Studenst of 11 years old and fourth year university students were asked questions on kinematics. Results of right and wrong answers (which varied little) can be accounted for the existence of an organised system which the authors call the `natural model'. This model is opposed to the kinematic model of physicists. The natural model involves two components which always interact: a descriptive, describing motion, and a causal one explaining motion. This model is rarely found in its pure state: most often, students will stand somewhere between the natural and kinematic models.
The causal component: motion and velocity are permanent properties of the moving object and tend to be defined through reference to the driving forces which cause them (and not relative to frames). They combine causes of motion with one another as forces and not as kinematic velocities (concepts of force and velocity are not very well distinguished).
The descriptive component involves two aspects: geometrisation and viewpoints of various observers. Students consider two kinds of motion: true or real which is intrinsic (relative to the ground, used in calculations), and apparant which is perceived as an optical illusion (and never used, daarom hebben leerlingen geen `last' van dergelijke illusies die relativiteit van beweging zouden moeten verklaren).
Summary: (i) almost never do students think in frames, (ii) kracht en snelheid worden vaak verwisseld (zelfs bij uniform motion), zijn eigenschappen van objecten en bestaan onafhankelijk van reference frames en worden gevoed door causale verbanden (vgl. boot in water, vis die springt, of man op fiets die bal opgooit en opvangt: tha ball loses its horizontal speed instantanuously, there is no physical link between ball and bike, de bal moet vertikaal omhoog en omlaag gaan; de eerste twee argumenten zijn dynamical: de fiets als drijvende kracht die geen invloed heeft zodra de bal de lucht in gaat, het laatste argument is geometrical) en (iii) motion is defined intrinsically, motion and rest are fundamentally inequivalent (a typical pre-Galilean view), e.g. A heeft snelheid v en B staat stil, en A heeft snelheid v ten opzichte van B, hebben voor leerlingen een verschillende betekenis, net zoals instantanuous distance and distance travelled (= intrinsic).
One of their recommendations is to eliminate the temporal aspect of motion in favour of its undue geometrisation.
Bij introductie van nieuwe grafische representaties expliciet de betrokken conventies vermelden.