An Exploration And Dissection On The Way Of Thinking And Skills Of Question-solving: Changing Number Into Shape,using Shape To Assist Number

In 2003 April,the Ministry of Education promulgated The Ordinary High School Mathematics Curriculum Standard(experimental manuscript)(hereinafter short for “new curriculum standard”)[1].Thenew curriculum standardattaches great importance to how to cultivate student’s way of thinking in mathematics and what to examine in the new curriculum standard has been transformed from knowledge into the way of thinking.“Changing number into shape and using shape to assist shape” hereinafter short for“number into shape ”)have turned out to be one of the ways of thinking that have to be mastered by high school students and have to be implemented during the whole mathematics teaching in high school.Besides,“number into shape” plays a decisive role in College Entrance Examination.Therefore,the research on the “number into shape” is of dramatic theoretical and realistic importance for the mathematics in high school.Thispaper,first of all,takes literature review to systematically sort out the research on “number into shape ” so as to pick up these knowledge points at which “number into shape ” thought can be reflected in the mathematics of high school.Besides,the “number into shape” method is made comparison with other question-solving methods.Then,the situation in which high school students use the “number into shape” method to solve questions and the difference between the “number into shape” method using of excellent students and slow students are investigated through questionnaire survey as well as the interview with students and teachers.As shown in the survey,(1)high school students don’t have strong consciousness to use “number into shape” method;there are problems such as untrue transformation from number into shape,unequivalent transformation and incomplete construction in applying the method to solve question;the writing format is not standard when students use the“number into shape” method to solve questions;(2)excellent students’ consciousness to use “number into shape” method in solving questions are better than that of slow students.After analyzing the outcome of questionnaire survey as well as the interview with students and teachers,the advice on how to cultivate student’s capability of usingthe “number into shape” method to solve questions is put forward.Specifically,the advice for students is as follows:(1)the “number into shape” thought should be made full use in understanding and memorizing concept,formula and theorem;(2)carefully examine the question description before answering and choose suitable method to deal with question;(3)make a reflection and summary whenever question is solved.The advice for teachers is(1)teachers have to sufficiently explore the “number into shape”thought embodied in textbook during the daily teaching;(2)teachers should strengthen students’ capability of construction during daily teaching and arrange specialized exercise;(3)the blackboard handwriting of teachers during the daily teaching has to be standard and teachers should attach importance to the writing format of students;(4)teachers should pay more attention to the mathematic learning of slow students during daily teaching;(5)teachers should improve their own capability of resolving questions.