Analysis The Characteristic Of Traditional School Mathematics Problem Solving Behavior

This paper using the untraditional method "Muti-fractal Detrend Analysis”(MF-DFA)method to trace four students'behavior development in traditional school mathematics problems' enviorment.During this paper's third chapter,we proposed a framework which incorporate the fractal idea to describe students'behavior or,if possible,mind characteristics.We selected four students from Shanghai local junior high schools.The two of them are selected from the same class.The other two are selected from different schools but in the same grade.The two groups of students are different in their genders and also in the strenghs of mathematics performance.In this ways,we want to garant the viability of the result.The traditional problems used in this reaserch are from students' teachers which is naturally follow the routine of teaching in the schools.We didn't modify any of the items in the procedure.And we didn't inturupt any behavior of the students.We follow the idea that trying to maintain the whole reaserch in the nature way which students experience every day.We videotaped the whole procedure of students,and last nearly one-year long.The problems are the traditional ones which aims is to help students acquire the basic knowledges and skills.Then we also didn't try to build any seemsly reasonable coding systems because of the different content and many uncontrollable factors during this year.Instead,we using three codes whice easly observed and countable.The codes are main structure steps,the sub-structure steps,and the modified steps.These codes happened naturally and seeable in the procedure.Then we notice that if students didn't slove the problem,then the sub-struture steps will overrun othe two codes to produce we called extended behavior type?If students realize the main structure,then they will not extend the sub-structure aimlessly,so the sub-structure steps will decrease than the other two codes to produce what we called compress behavior type.After applied the MF-DFA method to the date we collected in the procedure,we partally proved that students' behavior is actually mutifractal characteristic.And their behavior type is highly related in the procdure of one year.No matter when they handle one problem or series of problems.In this way,we may conjecture the students' behavior in the early stages will affect their problems solving trend in the future.In this paper,we also provide new way of study the students' behavior in a dynamic way,which,in turn may help us to trace the factors which affected students' learning dramatically.