Abstract
The Theory of Nuclear Concepts (TNC) is based on prior theories and ideas coming from Ausubel and Novak among others, who argue that concepts are organized hierarchically around general concepts. But the TNC differs from them in holding that the students’ cognitive structure is organized around specific concepts that are not the most general, but only the most significant for the students. TNC also argues that, as a result of the learning progresses, the students’ cognitive structure is transformed into a simpler structure. The associated technique to represent the cognitive structures is “Pathfinder Associative Networks” and to obtain them, it was developed GOLUCA software, which serves as a support on the analysis and representation of cognitive networks. The TNC has been used to understand and evaluate the cognitive structures of students and teachers in real situations.
TopBackground
The Theory of Nuclear Concepts
The origins of TNC date back to 2002, during the investigation of the doctoral thesis of Casas (Casas, 2002), studying the mathematical concept of angle. In this research (Casas & Luengo, 2004) is reflected on how the student's mind works, how they understand the basic mathematical concepts, how to represent the cognitive structure of students in a theme and how to apply these representations for research and educational use. Results were found that could not be explained on the basis of existing theories, so it required a new one (Theory of Nuclear Concepts), building on previous theories.
The theoretical foundation of TNC is based on the learning theories of Ausubel, Novak and Hanesian (1978), but proposes some differences with these theories in particular as related to the organization of knowledge, introducing new theoretical alternatives (Casas, 2002): geographical organization of knowledge, nuclear concepts and paths of least cost.
Geographical Organization of Knowledge
TNC does not agree to the hierarchical organization of knowledge and proposes a “geographical” organization. This kind of organization is a metaphor to explain that, like what happens with the knowledge of a map, at the start of construction of such knowledge it is not organized around general concepts that are derived from others (in the geographical analogy, we might consider as such the country, region and major cities), but about concrete concepts (in the geographical analogy might be landmarks that are familiar to the subject). According to this theory, the acquisition of a concept is similar to the acquisition of geographical knowledge, where there are points highlighted in the landscape within which to establish routes. Similarly, the learning of a new concept is always associated to others and never alone, forming a structure. When you dominate the relationships established in this structure is reached a general understanding of the concept.
Key Terms in this Chapter
Pathfinder Associative Network: Developed by Schvaneveldt, the pathfinder associative networks are representations of the relationships between concepts in the cognitive structure of an individual. The networks are graphically represented as graphs, in which concepts are represented as nodes and relations between them as line segments of varying length according to their semantic proximity.
Similarity: How two or more pathfinder associative networks are similar. This statistic is calculated by considering the number of links that share these networks.
GOLUCA: Software that collect, analyze and graphically represent Pathfinder Associative Networks. The statistical studies are made, such as Similarity, Average Network, Coherence Measure or Network Complexity Index.
Network Complexity Index: This measure is a quantitative indicator designed to measure the complexity of a network.
Theory of Nuclear Concepts: Cognitive theory developed by Casas and Luengo (2002). According to this theory, the learning of a new concept is always associated to others and never alone, forming a structure, with highlighted concepts. The elements of this theory are: geographical organization of knowledge, nuclear concepts and paths of least cost.
Nuclear Concept: In a cognitive structure, the highlighted points are called nuclear concepts. In a pathfinder associative network those concepts are represented with three or more links to others concepts.
Coherence: This measure reflects the consistency of the data collected. Corresponds to the degree of learning and indicates whether the user assign the values of similarity attentively or rashly.