Exploring well-gradedness in polytomous knowledge structures

IF 2.2 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Bo Wang , Jinjin Li
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引用次数: 0

Abstract

Enhancing learning effectiveness and comprehension, well-gradedness plays a crucial role in knowledge structure theory by establishing a systematic and progressive knowledge system. Extensive research has been conducted in this domain, resulting in significant findings. This paper explores the properties of well-gradedness in polytomous knowledge structures, shedding light on both classical confirmations and exceptional cases. A key characteristic of well-gradedness is the presence of adjacent elements within a non-empty family that exhibit a distance of 1. The study investigates various manifestations of well-gradedness, including its discriminative properties and its manifestation in discriminative factorial polytomous structures. Furthermore, intriguing deviations from classical standards in minimal polytomous states are uncovered, revealing unexpected behaviors.

探索多项式知识结构中的良好分级性
在知识结构理论中,良好等级性通过建立一个系统的、循序渐进的知识体系,对提高学习效率和理解能力起着至关重要的作用。人们在这一领域进行了广泛的研究,并取得了重要发现。本文探讨了多项式知识结构中良好等级性的特性,揭示了经典证实和例外情况。良好分级性的一个关键特征是非空族中相邻元素的距离为 1。本研究探讨了良好分级性的各种表现形式,包括其判别特性及其在判别因子多矩结构中的表现形式。此外,研究还发现了最小多项式状态与经典标准的有趣偏差,揭示了意想不到的行为。
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来源期刊
Journal of Mathematical Psychology
Journal of Mathematical Psychology 医学-数学跨学科应用
CiteScore
3.70
自引率
11.10%
发文量
37
审稿时长
20.2 weeks
期刊介绍: The Journal of Mathematical Psychology includes articles, monographs and reviews, notes and commentaries, and book reviews in all areas of mathematical psychology. Empirical and theoretical contributions are equally welcome. Areas of special interest include, but are not limited to, fundamental measurement and psychological process models, such as those based upon neural network or information processing concepts. A partial listing of substantive areas covered include sensation and perception, psychophysics, learning and memory, problem solving, judgment and decision-making, and motivation. The Journal of Mathematical Psychology is affiliated with the Society for Mathematical Psychology. Research Areas include: • Models for sensation and perception, learning, memory and thinking • Fundamental measurement and scaling • Decision making • Neural modeling and networks • Psychophysics and signal detection • Neuropsychological theories • Psycholinguistics • Motivational dynamics • Animal behavior • Psychometric theory
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