Investigating hypothetico-deductive reasoning using inductive approach

• Main Author: Escaran, Oliver M.
• Format: text
• Language: English
• Published: Animo Repository 2005
• Subjects: Geometry > Study and teaching (Secondary); Geometry > Problems, exercises, etc.; Euclid's Elements; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/3295; https://animorepository.dlsu.edu.ph/context/etd_masteral/article/10133/viewcontent/CDTG003909_P.pdf
• Institution: De La Salle University

This research investigated the hypothetico-deductive reasoning of the students in selected topics of the Euclidean geometry using a method in a constructivist perspective. Five basic topics on angles and lines, triangles, quadrilaterals, congruence and similarity had been used in this study to determine how the students could formulate hypotheses and write proofs on geometric problems. This study also sought to investigate the initial van Hiele levels that the students had acquired in high school geometry, using the interview protocol adapted from Burger and Shaughnessy. Then the study utilized the achievement test to find out if the students initial van Hiele levels had changed after they had been exposed to the inductive approach. The reliability of the achievement test was determined through the use of the Kuder- Richardson Formula 20. Item analysis was also employed to obtain the difficulty level and discrimination index of each item. The respondents were seven college sophomores majoring in mathematics, under Bachelor of Secondary and Elementary Education courses. They were enrolled in the geometry subject in the second semester of school year 2003-2004 at the Notre Dame of Jolo College, Jolo, Sulu. The data gathering was accomplished through the students exercises in the inductive approach that consisted of activity sheets, quizzes, interviews and the achievement test. The collection of data for the hypothetico-deductive reasoning in proving some geometric problems was conducted towards the end of the semester when all activities intended for this study in the inductive approach had been completed. The achievement test served as the final examination for the students. The data were interpreted through the level indicators set by Burger and ii Shaughnessy for van Hiele levels and the scoring criteria by Lawson for the concept acquisition on definitions of terms and conjectures. The results showed that the students who were expected to be at van Hieles level three of their high school geometry, upon investigation, had remained at the initial level or level one. The students ability to use their hypothetico-deductive reasoning in the given geometric proof tests was associated with the results of their achievement test in the inductive approach. In this light, results meeting the attainment of levels on topics in the inductive approach indicated an ability to write relevant proofs on similar topics in geometry problems, while results below the attainment of levels indicated inadequate performance in exercising ones hypothetico-deductive reasoning. The inductive approach helped the students list the needed concepts of a geometric figure by enumerating its properties or defining it, as they formulated conjectures or hypothesized statements. Although the students had been exposed to the preliminaries of proof writing, they lacked ample readiness to deal with the deductive level on formal proof writing in the Euclidean geometry. More time was needed for them to develop their proof writing skills.