Exploring Students’ Procedural Fluency and Written Adaptive Reasoning Skills In Solving Open-Ended Problems

Abstract

Developing students’ mathematical skills requires both procedure and reasoning. However, the declination of possessing these skills is still evident today. Hence, this study aimed to describe the students’ procedural fluency in terms of accuracy, flexibility, and efficiency and written adaptive reasoning in terms of explanation and justification in solving open-ended problems. The study employed descriptive-correlational design through purposive sampling of thirty students from a National High School in Laguna, Philippines. The quantitative data revealed that in procedural fluency, students can quickly submit a complete solution leading to correct answer. However, they fail to provide two or more solutions in solving open-ended problems. The results also showed that students can clearly explain the problem but struggle to justify their solution. Moreover, procedural fluency is positively correlated to their adaptive reasoning. Consequently, students with an average level of mathematical achievement scored significantly higher than those at a low mathematical level in terms of flexibility. Pedagogical implications suggest that problem-solving activities for students should not solely focus on getting the correct procedures and answers. Further, it is recommended that teachers should expose students in open-ended problems and allow them to try and justify their own unique solutions irrespective of their mathematical achievement.

Keywords

• mathematical achievement
• open-ended problems
• procedural fluency
• problem-solving
• written adaptive reasoning