We introduce the concept of the "sequence of the ratios of convex quadrilaterals," identify some properties of these sequences and use them to provide new characterizations for some classic quadrilateral families. The research involves aspects of geometry, arithmetic and mathematical analysis, which converge to produce the results.

Educational technology is shifting toward facilitating personalized learning. Such personalization, however, requires a detailed understanding of students' problem-solving processes. Sequence analysis (SA) is a promising approach to gaining granular insights into student problem solving; however, existing techniques are difficult to interpret…