Educational Studies in Mathematics

, Volume 58, Issue 2, pp 253–276 | Cite as

Teaching Undergraduate Mathematics on the Internet

  • Johann EngelbrechtEmail author
  • Ansie Harding


Internet education in mathematics is developing as a new mode of teaching with its own characteristics and possibilities, different from the traditional way of teaching. In a study presented in two parts, we attempt to capture the world of Internet teaching of undergraduate mathematics. In the first part of the study (Engelbrecht, J. and Harding, A.: 2004, ‘Teaching undergraduate mathematics on the web 1: Technologies and taxonomy’), we attempt to create some order in the huge number of activities that are available on the web with a graphical classification of the different types of web courses and discuss some of the technologies involved. In this, the second part of the study, we discuss attributes and implications of this mode of teaching/learning mathematics, also mentioning some of the benefits and concerns. Speculation about the future in such a fluid environment is both risky and fascinating but we nevertheless envisage some possible future trends. Research on this mode of teaching is sparse and open research questions are plentiful. We list possible research issues.

Key Words

mathematics teaching undergraduate mathematics web-based mahematics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allen, G.D., Stecher, M. and Yasskin, P.B. 1998, The Web-Based Mathematics Course, a survey of the required features for an on-line math course, Syllabus Magazine, Nov/Dec 1998.Google Scholar
  2. Allen, G.D. 2001, ‘Online calculus – the course and survey results’, Computers in the Schools 17(1/2), 17–30.CrossRefGoogle Scholar
  3. Becker, D. and Dwyer, M. 1998, ‘The impact of student verbal/visual learning style preference on implementing groupware in the classroom’, Journal of Asynchronous Learning Networks 2(2), 61–69. Retrieved 1 October 2003 from
  4. Berge, Z.L. 1999, ‘Interaction in post-secondary web-based learning’, Educational Technology 18(1), 5–11.Google Scholar
  5. Bookman, J. and Malone, D. 2002, ‘Negotiating roles and meaning while learning mathematics in interactive technology-rich environments–An exploratory study and emerging concept of collaborative learning styles’, Journal of Mathematical Behavior, in press.Google Scholar
  6. Booth, D., Butler, M., Emery, D., Horan, R., Middleton, W. and Pountney, W. 2001, ‘Issues for web delivered assessment’, in Proceedings of the Twenty Seventh Undergraduate Mathematics Teaching Conference, Birmingham, pp. 56–64.Google Scholar
  7. Branon, R.F. and Essex, C. 2001, ‘Synchronous and asynchronous communication tools in distance education’, TechTrends 45(1), 36–42.Google Scholar
  8. Brown, T.H. 2003, ‘Towards a model for m-learning in Africa’, International Journal of E-Learning, in press.Google Scholar
  9. Bruner, J. 1990, Acts of Meaning, Harvard University Press, Cambridge.Google Scholar
  10. Crowe, D. and Zand, H. 2000, ‘Computers and undergraduate mathematics. 1: Setting the scene’, Computers and Education 35, 95–121.CrossRefGoogle Scholar
  11. Czerniewicz, L. 2001, ‘Reflections on learning online – The hype and the reality’, South African Journal of Higher Education 15(3), 17–23.Google Scholar
  12. Daugherty, M. and Funke, B.L. 1998, ‘University faculty and student perceptions of Web-based instruction’, Journal of Distance Education 13(1), 21–39.Google Scholar
  13. Duderstadt, J.J. 1999, ‘Can colleges and universities survive in the information age’? in Z.L. Berge and M.P. Collins (eds.), Dancing with the Devil: Information Technology and the New Competition in Higher Education, Jossey-Bass, San Francisco, pp. 1–25.Google Scholar
  14. Dye, B. 2000, ‘Interactive mathematics online for school and home’, in Presentation at ICME-9, Tokyo, July 2000. Retrieved 29 October 2003 from
  15. Engelbrecht, J. and Harding, A. 2001a, ‘WWW Mathematics at the University of Pretoria: The trial run’, South African Journal of Science 97(9/10), 368–370.Google Scholar
  16. Engelbrecht, J. and Harding, A. 2001b, ‘Internet calculus: An option’? Quaestiones Mathematicae Supplement 1, 183–191.Google Scholar
  17. Engelbrecht, J. and Harding, A. 2002a, ‘Cooperative learning as a tool for enhancing a web-based Calculus course’, in Proceedings of the ICTM2, Crete, July 2002.Google Scholar
  18. Engelbrecht, J. and Harding, A. 2002b, ‘A qualitative investigation on the impact of web-based undergraduate mathematics teaching on developing academic maturity’, Technical Report UPWT 2002/13.Google Scholar
  19. Engelbrecht, J. and Harding, A. 2003a, ‘Online assessment in mathematics: Multiple assessment formats’, New Zealand Journal of Mathematics 32(Suppl.), 57–66.Google Scholar
  20. Engelbrecht, J. and Harding, A. 2003b, ‘Combining online and paper assessment in a web-based course in undergraduate mathematics’, Journal of Computers in Mathematics and Science Teaching, in press.Google Scholar
  21. Engelbrecht, J. and Harding, A. 2005, ‘Teaching undergraduate mathematics on the web. 1: Technologies and taxonomy’, Educational Studies in Mathematics 58(2), 235–252.CrossRefGoogle Scholar
  22. Firdyiwek, Y. 1999, ‘Web-based courseware tools: Where is the pedagogy’? Educational Technology 39, 29–34.Google Scholar
  23. Harasim, L.M., Teles, S. and Turoff, M. 1997, ‘Networked learning: A paradigm for the twenty first century’, ‘Learning Networks: A field guide to teaching and learning online’.Google Scholar
  24. Hawisher, G.E. and Pemberton, M.A.1997, ‘Writing across the curriculum encounters asynchronous learning networks or WAC meets up with ALN’, Journal of Asynchronous Learning Networks 1(1), 61–69. Retrieved 1 October 2003 from
  25. Herrington, A., Herrington, J., Oliver, R., Stoney, S. and Willis, J. 2001, ‘The development of an instrument to audit online units’, in Proceedings of the 18th conference of the Australasian Society for Computers in Learning in Tertiary Education, 2001, Melbourne, pp. 263–270. Retrieved 15 October 2003 from
  26. Hibberd, S. 1996, ‘The mathematical assessment of students entering university engineering courses’, Studies in Educational Evaluation 22(4), 375–384.CrossRefGoogle Scholar
  27. Hopper, K.B. 2001, ‘Is the internet a classroom’? TechTrends 45(5), 35–43.CrossRefGoogle Scholar
  28. Hopper, K.B. and Harmon, S.W. 2000, ‘A multiple-case study of exemplary internet courses’, Ed at a Distance Magazine and Ed Journal 14(9), 27–36.Google Scholar
  29. Isoda, M., Lee, Y.-S., Aoyama, K. and Ishizuka, M. 2002, ‘The study of mathematics communication on internet with palmtop computer’, in Proceedings of the 2nd International Conference on the Teaching of Mathematics at the Undergraduate Level, Hersonissos, Greece, July 2002.Google Scholar
  30. Johnson, C.M. 2001, ‘A survey of current research on online communities of practice’, Internet and Higher Education 4, 45–60.CrossRefGoogle Scholar
  31. Johnson, D.F. 2003, ‘Toward a philosophy of online education’, in B.G. Brown (ed.), Developing Faculty to Use Technology, Programmes and Strategies to Enhance Teaching, Anker Publishing Company, Bolton.Google Scholar
  32. Jones, B. 2002, ‘Synchronous and asynchronous communication in online instruction’, Retrieved 30 October 2003 from
  33. Kawski, M. 2003, Personal communication.Google Scholar
  34. Kearsley, G. 1995, ‘The nature and value of interaction in distance learning’, in Proceedings of the Invitational Research Conference in Distance Education: Towards Excellence in Distance Education: A Research Agenda, The American Center for the Study of Distance Education, Pennsylvania State University, pp. 366–374.Google Scholar
  35. Kearsley, G. 2002, ‘Is online learning for everybody’? Educational Technology, 41–44.Google Scholar
  36. Khan, B.H. (ed.): 1997, Web-Based Instruction, Educational Technology Publications, Englewood Cliffs.Google Scholar
  37. Leh, A.S. 2001, ‘Action research on training students to become independent learners’, TechTrends 45(1), 39.Google Scholar
  38. Macdonald, C.J., Stodel, E.J., Farres, L.G., Breithaupt, K. and Gabriel, M.A. 2001, ‘The demand-driven learning model: A framework for web-based learning’, Internet and Higher Education 4, 9–30.CrossRefGoogle Scholar
  39. Matthews, D. 1999, ‘The origins of distance educations and its use in the United States’, T.H.E. Journal 27(2), 54–66.Google Scholar
  40. Miskulin, R.G.S., Amorin, J.A. and Jorge, F.M. 2002, ‘Interactivity in mathematics education: Collaborative knowledge generation in internet based sharing environment’, in Proceedings of the International Conference The Humanistic Renaissance in Mathematics Education, Setembro 2002, Palermo, pp. 273-278. Retrieved 28 October 2003 from
  41. Myers, K.L. 1999, ‘Is there a place for instructional design in the information age’? Educational Technology 39(6), 50–53.Google Scholar
  42. Ng, K.-C. 2001, ‘Using e-mail to foster collaboration in distance education’, Open Learning 16(2), 191–200.Google Scholar
  43. Ory, J.C., Bullock, C. and Burnaska, K. 1997, ‘Gender similarity in the use of and attitudes about ALN in a university setting’, Journal of Asynchronous Learning Networks 1(1), 39–51. Retrieved 1 October 2003 from
  44. Parloff, R. and Pratt, K. 1999, Building Learning Communities in Cyberspace: Effective Strategies for the Online Classroom, Jossey-Bass, San Francisco.Google Scholar
  45. Pea, R.D. 1987, ‘Cognitive technologies for mathematics education’, in A.H. Schoenfeld (ed.), Cognitive Science and Mathematics Education, Lawrence Erlbaum.Google Scholar
  46. Porter, L.R. 1997, Creating the Virtual Classroom: Distance Learning with the Internet, Wiley, New York.Google Scholar
  47. Reeves, T.C. and Reeves, P.M. 1997, ‘The effective dimensions of interactive learning on the WWW’, in B.H. Khan (ed.), Web-Based Instruction, 59-66, Educational Technology, Englewood Cliffs.Google Scholar
  48. Sangwin, C.J. 2004, ‘Assessing mathematics automatically using computer algebra and the internet’, Teaching Mathematics and Its Applications 23(1), 1–14.CrossRefGoogle Scholar
  49. Schoenfeld, A.H. 1988, ‘Uses of computers in mathematics instruction’, in D.A. Smith, G. Porter, L. Leinbach and R. Wenger (eds.), Computers and Mathematics: The Uses of Computers in Undergraduate Instruction, Mathematical Association of America, Washington.Google Scholar
  50. Selden, A. and Selden, J. 1997, ‘Should mathematicians and mathematics educators be listening to cognitive psychologists’? M.A.A Research Sampler 2. Retrieved 15 October 2003 from
  51. Simonson, M., Smaldio, S., Albright, M. and Zvacek, S. 2000, Teaching and Learning at a Distance: Foundation of Distance Education, Merrill, Upper Saddle River.Google Scholar
  52. Sims, R., Dobbs, G. and Hand, T. 2001, ‘Proactive evaluation: New perspectives for ensuring quality in online learning applications’, in Proceedings of the 18th Conference of the Australasian Society for Computers in Learning in Tertiary Education, 2001, Melbourne, pp. 509–517. Retrieved 15 October 2003 from
  53. Smith, G. and Wood, L. 2000, ‘Assessment of learning in university mathematics’, International Journal for Mathematics Education in Science and Technology31(1), 125–132.CrossRefGoogle Scholar
  54. Stiles, M.J. 2000, ‘Effective learning and the virtual learning environment’, in EUNIS 2000: Towards Virtual Universities: Proceedings of the European University Information System 2000 Conference held at INFOSYSTEM 2000, Poznan, Poland, Poznan: Instytut Informatyki Politechniki Poznanskiej, pp. 171–180.Google Scholar
  55. Stokes, S.P. 2001, ‘Satisfaction of college students with the digital learning environment: Do learners’ temperaments make a difference’? Internet and Higher Education 4, 31–44.CrossRefGoogle Scholar
  56. Suanpang, P., Petocz, P. and Kalceff, W. 2003, Student Attitudes to Learning Business Statistics Online vs. Traditional Methods, Learning for unknown future, New Zealand, HERSA, 6–9 July 2003.Google Scholar
  57. Swan, K., Shea, P., Frederickson, E., Pickette, A. Pelz, W. and Maher, G. 2000, ‘Building knowledge building communities: Consistency, contact, and communication in the virtual classroom’, Journal of Educational Computing Research 23(4), 359–383.CrossRefGoogle Scholar
  58. Tall, D. 1994, ‘Computer environments for the learning of mathematics’, in R. Biehler, R.W. Scholz, R. Strasser and B. Winkelmann (eds.), Didactics of Mathematics as a Scientific Discipline, Kluwer Academic Publishers, Dordrecht.Google Scholar
  59. Tan, S.C. and Hung, D. 2002, ‘Beyond information pumping: Creating a constructivist e-learning environment’, Educational Technology 42(5), 48–54.Google Scholar
  60. Vygotsky, L.S. 1978, Mind in Society: The Development of Higher Psychological Processes, Harvard University Press, Cambridge.Google Scholar
  61. Vygotsky, L.S. 1987, (Transl. N. Minick), The Collected Works of L.S. Vygotsky: Vol. 1, Problems of General Psychology, Plenum Press, New York.Google Scholar
  62. Waldock, J., Gretton, H. and Challis, N. 2001, ‘Using the Web to enhance student learning, in Proceedings of ICTM2, Crete.Google Scholar
  63. Wepner, S.B. and Mobley, M.M. 1998, ‘Reaping new harvests: Collaboration and communication through field experiences’, Action in Teacher Education 20(3), 50–61.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Mathematics & Applied MathematicsUniversity of PretoriaPretoriaSouth Africa

Personalised recommendations