Abstract
This paper reported on the study of a good mathematical cognitive structure (GMCS) based on 43 top university students and 82 concepts of Calculus materials, using the social network analysis method. The results indicated that the GMCS has the following organizational features: (1) The mathematical knowledge (MK) in GMCS interconnected widely, especially in MK with a higher connection tightness; (2) Most connections between MK were direct; (3) MK of the basic and higher inclusive level had a greater impact; and (4) There were multiple MK accumulation points connecting others to form subsets. These new findings enrich the results of previous GMCS studies and promotes further exploration of GMCS. In view of this, teachers should pay closer attention to basic and abstract MK and help their students construct various direct connections of the MK in their mind.
Highlights
To describe the storage and the organization of internalized mathematical knowledge (MK) in the mind, the concept of mathematical cognitive structure (MCS) was proposed, based on the general cognitive structure concept in the field of psychology, in the 70s (Geeslin and Shavelson, 1975; Cao and Cai, 1989)
Good mathematical cognitive structure plays an important role in individual mathematical activities (Skemp, 1971; Yang, 1993; Ausubel, 1994; Zhang, 2003, 2007; Dixon, 2005; Zhang and Wu, 2012; Sofia et al, 2017)
Almost all teachers hope to help students form a good mathematical cognitive structure (GMCS) in mathematics teaching
Summary
To describe the storage and the organization of internalized mathematical knowledge (MK) in the mind, the concept of mathematical cognitive structure (MCS) was proposed, based on the general cognitive structure concept in the field of psychology, in the 70s (Geeslin and Shavelson, 1975; Cao and Cai, 1989) It was subsequently classified into the general MCS and the good mathematical cognitive structure (GMCS) (Yang, 1993; Wu and Guo, 1997; Guan, 1998). A series of studies on GMCS, especially on its characteristics, have been conducted over the past 30 years (Sun and Yang, 2015) These studies were based on an extensive and firm belief in the field of mathematic education, that the MCS was developed during learning activities and when applying MK. Once the characteristics of GMCS were discovered, teachers could provide purposeful guidance to form a
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