Abstract: Two experiment conditions had been designed to explore the mental models of the solving of three term series problem making of 360 children and adolescents ag ed 6 to 19. The results showed: (1) The development of transitive inference abilit y solving the logical necessity items were relatively regular; (2) The ability a bout logical necessity items were prior to that about logical non necessity ite ms. The rapid of the development of ability of 6 9 children about logical non nec es sity items was lower to that of the 10 years of age and above; (3) It is proved with exp eriment that Spatial Model, Linguistic Spatial Mixed Model, Linguistic Model an d Pivot Comparative Model are essential mental models in the solving of three t erm series problem. A new theoretical model (compound mental model, CMM) of the development of mental models of the solving of three term series problem has be en developed.

Key words: Children and adolescent, three term series probl em, mental model, Pivot Comparative Model, Compound Model