The study of errors in learning and the search for patterns to explain their causes have always been of great interest to researchers and educators alike. Mistakes are a constant in students’ solutions to mathematical problems and are inseparable from the learning process. It is essential, then, to diagnose and address the mistakes made by students so as to allow them to reflect on their errors and adjust their knowledge. To this end, we have created a system that tracks all the actions carried out by a student when solving a mathematical algorithm, not just the final results, and which is capable of diagnosing the faults and possible causes. It can also recommend the actions to be taken based on the individual difficulties encountered. In short, we have created a personalized teaching system whose features could be particularly useful for special-needs students, such as those with Down syndrome. This paper explains the error detection modules in the addition, subtraction and error-adapted assistance algorithms. This work is part of a multidisciplinary research effort financed by R&D project called “Divermates”, of the Ministry of Labor and Social Affairs, and involving personnel from the Computer Engineering and Mathematics and Fine Arts Education Departments of the University of La Laguna, as well as professionals from the Tenerife Trisomic 21 Association (ATT21).