Traditional vs Non-traditional Teaching and Learning Strategies – the case of E-learning!
AbstractThe traditional teaching approaches are generally teacher-directed and where students are taught in a manner that is conducive to sitting and listening. It is true that the traditional expectations and department philosophies often allow us to continue with the lecture-based model with some useful results as evident by the past accomplishments of many and this cannot be disputed as much. However it is often argued that the traditional approach may not provide students with valuable skills and indeed some even go as far as saying the traditional method leads to a student not retaining knowledge after exams - they have little or no recall of the body of knowledge learnt beyond the end of a semester, for example. The teaching of mathematics that is usually referred to or called non-traditional uses constructivist philosophy as its basis; this implicates strategies in which the individual is making sense of his or her universe. So the student is an active participant, which allows an individual to develop, construct or rediscover knowledge – a major goal that can be very time consuming process if taken literally for each student; alternately, there is also a philosophical position known as social constructivism; which suggests group work, language and discourse to be vital for learning in a cultural framework of the knowledge base; so the use of group work, discussion, and group solving problems in a cooperative manner lead to a discourse which is believed to be the most important part of learning process. It is argued that the non-traditional teaching is done using a problem solving approach; where the learner is the problem solver.
Typically, university lecturers in mathematics and engineering are often not trained in the non-traditional classroom methods. Some have argued that even if they included non-traditional teaching in their universities in fact they may not be in reality using the so called non-traditional methods and goals. They argue that lecturers are often lacking the underlying philosophical knowledge of the non-traditional goals and objectives, and therefore they are not in a position to implement such methodologies and assessment techniques, in reality, even when they say they are.
The non-traditional teaching and learning (NTTL) in mathematics and engineering needs to be well understood before any appropriate comparisons can be made with the older techniques if we are to do it in professional manner. For example the teachers of engineering courses need to reflect where the students are coming from, and where will they need to be after completing the course; also lecturers need to keep the context and goals of the course the degree program in mind while preparing for their class teaching content for the semester. So, we need to consider the knowledge, procedures, skills, beliefs and attitudes that will be expected for each student of mathematics or engineering at the end of the course that is to be taught in a time frame of 12 to 13 weeks; in addition to keeping the economic constraints of a university in modern times in check at all times.
The computer based teaching technology (e-learning) is now constantly used in mathematics and engineering courses. The e-learning methodology is considered to be in line with the non-traditional approaches than the traditional teaching approaches; and this paper critically reviews the literature on mathematics and engineering that have made comparisons of the approaches outlined. The paper will specifically examine the advantages/disadvantages of the approaches as well the manner in which they influence performance of students in mathematics and engineering courses.
Abdulwahed, M., Jaworski, B. and Crawford, A. (2012). Innovative approaches to teaching mathematics in higher education: a review and critique.
Academic Partnerships (2011). Research on the Effectiveness of Online Learning: A Compilation of Research on Online Learning [White Paper]. Retrieved from http://www.academicpartnerships.com/sites/default/files/Research%20on%20the%20Effectiveness%20of%20Online%20Learning.pdf
Albano, G., Coppola, C, and , Pacelli, T. (2013). The use of e-learning in pre-service teachers’ training. “Quaderni di Ricerca in Didattica (Mathematics)”, n. 23 Supplemento 1, G.R.I.M. Department of Mathematics, University of Palermo, Italy.
Aral, A. and Cataltepe, Z. (2012). Learning Styles for K-12 Mathematics e-Learning. In CSEDU (1) (pp. 317-322).
Ashman, A.F. and Conway, R.N. (1997). An introduction to cognitive education: Theory and applications. Psychology Press.
Baccaglini-Frank, A. and Mariotti, M.A. (2010). Generating conjectures in dynamic geometry: The maintaining dragging model. International Journal of Computers for Mathematical Learning, 15(3), pp.225-253.
Bernard, R.M., Abrami, P.C., Lou, Y., Borokhovski, E., Wade, A., Wozney, L., Wallet, P.A., Fiset, M. and Huang, B. (2004). How does distance education compare with classroom instruction? A meta-analysis of the empirical literature. Review of educational research, 74(3), pp.379-439.
Bidaki, M.Z., Sanati, A.R. and Semnani, M.N. (2013). Students’ attitude towards two different virtual methods of course delivery. Procedia-Social and Behavioral Sciences, 83, pp.862-866. http://dx.doi.org/10.1016/j.sbspro.2013.06.162
Bloom, B.S., & Krathwohl, D.R. (1956). Taxonomy of Educational Objectives: The Classification of Educational Goals: Handbook I, Cognitive Domain. New York: Longmans, Green.
Bosworth, K. and Hamilton, S.J. (1994). Collaborative Learning: Underlying Processes and Effective Techniques: New Directions for Teaching and Learning, Number 59 (Vol. 73). Jossey-Bass.
Bransford, J., Brown, A., Cocking, R., Donovan, M.S. and Pellegrino, J.W. (2000). Expanded Edition. How People Learn: Brain, Mind, Experience and School.
Bryan, V. C. (2015). Self-directed learning and technology. The Education Digest, 80(6), 42-44. Retrieved from http://search.proquest.com/docview/1651361328?accountid=12725
Burton, L. (2002). Methodology and methods in mathematics education research: Where is" The Why. Researching mathematics classrooms: A critical examination of methodology, pp.1-10.
Caiazzo, L., Nicodemo, M. and PALOMA, F.G. (2013). The contribution of neuroscience in cognitive transfer. Knowledge Cultures, 1(6), pp.41-53
Caprotti, O., Seppälä, M. and Xambó, S. (2007). Novel aspects of the use of ICT in mathematics education. Innovations in E-learning, Instruction Technology, Assessment, and Engineering Education, pp.295-299.
Carpenter, T. P. (1989). Teaching as problem solving. In R. I. Charles and E. A. Silver (Eds), The teaching and assessing of mathematical problem solving (pp.187-202). USA: National Council of Teachers of Mathematics.
Chang, C.S., Chen, T.S. and Hsu, W.H. (2011). The study on integrating WebQuest with mobile learning for environmental education. Computers & Education, 57(1), pp.1228-1239.
Colace, F., De Santo, M. and Greco, L. (2014). E-Learning and Personalized Learning Path: A Proposal Based on the Adaptive Educational Hypermedia System. International Journal of Emerging Technologies in Learning, 9(2).
Common Core Standards state from Engage NY, (2014). From EngageNY.org of the New York State Education Department. https://www.engageny.org/ [Pedagogical Shifts demanded by the Common Core State Standards.]
http://www.curriculumassociates.com/aboutus/Press-Release-i-Ready-Winner-eSchool-News-2014-15-Readers-Choice-Awards.aspx, Retrieved November 2, 2014.
Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
Descamps, S.X., Bass, H., Bolanos Evia, G., Seiler, R. and Seppala, M. (2006). E-learning mathematics. Panel promoted by the Spanish Conference of Mathematics’ Deans. In Proceedings of International Conference of Mathematicians, Madrid, Spain.
Dick, T. P., & Hollebrands, K. F. (2011). Introduction to Focus in high school mathematics: Technology to support reasoning and sense making. In T. P. Dick & K. F. Hollebrands (Eds.), Focus in high school mathematics: Technology to support reasoning and sense making (pp. xi - xvii). Reston, VA: National Council of Teachers of Mathematics.
Duval, R. (2006). A cognitive analysis of problems of comprehension in the learning of mathematics. Educational Studies in Mathematics, 61(1-2), 103-131.
Friday, E., Friday-Stroud, S.S., Green, A.L. and Hill, A.Y. (2006). A multi-semester comparison of student performance between multiple traditional and online sections of two management courses. Journal of Behavioral and Applied Management, 8(1), p.66-81.
Gardner, R.C. (1983). Learning another language: A true social psychological experiment. Journal of language and Social Psychology, 2(2-3-4), pp.219-239.
Hanover Research Council (2009). Best Practices in Online Teaching Strategies. Washington, DC. Retrieved from http://www.uwec.edu/AcadAff/resources/edtech/upload/Best-Practices-in-Online-Teaching-Strategies-Membership.pdf
Harrington, D. (1999). Teaching statistics: A comparison of traditional classroom and programmed instruction/distance learning approaches. Journal of Social Work Education, 35(3), pp.343-352.
Henderson, S. and Broadbridge, P. (2007). December. Mathematics for 21st century engineering students. In AaeE Conference, Melbourne, Australia.
Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Human, P., Murray, H., Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(12), 12-21.
Hirsh-Pasek, K., Zosh, J.M., Golinkoff, R.M., Gray, J.H., Robb, M.B. and Kaufman, J. (2015). Putting Education in “Educational” Apps Lessons From the Science of Learning. Psychological Science in the Public Interest, 16(1), pp.3-34.
Hollebrands, K. F., & Lee, H. S. (2012). Preparing to teach mathematics with technology: An integrated approach to geometry. Dubuque, IA: Kendall Hunt.
Jackson, S.A. (2014). Student reflections on multimodal course content delivery. Reference Services Review, 42(3), pp.467-483. http://dx.doi.org/10.1108/RSR-05-2014-0011
Lawrence, J.A. and Singhania, R.P. (2004). A study of teaching and testing strategies for a required statistics course for undergraduate business students. Journal of Education for Business, 79(6), pp.333-338.
Lewis, J.S. and Harrison, M.A. (2012). Online delivery as a course adjunct promotes active learning and student success. Teaching of Psychology,39(1), pp.72-76. doi:10.1177/0098628311430641
Macgregor, G. and Turner, J. (2009). Revisiting e-learning effectiveness: proposing a conceptual model. Interactive Technology and Smart Education,6(3), pp.156-172.
Marchese, T.J. (1997). The new conversations about learning: Insights from neuroscience and anthropology, cognitive science and work-place studies. Assessing impact: Evidence and action, pp.79-95.
McCann, B. M. (2006). “The Relationship Between Learning Styles, Learning Environments, And Student Success”. Journal of agricultural education, 47 (3), 14. 10.5032/jae.2006.03014
McLaren, C.H. (2004). A comparison of student persistence and performance in online and classroom business statistics experiences. Decision Sciences Journal of Innovative Education, 2(1), pp.1-10.
Milner, B., Squire, L.R. and Kandel, E.R. (1998). Cognitive neuroscience and the study of memory. Neuron, 20(3), pp.445-468.
Moeller, B. and Reitzes, T. (2011). Integrating Technology with Student-Centered Learning. A Report to the Nellie Mae Education Foundation.Education Development Center, Inc.
Nusir, S., Alsmadi, I., Al-Kabi, M. and Sharadgah, F. (2012). Studying the impact of using multimedia interactive programs at children ability to learn basic math skills. Acta Didactica Napocensia, 5(2), p.17-32.
Pajares, F., & Kranzler, J. (1995). Self-efficacy beliefs and general mental ability in mathematical problem-solving. Contemporary Educational Psychology, 20, 426-443.
Quigley, D. (2011). Internet and Independent E-Learning of School Age Children in Thailand (One Study). Online Submission.
Rausch, D.W. and Crawford, E.K. (2012). Cohorts, communities of inquiry, and course delivery methods: UTC best practices in learning—The hybrid learning community model. The Journal of Continuing Higher Education,60(3), pp.175-180. 10.1080/07377363.2013.722428
Ruthven, K., Hennessy, S. and Deaney, R. (2008). Constructions of dynamic geometry: A study of the interpretative flexibility of educational software in classroom practice. Computers & Education, 51(1), pp.297-317.
Savitz, R.M. and Savitz, F.R. (2010). Experience matters: Innovative techniques add up to mathematical achievement. Primus, 20(6), pp.517-528.
Schoenfeld, A. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics. In D. A. Grouws (Ed.) Handbook for research on mathematics teaching and learning (pp. 334-370). New York: Macmillian.
Schoenfeld, A. (1994). Reflections on doing and teaching mathematics. In A. Schoenfeld (Ed.), Mathematical Thinking and Problem Solving (pp. 53-69). Hillsdale, NJ: Lawrence Erlbaum Associates.
Seppala, M., Caprotti, O. and Xambó, S. (2006). March. Using web technologies to teach Mathematics. In Society for Information Technology & Teacher Education International Conference (Vol. 2006, No. 1, pp. 2679-2684).
Shallcross, D. E. and Harrison, T. G. (2007). Lectures: electronic presentations versus chalk and talk – a chemist’s view. Chemistry Education Research and Practice, 8 (1), 73-79
Skinner, B.F. and Holland, J.G. (1960). The use of teaching machines in college instruction. Teaching machines and programmed learning: A source book, pp.159-172.
Smith, G. G. and Ferguson, D. (2005). Student attrition in mathematics e-learning. Australasian Journal of Educational Technology, 21(3), 323-334.
Smith, G.G., Torres-Ayala, A.T. and Heindel, A.J. (2008). Disciplinary differences in E-learning instructional design. International Journal of E-Learning & Distance Education, 22(3), pp.63-88.
So, W.M.W. and Ching, N.Y.F. (2011). Pupil Science Learning in Resource-Based e-Learning Environments. Journal of Computers in Mathematics and Science Teaching, 30(2), pp.203-223.
Stacey, K. and Groves, S. (1985). Strategies for problem solving. Melbourne, Victoria: VICTRACC.
Steffe, L.P. (1983). The teaching experiment methodology in a constructivist research program. In Proceedings of the fourth international congress on mathematical education (Vol. 1, pp. 469-471). Birkhäuser: Boston, Massachusetts.
Tawil N.M., Zaharim, A., Ariff, F.H.M., Ismail, N.A., & Osman, M.H. (2010). Implementing E-learning in mathematics engineering for better understanding. AIKED'10 Proceedings of the 9th WSEAS. Iinternational Conference on Artificial Intelligence, Knowledge Engineering and Data Base.s.
Tawil N.M., Zaharim, Razali, N., Ismail, N.A., & Nopiah, Z. M. (2011). Importance-Satisfaction Analysis for Wiley Plus in Vector Calculus. 8th WSEAS International Conference on Engineering Education Technologies 2011, WORLD-EDU’11: Corfu Island.
Tawil, N.M., Ismail, N.A., Asshaari, I., Othman, H., Zaharim, A. and Bahaludin, H. (2013). Preference Learning Style in Engineering Mathematics: Students Perception of E-Learning. International Education Studies, 6(6), p. 61-65.
Temple, T. (2013). Focusing on Student Success: Assessment of Learning Outcomes in Blended Environments. Paper presented at the Lilly Conference on College and University Teaching, Greensboro, NC. https://delta.ncsu.edu/assets/Assessment-of-Outcomes-in-Blended-Environments.pdf
Thompson, P. W. (1985). Experience, problem solving, and learning mathematics: considerations in developing mathematics curricula. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp.189-236). Hillsdale, N.J: Lawrence Erlbaum.
Thorndike, E.L. (1913). The psychology of learning (Vol. 2). Teachers College, Columbia University.
Trawick, M.W., Lile, S.E. and Howsen, R.M. (2010). Predicting Performance for Online Students: Is It Better to Be Home Alone?. Journal of Applied Economics & Policy, 29(1), p.34-46.
Tularam, G. A (2013) Tertiary mathematics learning and performance in the environmental sciences: student preparedness for learning mathematics. Shaikshik Samvad; An International Journal of Education, 3(1). 24-33 Varanasi: Banares Hindu University
Tularam, G. A and Amri, S (2011). Tertiary mathematics learning and performance in first year mathematics in the environmental sciences: a case of student preparedness for learning mathematics', in Proceedings of Volcanic Delta 2011, the Eighth Southern Hemisphere Conference on Teaching and Learning Undergraduate Mathematics and Statistics, held in Rotorua, NZ during November 16-21; University of Canterbury and University of Auckland, Auckland.
Tularam, G. A. (1997). The Role of higher order thinking: metacognition and critical thinking in algebraic word problem solving: First Year in Higher Education - Strategies for Success in Transition Years. 5-8 July Auckland, New Zealand Auckland Institute of Technology, Auckland, NZ.
Tularam, G. A. (1998). The role of algebraic knowledge, higher-order thinking and affective factors in word-problem solving. In Proceedings of International Conference-Transformation in Higher Education (pp. 210), held 7-10 July in Auckland, New Zealand.
Tularam, G.A. and Hulsman, K. (2013). A study of first year tertiary students’ mathematical knowledge in non-mathematics majors–conceptual and procedural knowledge, logical thinking and creativity.
Tularam, G.A. and Hulsman, K. (2015). A Study of Students’ Conceptual, Procedural Knowledge, Logical Thinking and Creativity During the First Year of Tertiary Mathematics. International Journal for Mathematics Teaching & Learning.
Tunstall, L and Bosse, M. J. (2015) Promoting Quantitative Literacy in an Online College Algebra Course. Advancing Education in Quantitative Literacy, 8(2), 11: DOI: http://dx.doi.org/10.5038/1936-46184.108.40.206
Walker, J.D., Brooks, D.C. and Baepler, P. (2011). Pedagogy and space: Empirical research on new learning environments. Educause Quarterly, 34(4), p.n4. http://www.bgsu.edu/content/dam/BGSU/master-plan/documents/pedagogy-and-space.pdf
Ward, E., Morgan, T., McGowan, S., Spurgin, A.L. and Solley, M. (2012). Preparation, clinical support, and confidence of speech–language therapists managing clients with a tracheostomy in the UK. International Journal of Language & Communication Disorders, 47(3), pp.322-332.
Weber, J.M. and Lennon, R. (2007). Multi-Course Comparison of Traditional versus Web-Based Course Delivery Systems. Journal of Educators Online, 4(2):1-19.
Wegerif, R., Li, L. and Kaufman, J.C. (2015). The Routledge International Handbook of Research on Teaching Thinking. Routledge.
Wilder, R. L. (1981). Mathematics as a Cultural System. Pergamon, New York NY.
Wilder, R.L. (1953). The origin and growth of mathematical concepts. Bulletin of the American Mathematical Society, 59(5), pp.423-448.
Wilder, R.L. (1960). Mathematics: a Cultural Phenomenon. Dole, GE, 8.
Wilder, R.L. (1998). The cultural basis of mathematics. New directions in the philosophy of mathematics, pp.185-200.
Wilder, R.L. (2013). Evolution of mathematical concepts: An elementary study. Courier Corporation.
Wilson, D. and Allen, D. (2011). Success rates of online versus traditional college students. Research in Higher Education Journal, 14, p.1-9.
Wilson, J., Fernandez, M., & Hadaway, N. (1993). Mathematical problem solving. In P. S. Wilson (Ed.) Research ideas for the classroom: High school mathematics (pp. 57-78). New York: MacMillan.
Zang, Y (2005). An experiment on mathematics pedagogy: traditional method versus computer-assisted instruction. http://files.eric.ed.gov/fulltext/ED490695.pdf