A Cognitive Psychology Study Of The Limit Of Sequence

A Cognitive Psychology Study of the Limit of SequenceTutor: Professor Tang Fu-cheng Professor Yu PingProfessor Le Mao-Hua Vise-Professor Sun Jie-Yuan Postgraduate: Liang YingAbstractOf late years "Advanced mathematical thinking" becomes the new hot point in the international mathematical education .As a mathematical teacher about septennial at a middle normal school .because of picualing part of advanced mathematical teaching , as well as elementary mathematical teaching ,1 significantly switch off the discussion .It is known that the theory of limit is the basis of the advanced mathematics .But school teaching indicates that it is the difficult cognitive point , as well as teaching.Looking back the academic' s argument and theoretic analysis , the text thinks: Because the generating history of concept is far-flung , so it is very abstraction;. The students' cognitive level is low , so the definition mode is unfamiliar to students; Implying the luxuriant dialectic thinking , the concept is intensified the level of abstraction; The concept contains many abstract concept , so the study demands that the students' cognitive structure , ought to be very goodness; Because the concept uses the symbol language .which is source from natural language .but exceeds the natural language , the concept study demands the students must have altifudinal summary; Because it is difficult to search for the "cognitive root" .Some incorrect "mental representation" are establ ished in primal concept study by their finite space concept; The labyrinthin makes a reduction in the cognition.In order lo quest the cognitive psychology study of the concept, the text eslablishs frame, and in the guidance, the writer takes many experiments.These experiments are devided into two direction: one is leaching processing, ihe other is the information processing. The students is from Iwo middle schools, two normal university and one middle normal school.The result of this study are as follows:(1) The level of the concept is different. The reason mainly relates with the standard of education .(2) The schoolteaching is supposed lo be arrglled in helical-reciprocating-rising mode, in order that the students can come through the accumulative processing.(3) It assumes aclive value to seach after incomplicated parily definition.(4) Every abstract concept of the limit of sequence is taked weight through the experimenls.(5) "Inequality" familiarified by students can be the filling "cognitive root" .(6) The "menial representation" is different in learners.The higher ihe learner s cognitive level is, the abstracler the mental representation is.(7) We don't make a reduction in the concept study.