| 总结: | Eng: This paper presents a qualitative research in the line of Mathematical Education based on the research methodology proposed by Artigue et al. (1998) called Didactic Engineering. Its main objective was to understand the process of construction of the basic concepts of spherical geometry shown by the representations made by middle school students in the research classes proposed by the teacher in an official high school of a municipality of Boyacá.
It is a reflection on the implementation of the didactic and methodological strategy of research classes, based theoretically by Ponte et al. (2006), by introducing elements of spherical geometry in the mathematics curriculum of Secondary Education. In addition to carrying out a historical and epistemological analysis of the spherical geometry, the proposal incorporates designed activities with different task types, validated, and applied in mathematics classes and thought as triggers of the research process itself. The instruments used were participant observation, field diary, audio and video recording of classes, and subsequent analysis of the information collected. The research process showed that both the teacher and the student can assume the role of researchers to enrich the teaching and learning processes as pointed out by Ponte et al. (1998). It was achieved, through exploration processes, conjecture, proof, and validation typical of research classes, constructing meanings by comparing and contrasting some axioms, postulated theorems, and definitions proper to plane geometry versus spherical geometry.
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