A system framework for fuzzy sets in the van Hiele level theory of geometric reasoning
Steve C. Perdikaris · International Journal of Mathematical Education in Science and Technology · 1996
The transitions between the fuzzy subsets of the fuzzy variables of a system on the van Hiele level theory of geometric reasoning are examined. This process can be systematically performed within a system framework using an absorbing Markov chain. Thus, a measure of the number of steps needed for the acquisition of each van Hiele level is found. This measures the degree of difficulty in acquiring each van Hiele level and indicates how accomplished student groups are in a geometric task. Data from Gutierrez, Jaime and Fortuny's alternative paradigm is used to illustrate our work.