I've been trying to finish this book for review for over a year now. Recently I had a little push to get through the 137 page sixth chapter. In a previous chapter the author critiques several 'models' of learning with technology as simplistic. I wanted to use the 'Five dimensions' diagram, and decided to create a copy using googledocs. With reference to the design of the graphic, Mehlenbacher says (pp199-200):
Because our goal is to capture the fundamental dimensions of everyday instructional situations initially, it is not necessary to explicitly define where one dimension ends and where another begins, nor is it necessary to capture the rich interplay between dimensions. In the manner of an Escher print, figure 6.1 represents the five dimensions of everyday instructional situations graphically, suggesting how one or more dimensions, when grounding another, serve to figure the dimension under investigation. Thus an instructor interested in engaging learners in higher-level research activities might construct a simulated publishing environment that emphasizes collaborative peer review and conceptualize issues related to learner background and knowledge, tasks and activities, social dynamics, and environment and artifacts under instructor activities. Still, to one degree or another, all five dimensions are required to produce an everyday instructional situation.
Figure 6.1 appears to be a tessellation; tessellations, however, involve repeated use of a single shape to cover a plane surface, without gaps or overlapping between the shapes, like the tiles of a washroom floor. Tessellations cannot have any gaps and cannot overlap on another, as does this particular noncircular Venn diagram. Hexagons, squares, and triangles can tessellate; octagons and pentagons cannot. And instruction and learning with technology can be improved in certain situations and not in others, lacking as tessellations do mathematical precision and replicability.What I like about this is the brave attempt to represents the complexity of learning and instruction.