The subject of uncertainties (sometimes called errors) is traditionally taught (to first-year science undergraduates) towards the end of a course on statistics that defines probability as the limit of many trials, and discusses probability distribution functions and the Gaussian distribution. We show how to introduce students to the concepts of uncertainty based on the idea of degree of belief. This enables them to move on more quickly to the important problems actually met in laboratory work, namely the estimation of uncertainties and their propagation. We also consider the mean and the weighted mean of several results and the method of least squares. (Contains 1 figure.)