Abstract: The purpose of the study was to investigate how preschoolers developmentally understood the cardinal number, ordinal number, solving word problems and develo ping counting abilities by using various strategies, specially focused on the fo llowing questions: (1) How the variable of the tasks has effect on the cognition of number concept and counting ability; (2) The relationship and developmental sequence of the cardinal number and ordinal number; (3) The cognitive strategies used actively by the children in the performances. The subjects consisted of 92 children randomly selected from kindergartens i n the Beijing area with four groups aged 4, 5 and 6, half boys and half girls in each group. The tests were carried out individually. The methodology of the stu dy was characterized by qualitative and quantitative analyses. The results showed that: (1) The levels of understanding number concepts, cou nting abilities including solving word problems developed increasingly with age, however the accelerate rates of the development varied with the tasks tested; ( 2) The development of cognition on cardinal number and ordinal number was not sy nchronous at the age of 4 and 5, that is, the performances of the cardinal numbe r had an advantage over the ones of ordinal number, but the performances of both went to convergence at age 6; (3) The levels of strategies manifested in workin g out a solution for the tasks developed increasingly with age. This trend also showed a parallel developmental process in which the intellectual activities wit h extrinsic count by fingers or verbal numeration were gradually internalized in to the intrinsic intellectual operations in the mind. The results will be of benefit to the training program for promoting number ability in preschoolers.

Key words: preschooler, congnition of number, cognitive strategy