On a Typology of Errors in Integral Calculus in Secondary School Related to Algebraic and Graphical Frames

The present study falls into the efforts to improve practices for addressing errors produced by learners in various situations involving the calculation of integrals. We attempt to clarify as precisely as possible the types of errors that secondary school students produce when using integrals in algebraic and graphical frames. Based on the synthesis of several works dealing with errors specific to integral calculus, we have been able to outline a typology of possible errors that can be produced by students in secondary school. We determine some subcategories for the three known categories of errors: conceptual, procedural, and technical. After administering a test to a random sample of secondary school students and conducting a principal component analysis, we were able to deduce that in the algebraic frame, certain conceptual and procedural subcategories dominate, with a notable advance for errors due to failure to recognize the integrand function. In the graphical frame, errors related to technical subcategories represent a major source of the erroneous productions of the students tested.