Abstract

This study presents evidence that validates a cognitive model called genetic decomposition for the reconstruction of the exponential function concept. Twenty-two students enrolled in a mathematics teaching degree and in a master's degree in didactics of mathematics are surveyed through the application of a questionnaire using a mixed methodology approach. The results show that the students surveyed use both the logarithm operator and the exponential function in parallel. The results underscore the roles played by graphs and the use of patterns and the power operation to establish restrictions at the base of the exponential relationship. In addition, the results confirm the role played by recursive multiplication of a positive real number to highlight the monotony of the exponential function. It is concluded that these results validate the proposed model of genetic decomposition, vindicating the theoretical elements that support it.