Understanding of intransitivity of superiority, and design of teaching-learning “nontransitive” materials and problems

Abstract

Understanding of transitivity-intransitivity of superiority and mastery of these relations are considered. It is proved that the use of transitivity of superiority principle (if A>B and B>C then A>C) as an axiom in teaching and the use of teaching/learning materials and situations that are subject to this principle can lead to learners’ false beliefs about its universality and false conclusions about superiority in situations of comparisons of the objects being in intransitive (“rock-paper-scissors”) relations. Asymmetry of “transitive” and “intransitive” learning materials and problems in this area is noted. “Intransitive” learning materials, objects, and problems meant for compensation of this asymmetry are described.