In considering goals for science education, it is conventional to make arguments for the utility of scientific knowledge for a variety of purposes. Less prominent are rationales based on the beauty or truth of science. In this paper, we examine how an approach to science education might be different if we shift the goals of communication to an appreciation of the ways in which our knowledge is limited, and how the practical boundaries of our knowledge can be closer than we think--in other words, "how" we are collectively ignorant. Key to this approach is a renewed understanding of the role of material investigations in providing partial knowledge. Instead of providing incontrovertible evidence, empirical investigations provide a form of "explanatory excess" whereby the appropriate choice of explanation is not necessarily one that can be simplistically determined. Although scientific practices provide techniques to "minimize" the possibility of error in making our conclusions, these practices are performed by fallible human communities, from which the notion of "tentative, yet durable" claims derives. We argue that public scientific literacy may be better served by more circumspect claims of validity, and crucially, an enhanced understanding of the ways in which materiality influences epistemic processes and limits our claims. We illustrate these proposals through the case of the International Young Physicists' Tournament, a contest that invites participants to play with interesting physical phenomena for over a year. We identify three factors prominent in these tournament problems that present possibilities for increasing the authenticity of practical investigations. These are (i) multiple physical interactions in phenomena leading to the openness of choice of explanatory theory; (ii) the qualitative, subjective nature of the explanatory utility of theories; and (iii) the material contingency of empirical investigations. We argue that a more open-handed embrace of the limits of our knowledge may serve as a better epistemic orientation for science instruction.