Implementation of Inquiry Learning Model in Collaboration with PBL to Improve Student Understanding in Number Theory Course

The purpose of this study was to describe the presence or absence of the influence of the infusion learning model collaboration with Problem-Based Learning (PBL)  to develop students' understanding of proof and mathematical argumentation in number theory courses. This research is an experimental study with a randomized control group pretest-posttest design, two groups namely the experimental group and the control group. The experimental group is the group that uses the infusion learning model in collaboration with PBL, while the control group is the group that uses conventional learning. The subjects of this study consisted of 40 students at a university in Jombang, Indonesia. Data collection techniques through observation sheets, proof understanding tests and observation sheets of students' mathematical argumentation abilities. The results of the research show that the significant difference between the average proof of understanding of students in the experimental group and the control group. The difference between the average proof of understanding in the experimental group and the average proof of understanding of students in the control group was 21.75. Furthermore, the significant difference between the average argumentation ability of students in the experimental group and the control group. The difference between the average argumentation ability of students in the experimental group and the average argumentation ability of students in the control group is 5.25. Therefore, the implementasion of infusion learning in collaboration with PBL is more effective than conventional learning models for developing students' ability to understand mathematical proof and argumentation. This learning model promotes the development of critical thinking skills, problem-solving, conceptual and different understanding needed to construct a formal proof, and strong and valid arguments.