## Abstract

To link arithmetic with the practical and theoretical thinking of algebra, this exploratory research framed in the Modes of Thinking Theory conducted a case study to characterize modes of thinking about the set ℤ_{4} and its interactions in Chilean primary school teachers. For this purpose, the answers given by 30 in-service teachers to an online questionnaire were analyzed, based on a proposed cognitive model that defines the modes of thinking about the set ℤ_{4} with its articulators. The results show that these teachers, generally adhere to the cognitive model and evidence more articulation between synthetic-geometric and analytic-arithmetic modes than between analytic-arithmetic and analytic-structural modes, which shows less privileged theoretical thinking. In conclusion, the algebra of primary teachers can be activated by conceiving the set ℤ_{4} as a mathematical fragment with 4 elements constructed. Each one is considered a distinct set of congruent numbers modulo 4 that partition the set ℤ, making the concept of equivalence class contribute to the cognitive construction of the set ℤ_{4} as a cyclic graph of order 4.

Translated title of the contribution | Modes of thinking the set ℤ_{4} in teachers who teach algebra in the first years of school |
---|---|

Original language | Spanish |

Pages (from-to) | 170-195 |

Number of pages | 26 |

Journal | Educacion Matematica |

Volume | 35 |

Issue number | 2 |

DOIs | |

State | Published - 2023 |

## Fingerprint

Dive into the research topics of 'Modes of thinking the set ℤ_{4}in teachers who teach algebra in the first years of school'. Together they form a unique fingerprint.