The key questions are: is it true that persons with Down’s syndrome can study mathematics only at a very elementary level? Might it be possible that their difficulties are mainly restricted to some fields, such as numeracy and mental computation, but do not encompass the entire domain of mathematics? Is the use of a calculator recommended? Is non-elementary mathematics accessible at most for the brightest students with Down’s syndrome? Our experience with about 30 students with Down’s syndrome, attending Italian mainstream secondary schools, is that these students can solve mathematical problems, using simple algebraic equations, though they may have very poor numeracy skills and need to use the calculator even with the simplest computations. Moreover, a familiarity with more advanced topics, as algebraic computation and analytic geometry, can help to raise their self-esteem and improve their numeracy too. Surprisingly, these students can learn and apply mathematical procedures in a variety of other different contexts. For instance, Francesca, an Italian student attending a secondary mainstream school, with a mild impairment in numeracy and relatively good linguistic skills, started with algebra and then learned to solve problems in the areas of nutritional science and of business administration. In the same way, Martina, a student in a mainstream secondary school with severe linguistic and numerical impairments, learned to work with Cartesian coordinates and formulas in analytic geometry. She began connecting points on a Cartesian plane, given their coordinates, and colouring in the shapes, such as flowers and animals, that they define. Applying the two points distance formula and verifying the result, she learned to measure the distance of two points with a ruler and to understand the concept of ‘millimetres’. The role of the inclusion in mainstream Italian schools of every disabled student, regardless the severity of the disability, has been crucial for these results.