The concept of paradigm became, in the middle of the last century, a central concept in the philosophical discussion about the nature of scientific knowledge. However, little attention has been paid to the strength of this concept in the constitution of the senses in general and, in particular, about its role in the transmission and acquisition of new scientific concepts, not only in the community of scientists, but also among basic-science teachers and students. I argue that a Wittgensteinian-inspired reflection on the transcendental use of this concept, as part of the grammar of scientific concepts, can clarify not only fundamental questions about the nature of scientific activity (avoiding both dogmatic and relativistic conceptions), but can also provide us with clues to identify sufficient, though not necessary, conditions so that something becomes an object for scientific thinking in the context of school education.