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.

This article provides a validation framework for research on the development and use of science Learning Progressions (LPs). The framework describes how evidence from various sources can be used to establish an interpretive argument and a validity argument at five stages of LP research--development, scoring, generalisation, extrapolation, and use.…

This article provides a validation framework for research on the development and use of science Learning Progressions (LPs). The framework describes how evidence from various sources can be used to establish an interpretive argument and a validity argument at five stages of LP research--development, scoring, generalisation, extrapolation, and use.…

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…

Learning progressions (LPs) have seen a growing interest in recent years due to their potential benefits in the development of formative assessments for classroom use. Using an LP as the backbone of an assessment can yield diagnostic classifications of students that can guide instruction and remediation. In operationalizing an LP, assessment items…