LEARNING INTRANSITIVITY:FROM INTRANSITIVE GEOMETRICAL OBJECTS TO ‟RHIZOMATIC" INTRANSITIVITY
Poddiakov Alexander Technology and Psychology for Mathematics Education
ТИП ПУБЛИКАЦИИстатья в сборнике трудов конференции
ГОД2019
ЯЗЫКEN
АННОТАЦИЯ
A new class of intransitive objects - geometrical and mathematical constructions forming intransitive cycles A > B > C > A - are presented. In contrast to the famous intransitive dice, lotteries, etc., they show deterministic (not probabilistic) intransitive relations. The simplest ones visualize intransitivity that can be understood at a qualitative level and does not require quantitative reasoning. They can be used as manipulatives for learning in- transitivity. Classification of the types of situations in which the transitivity axiom does and does not work is presented. Four levels of complexity of intransitivity are introduced, from simple combinatorial intransitivity to a “rhizomatic” one. A possible version of the main educational message for students in teaching and learning transitivity-intransitivity is presented.
ЦИТАТА
Poddiakov, A. LEARNING INTRANSITIVITY:FROM INTRANSITIVE GEOMETRICAL OBJECTS TO ‟RHIZOMATIC" INTRANSITIVITY / A. Poddiakov // Technology and Psychology for Mathematics Education. : Proceedings of the PME and Yandex Russian conference. – 2019. – P. 178-187
