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Education: Technology and Modern Education Theories to the Rescue of Calculus

By Aqualed @aqua_led
Educación: Tecnología y teorías educativas modernas al rescate del cálculo
With particular reference to calculus, we are all aware of its importance for engineering sciences; however, sometimes the outcomes and the benefits are not well "advertised", resulting in a number of hours that may get reduced on behalf of contents that is more "profitable". As a result, lecturers in charge of transmitting such a relevant knowledge may be forced to simultaneously compress the contents and make it more appealing to the the new generations, i.e., the potential customers. Unfortunately, to turn the contents into some kind of "for dummies" version may not be an appropriate solution.
Education: Technology and modern education theories to the rescue of calculusThe China Papers
Researchers who have eventually faced such a problem have proposed potential solutions within their particular institutions. In some countries in Asia, however, the proposals can have broader, country-level, relevance. We visited China during the APD-IAHR meeting in 2008, when we were gladly surprised by the open personality, the talent (the snapshot shows a moment of the cultural night brilliantly performed by the students of Nanjing University), and the hunger for knowledge of both students, lecturers and researchers. Thus, it was no surprise to hear a comment of one of the attendants on the concern of the country in improving educational schemes. One of the outcomes of such concern is the series of papers (The China Papers) published by the programme "Teaching Sciences in English", which is an exchange programme for university science and mathematics teachers between China and the University of Sydney in Australia. My entry below shows a short comment on two papers that make reference to such topic.  
Technology and modern education theory
As pointed out by Yuan (2002) and Jiang (2006), the use of websites to post pre-lecture and post-lecture materials has become a common resource to make a better use of lecture time (demanding much more time from the lecturer, though). The use of software such as Matlab, Mathematica, R, Maple, etc, is also recognized as a powerful tool which turns tangible the contents of apparently abstract subjects. In addition, adding historical facts to the cold theoretical contents, and the use of "problem based learning" are as well interesting resources that can be used to demonstrate the usefulness of the contents being transmitted. However, the use of the mentioned resources is unlikely to provide relevant advances without turning passive learning into an active process, as accurately pointed out by the latter mentioned authors. Such advances are perhaps the most relevant part of modern educational theories, which for better understanding may be well defined through a single and simple term (Robert Krulwich):
Pace
 (To give the audience the experience of making a discovery on their own; to use active learning techniques to have students working out answers for themselves).
Of course, the situation becomes much more complex when we have to deal with multicultural environments. Teachers are to be required to be more flexible, in order to increase their capability to deal with individuals from different cultures, different interests, different motivation levels, and under various states of maturity. Thus, the approach of providing easy to follow recipes (the popular "for dummies" versions) becomes automatically dull and obsolete. Then, pace gains relevance again as the universal key term.
References.
Yuan Z. 2002. Improving the qualities of teaching calculus - By using modern education theories and modern technologies.  The China Papers.
Jiang Z. 2006. Some ideas on how to trigger students´ interest in learning calculus.The China Papers.

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