Resumo

FRANCO CARZOLIO, Gustavo Daniel; OLAVE BAGGI, Mónica Isabel  e  ROSAS MENDOZA, Alejandro Miguel. Genetic decomposition as a frame of reference for a priori analysis of activities. Educ. mat. [online]. 2021, vol.33, n.3, pp.39-66.  Epub 30-Maio-2022. ISSN 2448-8089.  https://doi.org/10.24844/em3303.02.

This paper presents the methodological aspects of an investigation based on APOS theory-accomplished with prospective middle school mathematics teachers in Uruguay-, in which phenomena related to the construction of functions addition schema are studied. It focuses on the a priori analysis of the questionnaires’ activities used for data collection. This analysis is based on the genetic decompositions of functions addition, set, function, binary operation, and sum function, and allows us to objectify and rationalize the cognitive demands involved in solving the offered activities. Furthermore, it makes clear that: (1) a wide range of the students’ mathematical performance can be addressed by the activities, and (2) the questionnaires were adequate instruments for gathering information to answer the research question and achieving this study’s goals.

Palavras-chave : APOS; genetic decomposition; schema; functions addition; prospective middle school mathematics teachers..