. (1985) Mathematical Problem Solving. Academic Press, Orlando.
45. Schoenfeld, A.H. (1992) Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics. In Handbook of Research on Mathematics Teaching and Learning (ed. D.A. Grouws) pp. 334-370. Macmillan, New York.
46. Self, J. (1990) Theoretical Foundations for Intelligent Tutoring Systems. Journal of Artificial Intelligence in Education, 1, 4, 3-14.
47. Silver, E.A. (1988) Teaching and Assessing Mathematical Problem Solving: Toward a Research Agenda. In The Teaching and Assessing of Mathematical Problem Solving (eds. R.I. Charles & E.A. Silver) pp. 273-282. National Council of Teachers of Mathematics, Reston.
48. Skemp, R.R. (1986) The Psychology of Learning Mathematics (2nd edition). Penguin, London.
49. Skemp, R.R. (1987) The Psychology of Learning Mathematics (expanded American edition). Lawrence Erlbaum, Hillsdale.
50. Sterling, L. & Shapiro, E. (1986) The Art of Prolog. MIT Press, Cambridge.
51. Stevenson, I. & Noss, R. (1991) Pupils as expert system developers. In International Group for the Psychology of Mathematics Education (ed. F. Furinghetti) pp. 294-301. Department of Mathematics, University of Genoa.
52. Sutherland, R. & Mason, J. (eds.) (1995) Exploiting Mental Imagery with Computers in Mathematics Education. Springer-Verlag, Berlin.
53. Tall, D. (1994) Computer environments for the learning of mathematics. In Didactics of mathematics as a scientific discipline (eds. R. Biehler, R.W. Scholz, R. Straesser & B. Winkelmann) pp. 189-199. Kluwer, Dordrecht.
54. Tessmer, M., Wilson, B. & Driscoll, M. (1990) A New Model Of Concept Teaching and Learning. Educational Technology Research and Development, 38, 1, 45-53.
55. Tripp, S.D. & Bichelmeyer B. (1990) Rapid Prototyping: An Alternative Instructional Design Strategy. Educational Technology Research and Development, 38, 1, 31-44.
56. Vygotsky, L. (1978) Mind in Society. Harvard University Press, Cambridge.
57. Wasson, B. & Lindström, B. (1998) Contemporary and Historical Perspectives on Pedagogical Information Technologies. http://www.ifi.uib.no/staff/barbara/courses/pivar98.html
58. Wilson, B. & Cole, P. (1991) A Review of Cognitive Teaching Models. Educational Technology Research and Development, 39, 4, 47-64.