New perspectives on mathematics teaching design: through the lens of mathematical aesthetics

Mathematics teachers always design specific instructional approaches based on their own understanding of particular mathematical knowledge, the characteristics of that knowledge, and the nuances of students' psychological activities triggered by these specific characteristics. Within this process, the teacher's mathematical aesthetic intention serves as a crucial technique for filtering mathematical knowledge points. The aesthetic engagement with a specific mathematical concept may be transient, may be situated within a particular mathematical era or cultural tradition, or may indeed stem from the teacher's profound experience derived from their own cognitive development of a certain mathematical concept or their exploration of an unconventional problem. This paper explores the practical value of utilizing mathematical aesthetics in instructional design, specifically from the perspectives of the beauty of strangeness and the beauty of anticipation, as they emerge from the researchers' authentic instructional design experiences.