This article analyzes the relationship between academic mathematics and school mathematics in the context of undergraduate mathematics courses. Definitions of both are provided, based on authors who argue on the subject. The importance of these conceptions in the training of mathematics teachers and mathematicians is also highlighted. The authors researched and their writings form the entire theoretical basis of the work, which consists of a bibliographical survey, so that it is possible to observe that, although there is a fundamental relationship between them, there is also a perceptible difference. In the mathematics degree course, it is possible to verify the existence of subjects that contemplate each of the two perspectives mentioned. In view of this, the aim of this paper is to establish an analysis of the contributions that Academic Mathematics and School Mathematics make to teacher training and performance, which facilitate student learning, with more descriptive definitions and the use of methodologies aimed at communicating mathematical knowledge in an objective and practical way.
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