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…

Educational research often requires mixing different research methodologies to strengthen findings, better contextualize or explain results, or minimize the weaknesses of a single method. This article provides practical guidelines on how to conduct such research in biology education, with a focus on mixed-methods research (MMR) that uses both…

The overall aim of this paper is to provide an epistemological rational for the measurement of intentionality. The purpose of this narrative is to identify "Intentionality" as an arena of action in the dispositional learning domain can be measured using an "Intentionality Measurement Instrument" [also referred by the acronym…

Early comprehension is an important, but not well-understood, contribution to early literacy and language development. Specifically, research regarding the nature of skills representative of early comprehension, including how they contribute to later reading success, is needed to support best practices to adequately prepare students. This article…

Early comprehension is an important, but not well-understood, contribution to early literacy and language development. Specifically, research regarding the nature of skills representative of early comprehension, including how they contribute to later reading success, is needed to support best practices to adequately prepare students. This article…

In spite of recent methodological developments related to quality assurance in mixed methods research, practical examples of how to implement quality criteria in designing and conducting sequential QUAN [right arrow] QUAL mixed methods studies to ensure the process is systematic and rigorous remain scarce. This article discusses a three-step…

Nursing education is a knowledge domain that requires higher order thinking (critical thinking) for making decisions that impact outcomes of human health. The goal of nursing education is to develop novice experts in nursing knowledge and clinical practice. In order to achieve this goal, nursing education must employ instructional approaches that…

Based on the generating functions, for any positive integers "n" and "k", identities are established and the explicit formula for a[subscript i](k) in terms of Fibonomial coefficients are presented. The corresponding results are extended to some other famous sequences including Lucas and Pell sequences.

The function 1 divided by "x"[superscript 2] minus "e"[superscript"-x"] divided by (1 minus "e"[superscript"-x"])[superscript 2] for "x" greater than 0 is proved to be strictly decreasing. As an application of this monotonicity, the logarithmic concavity of the function "t" divided by "e"[superscript "at"] minus "e"[superscript"(a-1)""t"] for "a"…

With Simson's 1753 paper as a starting point, the current paper reports investigations of Simson's identity (also known as Cassini's) for the Fibonacci sequence as a means to explore some fundamental ideas about recursion. Simple algebraic operations allow one to reduce the standard linear Fibonacci recursion to the nonlinear Simon's recursion…

Study is part of an ongoing research program whose cumulatime aim is to generate empirically validated hierarchical curriculum sequences in several basic skill areas appropriate to an early learning curriculum. (Author)