Spatial Thinking and Geometric Systems: Analysing Cognitive Demand in School Mathematics Tasks

Abstract

Background : The research context is the synchronous teaching of mathematics visualised through signs, as is the Colombian sign language, which is publicly accessible, especially for the schooled deaf. Objectives : To analyse the cognitive demand of four school mathematical tasks developed as synchronous geometry lessons proposed for the deaf schooled population in Colombia. Design : Qualitative research within the interpretative paradigm, in which the teaching phenomenon of synchronous geometry classes is interpreted from the content analysis of the cognitive demand from the theoretical model of school mathematics task on the classes. Setting and Participants : The research is developed under the non-participant observation of the video lessons hosted on the public channel of the National Institute of the Deaf in Colombia. The classes are taught by a single teacher, in which one hundred people participate, who followed the teacher’s signs. Data collection and analysis: Of the twenty-nine synchronous lessons hosted on the channel, we selected the ones that focused on the teaching of two-dimensional geometry (triangles, their characteristics and their properties, similarity, congruence, and Pythagoras theorems) in a way that allows analysing the scholastic meanings of concepts, definitions, and procedures from the cognitive demand on these. Results : The results point to the development of thirty tasks centred on memorisation and using procedures without connections. Conclusions : The need to reflect on the lesson plans, especially for the deaf population, is evidenced, besides the search for tasks that motivate the use of procedures with connections and the construction of mathematics. Moreover, it is necessary to include the exploratory-investigative in geometry teaching.