This paper performs a critical analysis of the consensual and family resemblance approaches to the nature of science. Despite the debate that surrounds them, between a pragmatic consensus and a more comprehensive understanding, both approaches have in common the goal of helping students to "internalize" knowledge about science in a "descriptive" level. In light of Wittgenstein's philosophy of language, we show how such choice is committed to particular conceptions of "understanding," "knowledge" and "language," and what some of the implications are. We argue that, besides preventing a qualitative understanding about science, both frameworks also tend to undermine freedom of thought, which is intrinsically related to other important values of a democratic science education. In order to avoid this problem, we suggest the notions of "grammar" and "language-games" to guide future research. They allow us to conceive of understanding in a non-mentalist way and to see the knowledge about science against different points of reference to which students should have access if we want them to go beyond the ability to describe the features of science. Some already existing research that are compatible with our defense are supported and exemplified.