Abstract
This paper presents a study based on didactic engineering and the theory of didactical situations on the complexification of the Leonardo sequence, addressing its numbers in a two-dimensional way, with the insertion of the imaginary unit i. This study is an excerpt from a masters’ thesis research done in the postgraduate programme in science and mathematics teaching of the Federal Institute of Ceará. It was conducted via Google Meet in an initial teacher education class in History of Mathematics. We will present a problem situation based on the research and the teaching methodologies assumed in it to evaluate the students’ investigative and intuitive side faced with the situation presented. We assessed the results according to the methodologies used and carried out an internal validation. Thus, we concluded that the students could build their knowledge themselves, becoming protagonists of this construction and obtaining an evolutionary understanding of the Leonardo sequence.
Highlights
The teaching of linear and recurrent sequences has become increasingly frequent in papers published in journals on mathematics education and mathematics teaching (Alves et al, 2019; Oliveira et al, 2018; Slisko, 2020)
We used the research methodology of didactic engineering, with its French aspects, and the teaching methodology of the theory of didactical situations to complement the analysis of the didactic teaching situations posed
This research is an excerpt from a research work developed in the Postgraduate Programme in Science and Mathematics Teaching of the Federal Institute of Cerará, Fortaleza campus, approved by the Research Ethics Committee (Opinion n. 4.141.910), which investigates a process of hybridisation and hypercomplexification of recursive linear sequences, specifying the Leonardo sequence and evidencing elements of didactic, cognitive, and epistemological order around the epistemic-mathematic field
Summary
The teaching of linear and recurrent sequences has become increasingly frequent in papers published in journals on mathematics education and mathematics teaching (Alves et al, 2019; Oliveira et al, 2018; Slisko, 2020). To investigate a classroom around the object of study, we used the teaching methodology based on the theory of didactical situations This methodology models a specific mathematical content to facilitate its exposition to the students during the teaching practice to achieve a successful teaching and learning process and the students’ knowledge evolution. The theory of didactical situations is a teaching methodology studied by Brousseau (1986), aiming to investigate didactical teaching situations and the interactions between students and teachers (Almouloud, 2007) To analyse these didactic teaching situations, some questions, called problem situations, are posed through activities, which are analysed based on their four phases: action, formulation, validation, and institutionalisation. To explore and investigate this mathematical content, we created a problem situation of this concept, supported by the TDS, to stimulate the students’ intuitive and investigative side
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