School science descriptions about Mendel and his story are problematic because several statements that are controversial among historians of science are repeated over and over again as if they were established facts. Another problem is the neglect of other scientists working on inheritance in the second half of the nineteenth century, including Darwin, Spencer, Galton, Nägeli, Brooks, Weismann and de Vries, who paved the way for the reinterpretation of Mendel's work in 1900. These problems are often found in textbooks and are likely to be present in school science throughout the world. Here, we discuss the contributions that history of science and papers published in journals that target teachers may bring to improve how school science deals with Mendel and his contributions. Evidently the idea is not that school teachers could solve problems still under discussion in the historical literature. The point is, rather, that it is important to avoid treating Mendel's contributions as uncontroversial, mentioning, for instance, that there are ongoing debates on whether he proposed the laws named after him by appealing to invisible factors underlying phenotypic traits that are seen as the heritable potentials for those traits, and would in due time be known as genes. History of science can contribute to put the mythic Mendel into question in the science classroom, bringing school science closer to the controversies around the interpretation of his work.