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32 | reyssat | 1 | |
2 | The rapid development of computer technology constantly chanllenges the |
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3 | education of mathematics at all levels. |
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4 | <p> |
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5 | On the one hand, the content of the education has to be adapted to the new |
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6 | situation. Not long ago, our schools and universities were teaching the use |
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7 | of logarithm tables and sliding rules; the advent of handheld calculators |
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8 | obsoleted these materials. Today, we (including the author of this document) |
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9 | are still teaching things like Newton's method for root, Simpson's method |
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10 | for numerical integration, or formal integration of a rational function. |
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11 | The reader has only to take a look at the tool |
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12 | !href target=wims_demo module=tool/analysis/function.$lang Function |
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17238 | bpr | 13 | on this WIMS site, to see how a simple web page can raise questions |
9071 | bpr | 14 | about the opportunity to spend hours or even weeks to |
32 | reyssat | 15 | teach these techniques to our students (while the solution is just one |
17228 | bpr | 16 | click away). <br> |
32 | reyssat | 17 | It is clear that computer technology allows (and forces) us to shift the |
18 | focus of our teaching more towards using mathematics to solve real-life |
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19 | problems, and towards a better understanding of fundamental mathematical |
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20 | concepts, away from techniques and skills of mathematical computations. |
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5798 | bpr | 21 | </p><p> |
32 | reyssat | 22 | On the other hand, new computer technology provides new means for our |
23 | educational system. A computer software can solve complicated mathematical |
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24 | problems very quickly, using methods and algorithms which are transparent to |
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25 | the user who doesn't want or doesn't has to know about them. The |
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26 | interaction between numbers and forms, very hard to implement under |
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27 | conventional methods, is very easily done on a computer screen. And a |
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28 | well-designed computer program can analyse or correct errors made by a |
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29 | student, and give him appropriate helps in real time. |
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5798 | bpr | 30 | </p><p> |
32 | reyssat | 31 | Obviously, adapting our mathematical education to the computer age requires |
32 | that computing technology be widely used in our teaching. This is still far |
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33 | from being today's reality, and the reasons are multiple. There is few, if not |
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34 | no, software dedicated to higher level mathematical education (because |
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35 | developping such a software is not cost effective?). The popular softwares |
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36 | currently widely used in universities are usually more destinated to experts |
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37 | rather than to students. A student has to invest a lot of time to learn how |
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38 | to use a software package, without being sure that such a knowledge about |
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39 | the package will still be useful when he finishes the study (the package may |
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40 | evolve or even disappear, the company he will work in may adopt another |
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41 | system, etc). Not to mention the logistical difficulty for an educational |
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42 | institution to install and maintain a large number of copies of softwares |
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43 | which change their versions often rapidly. |
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5798 | bpr | 44 | </p><p> |
32 | reyssat | 45 | In the opinion of the author, it is internet which will give the first real |
46 | solution to the above difficulties. Internet is a one-server, many-users |
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47 | system, which allows one installation to serve a large number of users. The |
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48 | html user interface is fool-proof and intuitive, and the user doesn't need |
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49 | to learn complicated manipulations in order to work on it. At the same time, |
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50 | it allows graphical and multimedia ingredients to be easily incorporated |
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51 | into applications. This interface is built on a language (html) which is easy |
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52 | to master and has become very popular nowadays. |
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53 | It is also easy to design student-supervisor interactions |
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54 | in various ways. Finally, the free-service and open-contribution nature of |
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55 | internet makes it possible to combine the knowledge and experience of the whole |
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56 | educational community, and redistribute them to the whole community. |
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5798 | bpr | 57 | </p><p> |
32 | reyssat | 58 | The basic problem for an immediate and direct use of http-html protocol into |
59 | mathematical education is the lack of some capabilities necessary for an |
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60 | educational use. Namely, the lack of support for building interactive and |
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61 | intelligent applications. Another problem is that the (current) html |
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62 | language has no support for mathematical expression. |
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5798 | bpr | 63 | </p><p> |
32 | reyssat | 64 | Existing experiences on the web are mostly based on java/javascript |
65 | interactivity. Due to the difficulty of java/javascript development for |
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66 | mathematics, these applications usually suffer from lack of power and of |
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9071 | bpr | 67 | interaction between applications. Please refer to the section |
1091 | bpr | 68 | $(ref1)compare$(ref2)compare">$title_compare</a> |
32 | reyssat | 69 | for more analyses about java/javascript. |
5798 | bpr | 70 | </p><p> |
32 | reyssat | 71 | There are also some web sites where dedicated mathematical softwares are |
72 | used as backend engine for web-based computational tools. While this |
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17238 | bpr | 73 | approach is close to the idea behind WIMS, the author did not find a |
32 | reyssat | 74 | systematic approach in this direction. |
5798 | bpr | 75 | </p><p> |
17238 | bpr | 76 | WIMS is designed to provide a systematic and evolutive way to add |
32 | reyssat | 77 | server-based interactivity to the html-javascript-java triplet. We have |
78 | adopted the concept of an open system, and special care has been taken |
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79 | to allow non-computer-specialists to make contributions to the system: a |
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80 | modular design with independent modules, a language with simple structure |
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81 | and close-to-natural syntax, and the concept of online development. Also, a |
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82 | tentative solution for including mathematical expressions in the html pages |
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83 | is provided. |
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5798 | bpr | 84 | </p> |