Design of interactive mathematical tasks that make up the reasoning and the Ethnomathematics program

The design of mathematical tasks has taken the replacement on the research agenda of Mathematics Education. In this article, we provide principles of design of interactive mathematical tasks that make up the reasoning and the Ethnomathematics program. The research context involved the design, the development, and the analysis of written and oral prospective mathematics teacher (PMT) in an initial training course. The methodology implemented was descriptive-interpretative and implicated the design of mathematical tasks by the PMTs based on the adaptation of the HiCuA analytical framework. Regarding to the analysis of the data collected, categories of mathematical task types were constructed because of a thematic analysis carried out with the purpose of characterizing the tasks designed by the prospective teacher. The findings of the study provide information on the design principles implemented by prospective teacher in the context of Reasoning and Ethnomathematics. Likewise, it was identified that promoting reasoning and Ethnomathematics through interactive mathematical task designs supports students by developing skills such as: justifying, criticizing, and reasoning the conclusions presented by others.