本研究對等量公理進行概念分析，探討等量公理所包含的概念成份及成份間的關係，並據此提出等量公理的概念結構，發展等量公理概念的層次性，最後嘗試建立評量學生對等量公理層次瞭解的工具。
本研究採用文獻分析法與調查研究法，進行方式是透過對所蒐集文獻的分析，以及使用自行開發的題目，並採用蓋特曼量表的理念對等量公理作層次性的評量。本研究的研究對象是以便利取樣選取台北市某國中七年級的五個班級，合計共安排159名學生進行調查。
研究分析的結果顯示，等量公理包含了「相等概念」與「等量操作」兩種概念，且等量公理的概念內涵具有層次性，由低至高的順序分別為：（一）相等概念；（二）等量公理基本理解；（三）等量公理交叉應用。
據本研究所蒐集的資料，有證據顯示，通過第一層的學生約為76.73%；通過第一層與第二層的學生約32.08%；通過第一、第二和第三層的學生約18.88%，而符合蓋特曼量表之常態表現的學生佔全體總數88.68%。
研究結果部分顯示，本研究題目可作為初步判別學生對等量公理概念瞭解程度的依據，故此份題目可提供教師作為教授等量公理課程時，判斷學生在學習上的差異，藉以發現學生在等量公理之學習狀況進行更深入的瞭解，並對於學習狀況較不足的學生，進行補救教學設計之依據。

關鍵字：等量公理、相等概念、等量公理基本理解、等量公理交叉應用、等量公理概念層次

This research proceeds conceptual analysis of Property of Equality to clarify the conceptual components and the relationship among components. Accordingly, it proposes the conceptual structure of Property of Equality, develops its hierarchy. Finally, for the students to understand the hierarchy of Property of Equality, it tries to establish the evaluation tools.
This study adopts content analysis method for survey research, utilizes questions developed by the researcher, and applies to Guttman Scale to conduct analysis of the hierarchical structure. The subjects are five classes in 7th grade in certain junior high school in Taipei City with a total of 159 students for the survey.
The research results show that Property of Equality consist of two concepts, “equality” and “operation of equality.” In addition, it is characterized with hierarchy, from the low to high are: (1) Equality; (2) Basic understanding of Property of Equality; and (3) Cross application of Property of Equality.
By Guttman Scale for analysis of hierarchical structure, it is found that the percentage of those who pass the 1st layer is around 76.73%; that of those who pass the1st and 2nd layer is about 32.08%; that of those who pass all the 3 layers is about 18.88%. Students who match the normal performance of Guttman Scale occupies 88.68% of the total.
The research results find that we can determine how the students understand the Property of Equality by model, including the hierarchical structure and the questions. We can offer the questions to the teachers to judge students’ variance in learning Property of Equality. By means of the questions, it can be found that the students are performing better in Property of Equality. As a result, the teaching content can be deepened and broadened to enhance students’ ability in this area. In contrast, for those who perform fair, we may raise their learning ability by the abovementioned model to make up the insufficiency of teaching design.

Keywords:Property of Equality, Equality, Basic understanding of Property of Equality, Cross application of Property of Equality, The Conceptual Hierarchy of Property of Equality

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