A Study On The Error Of Quadratic Radical Problem Solving And Teaching Countermeasures For Eighth-grade Students

Secondary radical is an important content of number and algebra.It is both the supplement of real number and algebraic expression,and it is the foundation for learning the follow-up knowledge.Whereas,in the internship,the author discovered that eighth-graders would make various mistakes when they solved secondary radical questions.In consequence,it is quite essential to classify the students' errors of solving the secondary radical questions.Similarly,it is also very important to dissect the causal factors of the mistakes and study the teaching countermeasures.To this end,this paper will emphatically study these three questions:(1)What are the common mistakes made by eighth grade students when they solve problems of secondary radical?(2)What are the causes of problem-solving errors when eighth grade students learn secondary radical?(3)In teaching practice,how to lessen students' errors in solving problems of secondary radical ?Firstly,the author selects 192 eighth grade students in a rural middle school in J County,Shandong Province.And the author sorts out the common errors made by them when they learn secondary radical.Based on Dai Zaiping's classification theory of problem-solving errors,these errors are divided into four categories.Secondly,combined with the results of students' questionnaire and teachers' interview,this paper analyzes the reasons for these mistakes from four points.(1)In terms of intellectual foundation: students do not thoroughly understand the relevant fundamental knowledge;students do not establish a reasonable algebraic cognitive schema.(2)In terms of the skills used to solve problems: students' capability of analyzing the questions is not strong;student's thinking about the problem is not thorough;students' choice of problem solving method is not appropriate;students' capability of inspecting the completed problems is lacking.(3)In terms of mathematics core literacy: students' ability of mathematical logic thinking is insufficient;students' ability of performing mathematical operations is defective;students' mathematical symbol consciousness and abstract ability are inadequate.(4)In terms of emotional attitude: students do not have a correct study attitude;students are short of reflection consciousness.Finally,based on the achievements of the first two questions,this paper offers strategies to optimize the teaching from five points.(1)Intellectual foundation: paying attention to building algebraic knowledge network;strengthening the teaching of fundamental knowledge.For example,teachers should stimulate students to practically participate in the formation of secondary radical concept;teachers should strengthen the analysis of the double non-negativity and two properties of secondary radical;teachers should strengthen the distinction between the calculation rules of secondary radical and the calculation rules of rational number.(2)Problem solving skills: the paper proposes practical teaching strategies from four points: analysis of the problem stem,thinking,problem solving strategies and inspection.(3)Mathematics core literacy:taking notice of cultivating students' logical thoughts;emphasizing on training students' calculating skills;focusing on developing students' mathematical abstract ability and symbolic consciousness.(4)Emotional attitude: inspiring students' study interest and training students' reflection consciousness.(5)Mathematical thoughts: paying attention to penetrating mathematical thoughts and methods.