近來，將資料轉成階層圖的方法，特別受到教育統計學者之青睐。例如：何氏圖、概 念圖等方面之研究，均以獨特之技術，將數據呈現爲階層結構圖。因此，以階層結構圖的 方式呈現資料，大大提高對資料分析的認同。然而，這類實證性研究顯示，所呈現之階層 結構圖若過於複雜，特別是因爲交錯邊過多，往往降低階層結構圖之可讀性與實用性。再 者，雖然目前已有很多方法可以解決降低交錯邊過多的問題，特別又以IM法最受推崇， 但是這些方法皆有其限制。基於此，本研究擬先以實例分析IM法演算法的問題點，其 次，根據劉湘川教授對IM法中重要度指數改良的兩種方法，以實例比較此二法與IM法 之成效。最後應用減少交錯邊之技術，建立可讀性高之數與計算主題教材地位圖。本研究 之發現： 一、 關於IM法之演算法之問題點方面：對於2階正規非循環有向圖之減少交錯邊處 理，IM法的處理成效有限。另外，以挑選能放置於離中心軸最近的頂點之準則， 有時反而無法得到最少減少交錯邊之圖。 二、 關於三種減少交錯邊方法之成效分析方面：IM法頂點之重要度小於等於邊路徑法 之重要度，且邊路徑法之重要度小於等於邊路徑位序法之重要度。其次，在某些條 件下，發現IM法、邊路徑法與邊路徑位序法之成效相同。此外，IM法、邊路徑 法與邊路徑位序法，在減少交錯邊處理上，各有處理得好與不佳的情形之實例。 三、 關於應用減少交錯邊之技術方面：建置數與計算教材地位圖，且得到三個概念分群 的效果。

Recently, the method which makes data to be converted to a layer diagram has drawn much attention to the educational statistics. These researchers used proper technique to let data present as a hierarchical graph, for example, Forrester diagram and Concept diagram. Thus, presenting data into hierarchical graph is important in data analysis. However, the empirical study shows that if hierarchical graph is over-complex, then it often reduces readability and practicability. Moreover, although nowadays there are many methods to solve the problem above, such as IM method, these methods have their restriction. Thus, our first purpose is to analyze the algorithm problem of IMM by using MATLAB program. Secondly, two methods developed by Liu are studied and compared with IM. Finally, we apply these methods to build hierarchical graph of teaching in the unit of number and count. Our main results are as follows. 1.On the algorithm of IMM, we point out two issues on reducing the number of crossing edges. 2.On the effects of three methods above, we find that the importance index of IMM is less than or equal to that of EPM. And the importance index of EPM is less than or equal to that of EPOM. Secondly, under certain conditions, the effect of IMM, EPM and EPOM is the same. 3.On the application, we propose a hierarchical graph of teaching with high readability. Besides, three important subgroups of concepts concerning number and count are found in this graph.