Open AccessLet’s tie circumferences up, so we count them all. An unconventional combinatorics problem in compulsory secondary school
Author(s) -
Aitzol Lasa,
Miguel R. Wilhelmi,
Jaione Abaurrea
Publication year - 2022
Publication title -
south florida journal of development
Language(s) - English
Resource type - Journals
ISSN - 2675-5459
DOI - 10.46932/sfjdv3n1-085
Subject(s) - olympiad , task (project management) , mathematics education , adaptability , mathematics , algebraic number , field (mathematics) , combinatorial analysis , semiotics , algebra over a field , computer science , combinatorics , pure mathematics , engineering , linguistics , management , mathematical analysis , systems engineering , economics , philosophy
Secondary school students (age 13-14) solve a combinatorial task in the Mathematical Olympiad, whose answers are analyzed and discussed using theoretical tools from two didactical frameworks: on one hand, the Onto-semiotic Approach (OSA), and, on the one hand, the Theory of Didactic Situations in Mathematics (TDSM). The statistical study is carried out by tools from Statistical Implicative Analysis (SIA). Results express that most participants possess sufficient arithmetic strategies to solve the task, without turning to combinatorial algebra. At the same time, the algebraization level shown by these same participants in their answers to other tasks of the Olympiad, is strongly correlated to their behaviors in the combinatorial task, and so, a student who masters an algebraic technique is also aware of the limitations of its field of application. Therefore, adaptability is a key element in the analysis of the observed strategies and their success rate.