International Journal of Recent Technology and Engineering (IJRTE) ISSN: 2277-3878, Volume-7 Issue-4S2, December 2018 305 Retrieval Number: ES2011501751918/18©BEIESP Published By: Blue Eyes Intelligence Engineering & Sciences Publication Abstract: we have been developing the visualization system of mathematical knowledge structure based on the hyperlink structure of mathematical e-learning website and expanding the knowledge structure to the field of STEM. We applied this technology to mathematical exercises which are incorporated into our mathematical e-learning website and developed a new visualization system which shows knowledge necessary for solving mathematical questions by using network graphs. This system support learners who don’t have enough knowledge to solve questions by indicating what knowledge is necessary. The learner can study basic knowledge by just clicking hyperlinks on the knowledge structure map. We also developed print materials combined with the new system via QR code. This visualization system is a good tool for self-adaptive learning. Index Terms: E-Learning; Network Graph; Hyperlink; Knowledge Structure; Mathematical Question. I. INTRODUCTION E-learning is widely used in modern education and will spread more in the future. There are many sorts of e-learnings and many ways to categorize them. S. Negash and M. V. Wilcox proposed six classifications according to presence and communication [1]. In the case of focusing on learning strategies, e-learnings were categorized into two types: instructive learning and constructive learning [2, 3]. There are many e-learnings of instructive type which are already used by many people such as Massive Open Online Courses (MOOC). Coursera, Udacity and edX are popular MOOCs. On the other hand, people tend to use online dictionary instead of a traditional paper dictionary. In addition, most of people use search engines on a daily basis to learn what they do not know when they encounter it. This action is a kind of constructive learning. We consider that learning using search engines is an essential action for learners who live in an Internet world. Therefore, Wikipedia becomes one of the most popular websites as learning materials. These two types of learning are complementary to each other. For example, when learners attend an e-learning of instructive type and encounter what they are not able to understand, they might use search engines to understand it. We focus on the latter type of learning and started to develop mathematics e-learning Revised Manuscript Received on December 30, 2018. Akira Nakamura, Mathematics and Science Academic Foundations Programs, Kanazawa Institute of Technology, Nonoich, Japan. Tomoshige Kudo, Mathematics and Science Academic Foundations Programs, Kanazawa Institute of Technology, Nonoich, Japan. Keita Nishioka, Mathematics and Science Academic Foundations Programs, Kanazawa Institute of Technology, Nonoich, Japan. website whose concept was an online dictionary on mathematics [4]. Therefore, our website is open to the public. We expand our e-learning website from the field of mathematics to the field of science, technology, engineering and mathematics (STEM). But we find demerit of dictionary type of e-learning materials. There is no instruction like syllabus which describes what kind of things learners study and shows them in what order to study them. In other word, instructive e-learning offers their learning path. On the other hand, in constructive learning, learners have to make their learning path according to their knowledge level and their interest. We consider this learning style belongs to self-adaptive learning. So we developed the visualizing system of knowledge structure of mathematics in order to support self-adaptive learning [5-8]. Exercise is very important to master mathematics. Every mathematics textbooks have exercise for learners to acquire mathematics knowledge deeply. We made exercise web pages and integrate them into our mathematical e-learning website using hyperlink connections. We incorporate our visualization system of knowledge structure into practice of mathematics exercise. We tried to combine print materials and web materials to establish a new learning style [9, 10]. Our purpose of developing STEM e-learning is to build an efficient learning environment for self-adaptive learning. In this paper, we introduce a previous research about visualization of knowledge structure of STEM and then present a new developed visualization system which shows important knowledge necessary for solving problem using network graph. DEVELOPING STEM WEB SITE A. E-Lerning Web Site Design We have been developing STEM website which integrates three websites which are open to the public on the Internet [11, 12]. The first is KIT Mathematics Navigation [13] which has been developed since 2004 dealing with precalculus and calculus. The acronym KIT stands for Kanazawa Institute of Technology. The second is KIT Physics Navigation [14] which has been developed since 2015, covering mainly mechanics at this moment and extending to other fields such as electricity and magnetism. The third is KIT Engineering Navigation [15] which has been developed since 2017, dealing with Euler–Bernoulli beam theory in material mechanics as of now. Development of Visualization System of Knowledge Necessary for Solving Mathematical Questions Akira Nakamura, Tomoshige Kudo, Keita Nishioka