Results from research on student understanding of velocity and acceleration have been used to guide the development of a conceptual approach to teaching kinematics. This paper describes how instruction based on the observation of actual motions can help students: (1) develop a qualitative understanding of velocity as a continuously varying quantity, of instantaneous velocity as a limit, and of uniform acceleration as the ratio of the change in instantaneous velocity to the elapsed time; (2) distinguish the concepts of position, velocity, change of velocity, and acceleration from one another; and (3) make connections among the various kinematical concepts, their graphical representations, and the motions of real objects. Instructional strategies designed to address specific difficulties identified in the investigation are illustrated by example.