本研究的目的是為了改善幾何證明學習成就偏低的現況，所進行的教學研究。首先根據文獻與實務的探討所得，發展四類幾何證明的教學套件一發展分析能力的套件、動手操弄幾何證明的套件、邏輯序列的套件、破除迷思的套件，以其進行實地教學，從中探討學生在幾何證明的學習現象與心智活動，以及教學成效。
研究樣本是國三已修畢幾何證明課程的自學班學生，其中主要參與教學的學生有15位，以中下程度者居多；採用的研究工具有：四類教學套件，省思問卷，以及評估學生表現的前、後測卷、范氏幾何學測驗，而依研究工具的目的與性質，分別以24位（全班）、及這15位學生作為研究對象。
研究方法以質的研究為主。所收集的資料除了研究工具所測得的結果外，還包括探究教學期間所得之錄影、省思札記等資料，以及針對後測卷進行事後訪的記錄。
針對研究目的，本研究主要的研究結果如下：
(一)在教學過程之後，學生於幾何思維、結構式證明、形體性質與數學概念三方面都所提昇。
(二)學生作證明題時缺乏整合資訊的能力，也沒有作解題計畫，或發展出事後監控的基模。
(三)對特定的單元，分析學生的表現如下：1.擷取三角形全等條件時有兩種錯誤類型：一是不完整邊角的關係，二是所擷取的條件不成為全等條件。2.學生不易分析出非水平的平行線所得的對應截角。3.對於求證不等的關係式（如邊角關係），學習經驗是較負面的。4.使用「三角形平行線性質」時，此命題被學生視為是三個條件的組集，所運用的數學語言沒有邏輯關係存在。5.某些特定圖形下的平行線，會造成附加條件或是序列跳躍等邏輯推演上的盲點。
(四)幾何證明學習成就較低的學生，在「三角形全等」的證明表現，仍可達到某種程度的能力，但他們傾向直接憶取視覺上的訊息，不能將資訊加以分析。
(五)多數學生對譓有效性、自我確定度、以及證明附圖的看法，有別於數學家族群的看法。而多數學生覺得要驗證數學敘述，證明是必要的。
(六)在學習經驗方面，約四分之一到三分之一的學生以記憶為其學習策略；而近三分之一的學生對幾何證明抱持負面的情緒。

In order to improve low achiever in geometry proof, the study aims to investigate teaching modules in helping them, particularly at Junior High School level Firstly, according to the result of literature review and practical teaching experience, we develop four sets of teaching modules including developing analysis-level set, manipulation set of geometry proof, logic sequence set, and breaking misconception set Secondly, we use developed material to achieve the treatment in which we probe into learning phenomenon and evaluating the effect of the treatment.
In addition to the teaching material, we use four instruments including pretest, posttest, van Hiele Geometry Test, and students' reflection questionnaire. The whole sample of the study had studied geometry proof course for a semester, and according to different instruments, we select separately 24 (the whole class) and 15 (the main sample) students to be subjects. Most of the main sample who participated in the treatment are middle-lower level. And we mainly use qualitative methods. In addition to outcome from four instruments, the data collection included videotapes, students' script performance, and researcher's note during the treatment, and interview with 15 students participated after the treatment.
The main results of the study are as follows:
(1) After the treatment, sample students make progress in three aspects including geometric thinking level of van Hiele model, proving, and understanding properties of shapes and mathematical concepts.
(2) Through analyzng the students' performance in doing geometry proof, we find the following situations: (a) students lack the ability of integrating information and rarely plan for problem-solving in process of proving, and it is necessary to develop their meta self-control schemas; (b) there are some misconception and learning difficulties; (c) students whose van Hiele level are the lowest can do some dind of proving after the treatment.
(3) From van Hiele Geometry Test, we infer that about a half of the whole class is below level 0 after one semester studyng geometry proof.
(4) From students' reflection questionnaire, we get the inference as follows: (a) in the validity of mathematical proof, degree of self-certainty, and, the awareness of the representation of a picture attached to proof, most students are different from mathematician; (b) From the perspective of learning experience in geometry proof, about one fourth to one third of students adopt memory strategy, and about one third hold learning attitude.