Mathematics and Computer Science: Research Updates Vol. 12

Integral calculus is a fundamental area of mathematics that supports the calculation of areas, volumes and averages, as well as the modelling of phenomena in several scientific and technical fields. In secondary schools in Goma, Democratic Republic of the Congo (DRC), the teaching and learning of integrals take place in a socio-educational context marked by limited resources, insufficient continuing teacher training and weak contextualisation of textbooks and classroom activities. This study analysed the conditions under which integrals are taught and learned in Goma secondary schools, with particular attention to contextualised pedagogy and educational innovation. A descriptive mixed-method design was used. Data were collected from 16 mathematics teachers and 295 students drawn from 16 schools through textbook analysis, questionnaires and diagnostic tests. Quantitative data were processed using descriptive statistics, while open-ended responses and textbook content were examined through thematic content analysis. The findings show that the textbooks used in the schools introduce integrals mainly after derivatives and present them predominantly as inverse operations, with exercises that are largely procedural and weakly connected to local situations. Teachers reported limited access to continuing training and teaching resources, and classroom practice remained mainly lecture-based. Students perceived integral calculus as difficult and abstract, frequently confused the integral with the primitive, and encountered substantial difficulty when solving contextualised problems. However, many students indicated that practical examples, guided exercises and visual or digital supports could improve their understanding. The study concludes that improving the teaching and learning of integrals in Goma requires stronger didactic transposition, locally contextualised resources and sustained support for mathematics teachers.