This talk begins with the development of mathematical concepts, explaining how mathematical ideas arise from the need to solve problems in everyday life and continue to evolve within mathematics through idealization, abstraction, and generalization. By tracing the development and connections of mathematical knowledge, the talk helps learners build a clearer and more integrated understanding of mathematics and apply this understanding to both learning and teaching. The talk further introduces mathematics sense, using the ability to clearly articulate one’s understanding as a starting point for learning. It highlights five core practices—giving examples, simplifying, drawing diagrams, asking “why,” and reflecting—to guide learners from conceptual understanding toward problem solving, making connections, reasoning, and metacognition. Through these practices, learners can integrate fragmented knowledge into meaningful mathematical structures. In addition, the talk connects conceptual understanding in mathematics with preparation for National Teachers' Qualification Examination and Teacher Recruitment Exam. Covering general mathematics, mathematics teaching methods, multiple-choice questions, and constructed-response questions, it emphasizes that learners should not merely know the correct answer but should also ask “why,” understand the mathematical concepts and reasoning underlying each option and solution, and integrate their knowledge systematically. In doing so, prospective teachers can strengthen both their mathematical competence and professional teaching knowledge, laying a solid foundation for future learning, examinations, and classroom practice.

Implemented by Department of Data Science and Mathematics
Date: 2026/10/05