Asian Research Journal of Mathematics

Learning the concept of derivatives often poses difficulties for secondary school students. This study analyzes the errors produced by 3rd year science students (3rd HTS) from a school in Goma (DR Congo) during three assignments on the derivability and calculation of derivatives. 37 copies from two classes (3rd Scientific A: 20; 3rd Scientific B: 17) were analyzed. An a priori analysis of the statements was carried out in order to anticipate potential difficulties. The error analysis is based on Charnay 's typology (1989). Error coding was carried out by two independent raters and inter-rater reliability was assessed by Cohen's kappa coefficient (K = 37). The observed errors are mainly divided into: (i) errors related to the lack of mastery of the formal definition of the derivative, (ii) errors in algebraic calculation (manipulation of radicals and simplifications), (iii) difficulties related to absolute value and left/right differentiability. The analyses show that the statements, although not ambiguous, push some students towards heavy strategies (systematic passage through the definition instead of applying a simpler rule). The results suggest that many of the observed errors are more attributable to pedagogical inadequacies and previous shortcomings than to a lack of student effort. We recommend targeted teacher training actions and didactic sequences focused on mastering algebraic knowledge and common differentiation procedures.