Manipulative interactive didactics with puzzles: An effective solution for overcoming junior high school students' learning obstacles to quadrilateral materials

The study of learning obstacles is essential to develop students' competencies and improve the quality of learning that is responsive, inclusive, and relevant in the 21st century. The purpose of this study is to identify learning obstacles related to misconceptions regarding quadrilateral material and students' mathematical creativity, and to find effective empirical didactic designs to overcome these learning obstacles. The research methodology used is didactic design research (DDR), which consists of four frameworks: Initial data collection, prospective analysis, metapedidactic analysis, and retrospective analysis. These stages are cyclical. The study involved 172 junior high school students and six model teachers. Data was collected using the quadrilateral writing creativity test, interviews, documents, and field notes. Data analysis was conducted simultaneously using quantitative and qualitative approaches. The study produced empirical didactic designs, namely manipulative interactive didactics with puzzles, which are equipped with a guide for teachers to manage learning. This empirical didactic design includes seven frameworks that have been shown to be effective in overcoming didactic and epistemological barriers—scaffolding, questioning skills, brainstorming, learning opportunities, conceptual representation of mathematical creativity, misconceptions, and concept representation. Teachers can implement or adapt this empirical instructional design for use in geometry subtopics or other mathematics materials. For instance, they can use it for subtopics such as flat shapes with the same area, spaces with the same volume, or spaces with the same surface area.