本文擬透過教學績效獎金制度的設計，改善目前教育資源過度集中在少數菁英學生的不合理現象。前述作為，在目前少子化現象、學生受教機會不均等與現行教師獎金流於形式之今日，格外顯得重要。本文假定諸小學各學科試題皆已建立題庫，且題庫中各試題皆訂定有反應試題難易參考指標，可以將學生學科考試成績，依試題難易程度調整成為正規化後的成績；此外，不同學科正規化成績可以進一步依其上課時數比率，加權成單一綜合成績。為了說明方便，本文所謂學生學科考試成績，皆是指其各學科成績正規化後之加權成績。本模式假設班導師在接受班上學生學習潛力分布不均已成事實的情形下，如何將其教學關照資源做合理的分配，以獲得其最佳的教學績效獎金，為班導師所面臨的問題。在此問題狀況下，發放教學績效獎金之決策者(校長)，如何在班上學生學習能力分配不均下，以學生學科成績的努力度為基礎衡量班導師之教學績效，為本數學模式的主要內容。本數學模式具通用性:它不但可應用於誘導全校班導師，重視學科能力較差學生之教學績效獎金制度的設計，亦可應用於誘導全校班導師，重視學科能力較佳學生之教學績效獎金制度的設計。前述不同教學績效獎金制度的屬性比較則為本文主要研究結果。 In this study, we design a teaching performance reward system to improve the situation whereby unequal education opportunities provide only a minority of elite students with access to educational resources and thus provide a balancing effect on school education. This issue is importance with the dwindling birth rate. We also assume that a database of tests has already been established in primary schools for each subject, and that each question has been rated according to a Difficulty Index for normalizing student test scores. We will also obtain weighted averages for these normalized test scores based on the ratio of teaching hours. On the basis of the aforementioned assumptions, the issue provides the background for the mathematical modeling of a method by which decision makers will be able to measure teacher performance based on student academic performance in the face of unevenly distributed student learning abilities. This model can be applied to the design of a teaching performance reward system in which teachers focus on students with either poorer or higher academic achievements; the main results of this study are comparisons of the different attributes of this system.
