This dissertation reports on an investigation of transition-to-proof students' understanding of proof by contradiction. A plethora of research on the construction aspect of proof by contradiction is available and suggests that the method is one of the most difficult for students to construct and comprehend. However, there is little research on the students' comprehension of proofs and, in particular, proofs by contradiction. This study aims to fill this gap in the literature. Applying the cognitive lens of Action-Process-Object-Schema (APOS) Theory to proof by contradiction, this study proposes a preliminary genetic decomposition for how a student might construct the concept `proof by contradiction' and a series of five teaching interventions based on this preliminary genetic decomposition. Data was analyzed in two ways: (1) group analysis of the first two teaching interventions to consider students' initial conceptions of the proof method and (2) case study analysis of two individuals to consider how students' understanding developed over time. The genetic decomposition and teaching interventions were then revised based on the results of the data analysis. This study concludes with implications for teaching the concept of proof by contradiction and suggestions for further research on the topic.

職司審判之法院，其職權係為「認定事實」與「適用法律」。就事實之認定，我國採取「自由心證原則」，亦即事實應如何透過證據證明、推論而得，授權由法官於個案中認定，然該原則中「自由」之意義，係具有其具體之內在內涵與外在限制，並非由法官恣意判斷。過去之實務與學說並未就此為深入之闡釋，迭生審級平行與垂直判決之歧異，及人民對法院判決之非議。從而根本之道，應係完整建構自由心證原則之實質意義，由運用之主體、客體、內在內涵、外在限制及其作用等面向，並提出其運用之模組，具體化此立法者規範之不確定法律概念，使運用該原則之法官，得以有依循及參考之路徑。 而自由心證原則內涵中，最常於訴訟中運用者，即為「間接證明」，因主要事實由直接證據直接證明乃少見之情狀，而由間接證據證明間接事實，進而依間接事實之推理作用，推論主要事實存否之情形，乃訴訟中之常態。然間接證明之內涵中，「間接事實之內容與數量」、「推理作用之內涵」、「間接事實間推理作用所得證明主要事實之射程」，皆係高度個案裁量運用之認定，然現今實務之運作，卻出現審級間運用內容及結果極為歧異之現象，從而應探究其內涵，並嘗試提出運用之模組，供運用之法官思考。 自由心證與間接證明作為具有高度實務操作性格之訴訟法原則，其運用之 良窳，已實際影響具體個案事實認定之問題。為改善及斧正目前實務運作上出現之認定歧異、迭經發回之問題，亟須透過以上之研究，提出訴訟中運用之方式，以及其於事實審間、事實審與法律審間運用之審查、互動關係，使該二抽象原則具有一定法安定性，而有一定運用之軌跡可循。 / The court, to act as trial institute, has its major authority to “determine the fact” as well as “apply the law”. As for the fact-finding, our country adopts “Free Evaluation of Evidence Principle”, which authorizes the judge to determine case by case how the fact is proved and inferred through the evidences. However, the meaning of “Free” in that principle is constructed with concrete inner connotation and outer restriction, and not decided by the willfulness of the judge. In the past, courts and scholars didn’t elaborate that principle in depth, which has given a rise to the discrepant verdicts between different courts and criticisms from the people. Consequently, the fundamental solution is to build the substantial connotation of free evaluation of evidence principle, by means of the observations of its operating subject, object, inner connotation, outer restriction and function as well as its operating model, and to reify this uncertain concept of law regulated by legislator, so as to find a way to follow and refer to by the judge. The most commonly-adopted content of free evaluation of evidence principle is “Indirect Proof ”. Owing to proving the direct fact through direct evidence is rarely seen in lawsuit, the application of proving indirect fact by indirect evidence, and then inferring the existence of direct fact through the inferring function of indirect fact, is much common in each case. Nevertheless, in the meaning of Indirect Proof, the “content and amount of indirect fact”, “content of inferring function” and “scope which the direct fact could be inferred from the direct fact” are determined by large-scale discretion of the judge case by case. As a result of the discretion, the circumstances of divergent operating contents and consequences are emerged. Therefore, the connotation of that principle should be analyzed and the operating models are tried to addressed, hoping to provide for the judge to take into account. “Free Evaluation of Evidence Principle” and “Indirect Proof”, which are conducted as civil procedural principle in a highly individually case-operating nature, substantially influence the fact-finding in specific lawsuit with its odds and ends of operation. In order to improve and correct the discrepant fact-finding and constantly-verdict-reversing problems appearing in the courts at present, it is necessary to bring up the ways to operate the two principles as well as the reviewing and interacting relationships between trial courts and trial court and trial of law, and to establish specific legal certainty, legal steability and operation standards.