The Effects of Discovery-Based Mathematics Instruction Using Circular Paper Folding Activities Focus on Grade 9 Students’ Problem-Solving Ability on Circles

Abstract

Background and Aims: Problem-solving ability is a crucial competency in mathematics learning. Students should continuously be supported in developing this ability. Discovery-based mathematics instruction provides opportunities for students to construct mathematical concepts and theories independently. This study integrated circular paper-folding activities grounded in the Concrete–Pictorial–Abstract (CPA) approach, which guides students from tangible experiences to pictorial representations and ultimately to abstract mathematical symbols. This process facilitates concept discovery and enables the application of these concepts in problem-solving contexts. The objectives of this research were: (1) to study Grade 9 students’ problem-solving ability on circles after learning by discovery-based instruction using circular paper folding activities, and (2) to study students’ learning behaviors during the implementation of this instructional approach.

Methodology: The target group consisted of 33 students from Grade 9/1, second semester of the 2024 academic year, at Nong Chok Pittayanusorn School, under the Nong Chok District Office, Bangkok. The instructional intervention comprised five lesson plans developed based on discovery learning principles and incorporating circular paper-folding activities. Research instruments included: (1) a set of five lesson plans on circles, and (2) a subjective problem-solving test consisting of four items. Quantitative data were analyzed using the arithmetic mean and percentage. Qualitative data were analyzed through students’ problem-solving traces and behaviors using content analysis and behavior observation techniques.

Results: The findings revealed that: (1) 75.75% of the students demonstrated problem-solving ability at a good level or higher; (2) Students’ performance on specific aspects of problem-solving ability was as follows: Application of theoretical concepts related to circles: Mean score of 6.81 out of 8 (85.13%). Logical reasoning: Mean score of 4.97 out of 8 (62.13%). Language use and written explanation: Mean score of 4.24 out of 8 (53.00%). (3) Most students were able to correctly apply theoretical concepts, use appropriate formulas, perform accurate calculations, reference relevant properties or theorems, and employ proper mathematical vocabulary and coherent explanatory structures in their written responses.

Conclusion: Discovery-based mathematics instruction employing circular paper-folding activities enhanced students’ problem-solving ability in the topic of circles. The instructional design, which emphasized students’ active engagement in discovering concepts through hands-on manipulation, visual representation, and abstraction, enabled learners to internalize mathematical theories and apply them effectively in solving problems.