FACTORS INFLUENCING STUDENTS' PREFERENCES ON EMPIRICAL AND DEDUCTIVE PROOFS IN GEOMETRY

The purpose of this study is to investigate what influences students' preferences on empirical and deductive proofs and find their relations. Although empirical and deductive proofs have been seen as a significant aspect of school mathematics, literatures have indicated that students tend to have a preference for empirical proof when they are convinced a mathematical statement. Several studies highlighted students'views about empirical and deductive proof. However, there are few attempts to find the relations of their views about these two proofs. The study was conducted to 47 students in 7~9 grades in the transition from empirical proof to deductive proof according to their mathematics curriculum. The data was collected on the written questionnaire asking students to choose one between empirical and deductive proofs in verifying that the sum of angles in any triangles is $180^{\circ}$. Further, they were asked to provide explanations for their preferences. Students' responses were coded and these codes were categorized to find the relations. As a result, students' responses could be categorized by 3 factors; accuracy of measurement, representative of triangles, and mathematics principles. First, the preferences on empirical proof were derived from considering the measurement as an accurate method, while conceiving the possibility of errors in measurement derived the preferences on deductive proof. Second, a number of students thought that verifying the statement for three different types of triangles -acute, right, obtuse triangles - in empirical proof was enough to convince the statement, while other students regarded these different types of triangles merely as partial examples of triangles and so they preferred deductive proof. Finally, students preferring empirical proof thought that using mathematical principles such as the properties of alternate or corresponding angles made proof more difficult to understand. Students preferring deductive proof, on the other hand, explained roles of these mathematical principles as verification, explanation, and application to other problems. The results indicated that students' preferences were due to their different perceptions of these common factors.

중학생의 경험적 증명과 연역적 증명에 대한 선호 요인 분석

본 연구는 중학생을 대상으로 학생들이 경험적 증명과 연역적 증명에 대한 선호를 결정할 때 영향을 미치는 요인을 분석하였다. 47명의 중학생에게 설문지를 통하여 자료를 수집하고 응답들을 분석한 결과, 경험적 증명과 연역적 증명의 선호에 영향을 미치는 요인들로 측정, 수학적 원리, 다양한 예를 통한 검증과정에 대한 인식들이 공통적으로 나타났다. 이 요소들은 경험적 증명과 연역적 증명의 선호와 비선호를 결정짓는 요인으로써, 선호하는 증명에 따라 상호 배타적으로 나타나지 않고 증명 선호에 영향을 미쳤다. 이를 통해 본 연구에서는 학생들이 특정 증명을 선호할 때, 한 증명에 대한 비선호와 다른 증명에 대한 선호가 동시에 작용할 수 있다는 결론과 함께 한 증명에 대한 선호요인을 보는 것만으로는 학생들의 증명 선호 이유를 정확히 파악할 수 없을 것이라는 가능성을 제언한다.