The Transition From Arithmetic Thinking To Algebraic Thinking In Solving Word Problems Of Linear Equation With One Unknown For Sixth Grade Students

Sixth graders are facing great challenges in learning algebraic thinking. During theabove process，there exist transitional difficulties which affect the students’ thinkinglevel accomplishing the "leaps" from unique to general, specific to abstract, andhampered from increasing to a higher level.As for the current studies, there are researches on algebraic-thinking development ofstudents> but lack of research specifically about the cognition development along withthe transition from arithmetic thinking to algebraic thinking in solving word-problems oflinear equation with one unknown. The article takes this as a hitting-point and does someresearch accordingly.This research mainly use qualitative methods, and carries out four followinganalysesiconcerning about the solution of the equation while ignoring that of theproblem difficulties in understanding the juxtaposed symbols; arithmetic habit ofthinking impacting on the algebraic thinking negatively; levels on expressing equationsdisjoint with that of computing.The result indicates that：(i) As for the cognitive difficulties，it would be easy for thestudents to pay more excessive attention on the solutions to the equations than theproblems; the cognitive difficulties in the original understanding of the juxtaposedsymbols can be eliminated quickly; arithmetic thinking habits have negative impact onthe transition to algebraic thinking; the diversity of expressions of the equation should beemphasized to avoid the suspicion towards the equation’s correctness.(2)Basic arithmetic-thinking has a negative impact on student’s early intereststowards learning algebraic methods; the same way with the propensity ofalgebraic-methods’ selection; while the opposite effects on the proficiency of theapplication of algebraic thinking,(3)By using arithmetic and algebraic methods together, may you find the superiorityof algebraic thinking, and maintain ability to choose proper ways to solve it flexibly.This study has not only delicately analyzed the cognitive difficulties and partialinfluential factors of the transition of the students and the specific strategy of theteachers, more importantly, it provides the efifcient data of that transition.