Um estudo sobre os estilos de pensamento matemático mobilizados por um sujeito cego ao resolver sistemas de equações lineares - Martins, Elen Graciele (2019)
The purpose of this research is to identify which mathematical thinking styles are mobilized by a blind subject when solving problems involving linear equations systems. The researcher’s gaze was focused at different representations of mathematical object systems of linear equations used by our subject and their reactions and perceptions during the study. They sought as theoretical foundation the mathematical thinking theory of styles by Ferri, which, based on Sternberg's definition of thought styles, indicates the existence of three mathematical thinking styles: analytical, visual and integrated. The style of visual mathematical thinking is characterized by using internal images and external pictorial representations, such as drawings, sketches, graphics, etc., to solve mathematical situations. The analytical mathematical thinking style is characterized by using formal internal representations and the formal algorithms externalization. The integrated mathematical thinking style is the combination of visual and analytical styles. The analysis of the representations used by our subject, in order to solve both linear equation system activities, was based on the studies of semiotic representations registers, vision and visualization of Duval. The work with linear equations systems had as reference Coulange’s research that indicates that it is possible to identify eight variables in situations proposed with this mathematical content, and how these can contribute to the resolution of the activities. We have adopted as a methodology the Design Experiment de Cobb et al. where all the elements that are part of the study (subjects, activities, materials, etc.) belong to an ecology and are analyzed all their variations during the research development. The search involved a blind adolescent who attended elementary school 9th grade. We noticed with Activity 1 that our subject had no contact with the linear equations system graphical representation which prevented him from answering an Activity 1 question. The styles of visual and integrated mathematical thinking were not mobilized in this Activity. The data analysis indicated the predominance of analytic mathematical thinking style and the use of algebraic and symbolic semiotic representation registers, and there were also treatments in these registers. Regarding variables described by Coulange, we identified that in the subject, although implicitly, he used more frequently the variable which refers to the numerical domain and cultural knowledge needed to solve the proposed situations. Our empirical study indicated the need for an adaptation in the definition of the mathematical visual thinking style given by Ferri. We consider that in the case of blind subjects, the representation of this mathematical thinking style involves all remaining sensory resources, we define thus the mathematical tactile sense thinking style. We consider that the mental representations of blind individuals can be materialized not only by using the tactile resource, but also by all their sensory pathways