Abstract:

We have developed mathematical e-learning site which consists of over two thousand pages to produce effective and efficient mathematical learning environment for more than ten years. The concept of our e-learning website is “Online Mathematics Resources”. We allocate one unit of mathematical knowledge to one web page and then insert hyperlinks on important keywords and key phrases carefully so as to refer to other web pages efficiently. As a result, hyperlinks generate complicate network, which resembles the knowledge structure of mathematics. Recently we engaged two researches. The one is “Graph Drawing of Knowledge Structure of Mathematics”. The other is “Hierarchy Construction of Mathematical Knowledge”. Based on the previous researches, we developed a new interface between human and e-learning materials which is graph drawing of knowledge structure of mathematics combined with knowledge level. We used Gephi which was open source software to draw the network graph. Network graph is displayed on a web page by using the JavaScript GEXF (Graph Exchange XML Format) Viewer for Gephi which is under the MIT (Massachusetts Institute of Technology) license. We added some functions to the Viewer. The number of nodes is 759 and the number of edges is 2194. Titles of web pages are allocated to node labels. Node size depends on the number of inbound links to the web page. Large node means the node which have many inbound links or key knowledge of mathematics. We divided hierarchy of mathematics knowledge evenly into 11 parts and allocate each part to each color. 11 colors are 11 gradations from blue to red via green. That is, blue color nodes indicate the most basic level knowledge group, green color nodes indicate mid-level knowledge group and red color nodes indicate the most advanced level knowledge group. We can intuitively know the importance of mathematical knowledge by the size of nodes and the knowledge level of mathematics by the color of nodes. If we select a node (i.e. a mathematical knowledge on the graph drawing), a side menu appears on the left of the graph drawing. On the side menu, there is a hyperlink connected to the web page of the selected node, inbound links list and the outbound links list. The inbound links list shows the nodes linking to selected node which are listed in order of hierarchy. These nodes (i.e. mathematical knowledge) are more advanced knowledge than the selected knowledge. The outbound links list shows nodes linked to form selected node which are listed in order of hierarchy. These nodes (i.e. mathematical knowledge) are more basic knowledge than the selected knowledge. The JavaScript GEXF Viewer has a function to zoom in and zoom out the graph drawing. We can grasp the outline of mathematical knowledge by zooming out the graph drawing and we can understand the micro structure of mathematics knowledge by zooming in the graph drawing. This interface is a very effective tool to learn and to navigate the learning materials which learners wish to learn. This interface guides the learner who has good motivation for learning advanced level to web pages whose contents are advanced level. This interface also guides the learner who has poor knowledge about the selected knowledge to web pages whose contents are basic level. The interface is already open to the public on the Internet.

Keywords:

Graph drawing, Knowledge structure, mathematics, network.