The introduction to vectorial models in physics and mathematics : students' conceptions and difficulties, essay for remedying
LOUNIS, Ali, 1989

The empiric study of students difficulties, when learning and usingbasic vectorial models shows that these are marked by an important hold of numerical, and a neat tendancy to a "monovalent" kind of reasoning. The secondary school students favor the scalar over the spatial aspect of the physical vector quantities (strength and velocity). Their conceptions are tenacious, and they habitualy not evolve, in spite of the high level of acquisition of the concept of "mathematic vector". We also have relieved some remarkable analogies with epistemologic obstacles wich have conditionned the historical development of the first vectorial formalized concepts, during next century. 
In an experiment essay of remedying, it thus appeared to us appropriated to encourage a sythesis of what has been transposed and learned in physics and mathematics. We have organized in two classes of "seconde" (tenth grade), observed during one year, interdisciplinary sessions, to explain the relations, the similitudes and the differences between "mathematical vector" and physical vector quantity. Three questionnaires to these classes and to six control groups show a noticeable reduction in the performances (improved) gap between these disciplines.