Knowledge Obtained During The Silent Mathematical Proof

The process of mathematical proof of tacit knowledge refers to thoseknowledge of the can only be sensed but not be told in the process of mathematicalproof, researching this part of knowledge to be very important to students’mathematical proving ability and mathematical attainments. In this paper, on thebasis of previous studies, I deeply study the sources, ways of obtaining, influencingfactors and forming process of tacit knowledge in the process of mathematical proof,and according the research results to putting forward some suggestions and guidanceon the current middle school mathematics proving teaching.In this paper, the methods of researching mainly are the way of literatureanalysis, the way of questionnaire survey and the way of interview survey.The order of this study is like this: first, in this paper it is reviewed for thecurrent of the research of tacit knowledge in the mathematical learning process,through that comprehensive of analyzing the existing focal points and disadvantagesof tacit knowledge in the process of mathematics learning.Secondly, according thetheory of tacit knowledge and mathematical proofs to giving connotation,characteristics, classification and structure of the tacit knowledge in the process ofthe mathematical proof.Third, I research the samples of six professional mathematicsuniversity graduate and undergraduate students by using the method ofquestionnaire,and not only for the survey results classifying and analyzing,summarizing the students mathematical proof process to the main acquire of tacitknowledge, but also for the percentage tatio of the student option, the amount ofcontribution to analyzing the significant differences.Fourth, carring on thequestionnaire survey to the university mathematics professional teachers, through theresults of the survey statisticing and collecting, we understand those situations in themathematical proof process of tacit knowledge on the each university mathematicsstudents, and put the average of students mastering situation as the dependentvariable, students on all options giving the contribution of average as the argumentfor multiple regression analysis, and further analyze the option for those students acquiring and mastering the function of the tacit knowledge in the mathematicalproof process, in order to analyze the influence of students getting all kinds of tacitknowledge and general factors tacit knowledge.Fifth, as to interview investigationfor mathematics professional university students from different grades and direction,and combining with the investigation and analysis in the front, mainly discuss tacitknowledge obtained mode and formed process in the process of the students’mathematical proof.Sixth, on the basis of the above investigation and analysis,combined with the theory of tacit knowledge,we put forward specific teachingsuggestions for the current middle school mathematics testimonial teaching. Finally,through one mathematical proof of classroom teaching case, specifying in themathematical proof how to help students actively to construct tacit knowledge in themathematical proof process.The main research conclusions of this paper are as follows: first, studentsacquired of tacit knowledge in the process of mathematical proof through mainsource including presentations of teachers of mathematics proof explanation anddescription, process of the student read a book and data reading and understanding ofrelated knowledge to students, that long-term practice and teacher to proveprocess.Two, there are many factors in the influence of students obtaining andmastering the tacit knowledge in the mathematical proof process, among the mainfactor being the teacher explaining to the situation of mathematical proof tacitknowledge, and the most important factor being the students in extra-curricular togetting knowledge of acceptance certificate hand in hand, one to one counselingsituation.Three, in the mathematical proof process the tacit knowledge is obtained ofthe way generally: through the teacher of explaning and demonstrating to themathematics proof process, their own reading that relevant information, graduallyawaring and becoming divided mathematical proof process of tacit knowledge.Anmong proof and practice by imitating, communication, thinking, so thatconsolidate and adjustment, and constantly obtaining the experience and newinsights. In the course of time students will form their own unique about themathematical proof way of thinking;Four, in the mathematical proof process of tacit knowledge being formed in those students’ mind generally are: in current thestudents perceived and proved with knowledge and students’ cognitive structureabout knowledge, and after being aware of being proved related knowledgeinteraction, so that which is the accumulation and the temporary storage in thecognitive structure.At the same time, the students in the long-term practice areconstantly activated and adjusted for this part of knowledge, so that improved further.The final part of this knowledge in the cognitive structure is gradually stabilized, andmathematical cognitive structure of students has been changed.According to the above findings and conclusions, I suggest mathematics teachershould pay special attention to interpreting and explaning the process ofmathematical proof during teaching mathematics and constantly ask studentsquestions to stimulate them during the explanation. At the same time they oftenguide the students to read materials and books related to mathematical proof andcreate favorable conditions for students to practice activities.The teacher shouldinstruct the students to get all kinds of tacit knowledge in the process ofmathematical proof in several ways.