Abstract
Motivated by the diverse uses of concept maps in teaching and educational research, we have developed a systematic approach to their structural analysis. The basis for our method is a unique topological normalisation procedure whereby a concept map is first stripped of its content and subsequently geometrically re-arranged into a standardised layout as a maximally balanced tree following set rules. This enables a quantitative analysis of the normalised maps to read off basic structural parameters: numbers of concepts and links, diameter, in- and ex-radius and degree sequence and subsequently calculate higher parameters: cross-linkage, balance and dimension. Using these parameters, we define characteristic global morphologies: ‘Disconnected’, ‘Imbalanced’, ‘Broad’, ‘Deep’ and ‘Interconnected’ in the normalised map structure. Our proposed systematic approach to concept-map analysis combining topological normalisation, determination of structural parameters and global morphological classification is a standardised, easily applicable and reliable framework for making the inherent structure of a concept map tangible. It overcomes some of the subjectivity inherent in analysing and interpreting maps in their original form while also avoiding the pitfalls of an atomistic analysis often accompanying quantitative concept-map analysis schemes. Our framework can be combined and cross-compared with a content analysis to obtain a coherent view of the two key elements of a concept map: structure and content. The informed structural analysis may form the starting point for interpreting the underlying knowledge structures and pedagogical meanings.
Highlights
Concept maps as developed by Novak (2010) are a ‘very powerful and concise knowledge representation tool’ (Novak & Cañas, 2006, p. 332)
This paper presents a standardised, systematic approach to topological and morphological concept map analysis to provide a consistent, repeatable and methodological robust platform on which to build subsequent content analysis and interpretation
We have briefly indicated how they may be related to existing morphological classifications of nonnormalised maps
Summary
Concept maps as developed by Novak (2010) are a ‘very powerful and concise knowledge representation tool’ (Novak & Cañas, 2006, p. 332). Hay, and Adams (2000) have identified spoke, chain and network as distinct morphological classes Their scheme was extended by Yin, Vanides, Ruiz-Primo, Ayala, and Shavelson (2005) who added circular and tree classes. Based on their topological analysis, Koponen and Pehkonen (2008) have proposed an alternative classification as chains, loose and connected webs. These qualitative approaches to concept-map analysis use graphic and topological analysis to generate morphological classifications and often go on to suggest links between these structures and characteristic learning ‘attributes’. This paper presents a systematic approach to topological analysis and morphological classification that builds on Kinchin’s (2000) suggestion to take a combined approach to analysis, in an attempt to form a standardised and reliable basis for interpreting topology and morphology and provide a more consistent, reproducible and methodologically robust platform on which to build subsequent qualitative analysis and interpretation
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