體育系學生在相關課程的學習上，除了對於傳統體育技能、心理、生理與訓練等學能力求精進外，為求增進體育的多元發展，更需要對於資源管理、行銷傳播等領域加強跨領域學習，學習難度與壓力也與日俱增。也因此，知覺教師自主支持、心理需求與期望價值之於相關課程的學習動機與成績的角色與比例也益發重要。而另一方面，在社會科學的領域中，機率與統計的相關方法與概念也常被應用在設定比例的評估與計算。所以，本研究的目標是利用機率與統計中的一些比例分配概念來針對體育系學生知覺教師自主支持、心理需求與期望價值之於相關課程的學習動機與成績的比例來尋求有效的分析與制訂方法。然而，學生知覺教師自主支持、心理需求與期望價值的屬性多元複雜，所應考慮之主客觀因素之間的關係更是盤根錯節，因此，本文先以社會科學中既有機率與統計方法進行初步基礎理論分析，再參酌實際狀況發展相關學術理論，藉此提供拓展至實際課程實施模式的可行性。主要步驟如下：
一、首先，我們先分析一些關於體育系學生知覺教師自主支持、心理需求與期望價值的行為，將這些行為模式化，並且拓展到相關體育系課程實施模式的架構。
二、接下來，我們研究機率與統計中最基本的邊際貢獻（balanced contributions）與期望值（the expected value）的概念、以邊際貢獻與期望值為基礎而發展的比例計算方法—不可分割消費均等分配（the equal allocation of nonseparable costs, the EANSC）、一些公平公正的性質以及一些已經被學者們針對邊際貢獻以及不可分割消費均等分配所提出的相關理論概念與計算結果。
三、緊接著，這些公平公正的性質和相關的理論與應用結果會根據現實狀況的現象而被賦予在管理科學、教育學與課程教學上各自的意義。我們也會將這些性質以及不可分割消費均等分配的相關理論與應用結果拓展到實際相關體育課程實施模式的架構。
四、藉由分析體育系學生知覺教師自主支持、心理需求與期望價值的行為模式，配合現實管理科學、教育學和課程教學特性以及相關課程教學策略之間的交互關係來呈現理論的適用可行性。
本研究的結論期望藉由邊際貢獻、期望值與不可分割消費均等分配的比例分配概念針對體育系學生知覺教師自主支持、心理需求與期望價值提出最均衡的比例，可以有效提升課程學習動機與成績。而衍生出的建議也希望社會科學或管理科學領域的其他策略比例分配方法，比如決策分析（decision-making），或許也可以在日後被嘗試應用在學生知覺教師自主支持、心理需求與期望價值的相關研究。

In addition to improving the soprts skills and the abilities of psychology, physiology and training, the students of department of physical should interdisciplinary study more fields to increase diverse development in the framework of physical education, such as resouce management, marketing communication, and so on. Moreover, related difficulty and stress may increase with each learning day. Therefore, the proportion among perceived teacher autonomy support, psychological needs and expectancy-value plays important role on learning motivation and academic record in physical education classes. On the other hand, probability and statistics applied always in the setting of evaluation and computing for proportion in the framework of social sciences. In order to find the optimal proportion among perceived teacher autonomy support, psychological needs and expectancy-value due to learning motivation and academic record of students of department of physical education, the goal of this paper aims to introduce efficiency analysis and rules by considering some notions of probability and statistics. However, the characteristics, the factors and relations among perceived teacher autonomy support, psychological needs and expectancy-value due to learning motivation and academic record of students of department of physical education are various and complicated. In order to provide the feasibility under the setting among perceived teacher autonomy support, psychological needs and expectancy-value due to learning motivation and academic record of students of department of physical education in future, we firstly adpot pre-existing results of probability and statistics on social sciences to introduce elementary theoretical analysis, and further propose related theoretical results by considering real situations. The main steps are as follows:
1.First, we analyze some theoretical models and results of probability and statistics on social sciences, and adopt these models and results to build the framework of the behavior and strategies of perceived teacher autonomy support, psychological needs and expectancy-value due to learning motivation and academic record of students of department of physical education.
2.Further, we study the notions of the balanced contributions, the expected value and a generated evaluation and computing method—the equal allocation of nonseparable costs (EANSC), some theoretical properties and pre-existing results of the balanced contributions, the expected value and the EANSC.
3.Subsequently, these theoretical properties and academic results of the balanced contributions, the expected value and the EANSC will be asserted by some meanings of real-world management, physical education and related teaching. Also, we apply these theoretical properties and academic results to analyze the models of the behavior, strategies of teaching in the framework of physical education classes.
4.Finally, we provide provide the feasibility for the application of our theoretical results by analyzing the relationships among our theoretical results, the properties of management sciences, education sciences and class-teaching in real-world, and the behavior and strategies of perceived teacher autonomy support, psychological needs and expectancy-value due to learning motivation and academic record of students of department of physical education.

The conclusion of this paper shows that the allocation notions of balanced contributions, the expected value and the EANSC may be applied to the framework of optimal proportion for the behavior and strategies of perceived teacher autonomy support, psychological needs and expectancy-value due to learning motivation and academic record of students of department of physical education. The further suggestions also show that different allocation notions for proportion and related results on social sciences or management sciences may be applied to the framework of the behavior and strategies of perceived teacher autonomy support, psychological needs and expectancy-value due to learning motivation and academic record of students of department of physical education, such as decision-making and so on.

第壹章 緒論 1
第一節 研究背景與重要性 2
第二節 研究動機 7
第三節 研究問題與研究目的 9
第四節 名詞釋義 12
第五節 研究範圍與限制 14
第貳章 文獻探討 17
第一節 模型結構、邊際貢獻、期望值與不可分割消費均等分配之簡述 17
第二節 已經存在的公設化理論結果 19
第三節 知覺教師自主支持、心理需求與期望價值之於相關課程相關文獻回顧與探討 24
第參章 研究設計與實施 51
第一節 研究所需之模型架構 51
第二節 研究對象 54
第三節 研究工具 55
第四節 研究流程 56
第肆章 研究結果與討論 61
第一節 邊際貢獻與期望值理論相關之學術研究結果 61
第二節 體育系學生知覺教師自主支持、心理需求與期望價值在體育相關課程的學習動機與成績等各類因素的比例分配與社會科學、管理科學之間的關連性分析 69
第伍章 結論與建議 79
第一節 研究結論 79
第二節 研究建議 82
參考文獻 85

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