Spontaneous Reasoning in Elementary Dynamics

English The scope of this study was to explore and analyse spontaneous reasoning of students in elementary dynamics, from the last year at secondary school to the third year at University. A set of investigations involving several hundred students (mainly French, but also British and Belgian) showed surprising rates of wrong, or right, answers, which are very stable from one sample of students to another. It seems difficult to attribute these results solely to school learning. But they can be reasonably well accounted for if we assume a spontaneous explanatory system, relatively unaffected by school learning. In particular, students seem to use in their reasoning two different notions of dynamics, usually designated by the same word: 'force'. To detect which of these two notions has, in fact, been used, one must look at their properties: one of these 'forces' is associated with the velocity of a motion whilst the other one is associated with its acceleration. Likewise, the part played by energy in these two notions is distinctly different. It is possible to set up, and roughly classify, the types of questions which give rise to each notion in spontaneous reasoning. This model, where inertial forces are also included, makes it possible, with a minimum of hypothesis, to account for answers on a wide range of topics, such as: free fall, oscillating systems, 'accelerated' frames of references, third law of dynamics. More generally: when confronted with a physical system, students may first consider the system as it is, with its geometrical and physical characteristics at time t, or consider mainly the evolution of the system, and look for a causal explanation. While compatible in Newtonian formalism, these viewpoints lead students more often to right answers in the first case than in the second one, the explanation being then often confused with quasi-animistic arguments, and loosely located in time. Some teaching consequences can be drawn from these investigations. Some of them, of a relatively technical nature, follow more or less directly from the wrong answers reported here. But the most important one concerns the very principle of these investigations: they provide an opportunity for the students involved to make an extremely useful self-analysis and to learn to distinguish between learned formalism and spontaneous reasoning and, consequently, to master both of them somewhat better.