The results in Appendixes D x E x F should provide reliable and valid guides to core concepts for Astro 101. In fact, the expert ratings and relatedness pretty much defined the content in the Conceptual Astronomy Project at UNM, especially the concepts with scope scores greater than 200. We intentionally included these 32 terms in instructor-constructed concept maps (see Zeilik 2002 for examples of these maps in a textbook).
We then took the work one additional step. To quantify the relatedness of pairs of concepts, each pair was given an association score that was the number of times across all experts that those two concepts were associated as a pair. We define the concept relatedness as the pair scores from the association task. The concept relatedness results are proximity data in that they show the closeness of pair connections. This kind of association task is a well-developed tool in cognitive psychology (Acton et al. 1994).
We then transformed the experts' similarity ratings into a conceptual map, using a tool developed in cognitive psychology. The algorithm, called Pathfinder, constructs a network map (Figure 1) in which related concepts are in near vicinity, and concepts with high scope scores have the greatest number of links (see http://interlinkinc.net/index.html). From this analysis, we found that 60 concepts with highest scope scores cluster around four nodes: electromagnetic spectrum/photons, stars, mass, and cosmology. We interpreted this result as a community consensus on the overall concepts, and used these results as global guides in course development at UNM.Figure 1.
Note that the result is not a concept map! A concept map ideally has a hierarchy of concepts, usually from top to bottom, and their links have a direction and are named by verbs (see Novak & Gowin 1984).
From my own (MZ) experience, I sense that about 100 concepts sufficiently define a core for Astro 101. I have accomplished the pruning by dropping the “planets as places”—yes, the Solar System!—from my course and placing more emphasis on stars, stellar evolution, galaxies, and cosmology. The planets only serve as “test masses” for Newton's and Kepler's laws. I also do not cover astronomical technology as such, but do examine results (many of the cooperative learning team activities are based on real data). I do not include tools and telescopes, the Solar System, and stellar magnitudes (compare with Appendix A); I use fluxes instead. I am moving away from stellar spectral classification as such, and focusing on physical properties such as color and luminosity. Of course, students still complain on their UNM course evaluations that the course covers “too much”!
In this work, we used the expert panel to define the core concepts and obtain a concept relatedness score among pairs of these concepts. These data are proximity judgments, and a number of valid analyses can be applied to these results. We chose to use the Pathfinder algorithm (Schvaneveldt 1990), which transforms the proximity matrix into a network in which each concept is represented by a node, and the proximities are represented by how closely the concepts are linked. We used the Pathfinder analysis to discover that the structural network has four main nodes.