Abstract:

Differential and integral calculus (DIC) is considered one of the greatest inventions of mathematics. Science, technology, engineering and mathematics (STEM) courses usually have at least one semester of DIC. For many students, this requirement is an overwhelming or discouraging obstacle in pursuing degrees in these areas. In Portugal, a first approach to integral calculus is included in Mathematics syllabus of 12th year of schooling (year prior to entering higher education). We consider that this is an opportunity to be taken, given its usefulness in university courses in the STEM area. Our focus is in the development of students’ proficiency in the recognition of the integral rule and their components given a certain integral to compute. We propose original computer learning games to contribute to this goal. The principles of perceptual learning supports the construction of two games: Memory game (levels I and II) and Build your integral (levels I and II). The Memory game I intends to increase the memorization of the derivation rules and to highlight the relationship between derivation and integration. The game Build your integral I and II intends to give the student the ability to visualize the various forms that a basic integral can take, as advocated in the PL. Student has to analyse the structure of the shown expression, and choose among the available options, the one that transforms the expression, into a basic integral.

The games were implemented in a class of the 12th year of Mathematics in a Portuguese public school with 20 students, 10 boys and 10 girls, aged between 16 and 18. After taught the chapter on integrals and integral calculus in a context of distance learning (given the pandemic COVID-19), using the Teams platform, supported by a PowerPoint with theoretical explanation of the contents and some examples. Students did exercises from the workbook as usual and after that, the original computer learning games were implemented.

This study has shown that the use of these games had a positive impact in the students’ basic integral calculus ability. This kind of approach stimulates student to perceive the structures of the basic integrals, allowing them to achieve better results in this kind of calculation. The students found the use of these games useful to practice and consolidate their knowledge.

Keywords:

Mathematics teaching, secondary education, anti-derivation, integrals, perceptual learning, learning games.