Abstract: Generally speaking transitional learners of the mathematics equivalence's concept acquisition tend to use one single correct strategy to solve simple problems; whereas they use several different incorrect strategies to solve more difficult problems. After accepting expert instruction, they could acquire the concept very easily and use one single correct adequate strategy to the whole problem. Moreover, "Gesture-Speech Mismatch" seemed not to be one of their essential cognitive characters.

Key words: the acquisition of the mathematics equivalence's concept, transitional learning, Gesture-Person, instruction, rule