*Concept Maps—Hierarchy and Scoring*

Concept maps are unique for their graphical structures that exhibit how one concept is sub-ordinate to other concepts and how learners' understand the concepts [12,30]. A hierarchical concept map (also called a "Novakian concept map") is recognizable for its top-down fashion, where more general subordinate concepts are on top and more specific concepts are at the bottom. For instance, Novak and his colleagues claim, "A well-organized cognitive structure (which is necessary for meaningful learning) usually leads to graphically well-organized concept maps; in turn, building good concept maps helps to build a good knowledge structure" [31].

Several authors [11,30,32–34] associate the map hierarchy with the learning context. As stated earlier, the propositional structure is an essential part of concept mapping and shows learners' meaningful learning. However, not all 'concept-link-concept' triads form a meaningful proposition because they might miss the proper structure, have no logical meaning or constitute a large grammatical structure (e.g., sentence) that has no meaning independently within this bigger structure [35]. There are many authors, who consider di fferent aspects of quality and complexity of concept map structure within their scoring rubrics.

The semantic scoring rubric of Miller & Cañas consists of six key criteria that are inherent for all concept maps [35]: (1) the presence of focus question and root concept, (2) the correct propositional structure—link reworking and overall map reorganization; (3) the presence on inaccurate propositions (misconceptions); (4) the presence of dynamic propositions that involves, movement, action, change of state or dependency relationships (e.g., roots absorb water, electric charge generates electric fields, etc.); (5) the number of quality cross-links that establish correct, suitable, and instructive relationships and (6) the presence of cycles in which the direction of the arrows allows traversing the entire closed path in a single direction. All of these six levels are also translated to the content-quality scale that is followed by the categories of unevaluated, very low, low, intermediate, high and very high.

Other studies have suggested that the structure of the concept map carries important information about the understanding and quality of learners' knowledge [11,12,30,36]. Many authors [7,30,37–40] emphasize the e ffectiveness of the qualitative scheme that di fferentiates three morphological types of concept map categories—spoke, chain and network [11]. Their model is based on map morphology that has following characteristics [12,41,42]:


Extreme versions of each of these morphological types are depicted within the quadrants of the semantic plane (Figure 1) to indicate the stereotypical structures that may be found to depict novice knowledge, theoretical knowledge and practical knowledge. However, each of these extremes is not 'fixed' and may evolve into another in response to student learning. For example, a spoke structure may develop into a chain or a network over a period of time as the student's understanding develops and is more systemized and complex in response to further learning [12]. Besides that, Kinchin discusses what is a "good" and "poor" map by comparing the exam results with the maps [12,43]. He concludes that "poor" maps are not always indicators of poor performance and "good" maps not always predictors of good performance. There is no one common determination whether a concept map is really good in terms of indicating the presence of a sophisticated understanding. In addition, Kinchin [17] claims, "bigger does not always mean better when evaluating concept maps."

Cañas [31] uses the idea of an "excellent map," and considers that both content and structure are important to determine the map quality. Cañas and colleagues [31] describe excellent concept maps as being concise and explanatory, exhibiting a high degree of clarity and presenting a clear message. In addition, excellent maps should also be well balanced, well-structured and demonstrate learners' understanding.
