Development of a Problem-Based Learning Model Integrated with 21st Century Skills

This research aims to develop the PBL-4C Learning Model to promote mathematical problem-solving skills among students and to create a valid, practical, and effective PBL-4C learning model. It falls under the category of research and development (R&D). The model development process follows the Plomp development model, which comprises four phases: (1) initial investigation phase, involving student needs analysis, task analysis, concept analysis, and learning objective formulation; (2) design phase, encompassing the design of the PBL-4C learning model, including model syntax, social principles, reaction principles, instructional impact, facilitation, and support system; (3) implementation phase, which involves the complete construction of the PBL-4C model based on the previous design phase; and (4) testing, evaluation, and revision phase, which includes validation and pilot testing. The validation results of various validity instruments include the average score of the PBL-4C learning model book (3.67), student’s book (3.98), student’s worksheets (4.35), lesson plans (4.48), learning outcome tests (3.71), students’ response questionnaires on the implementation of the PBL-4C learning model (4.12), students’ response questionnaires on the student’s worksheets (3.73), students’ response questionnaires on the student’s book (3.75), teacher’s response questionnaires (3.65), students’ activity observation sheets (3.75), and learning implementation observation sheets (3.40). Each of these validity instruments falls under the highly valid category, indicating that the PBL-4C learning model book and its supporting instruments meet the validity criteria. The PBL-4C model product is effectively implemented in teaching mathematics, specifically the topic of systems of linear equations with two variables. The effectiveness of the PBL-4C learning model is evaluated based on data analysis of its effectiveness components: (a) the average percentage of student activities during the implementation of the PBL-4C model in pilot test I is 63.25%, which falls under the "good" category, and the average percentage of student activities in pilot test II is 79%, falling under the "good" category; (b) the average percentage of student responses in pilot test I is 76% with positive responses, and in pilot test II, it is 82% with positive responses; (c) the learning outcome test results indicate that in pilot test I, 80% of students achieved mastery, while in pilot test II, 92% of students achieved mastery, thus meeting the criteria for classical mastery.