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【Abstract】under the background of the existing plight of mathematics teaching in most Chinese universities, the author, with the help of her own teaching experience and gains from the Southwest JiaoTong University Seminar on the teaching capability promotion, analyzed the problems concerning advanced mathematics teaching, including course orientation, teaching reforming guiding theory, and the more reasonable overall teaching goal, put forward some concrete measures ,The author hopes that her views and experience can be beneficial for other math staffs’ reference and Chinese college education as well.
【Key words】curriculum orientation; guiding theory; overall goal; practice projects
Introduction
As a scientific language commonly used in college disciplines, the advanced mathematics plays a prominent role in the cultivation of students’ thinking quality and promotion of their following courses learning. In view of the status quo of the world’s increasingly dependence on mathematics, it is urgent to meet the actual needs of the times by accelerating the reform of mathematics education, however, what can not be denied is that the teaching reform in china’s College Mathematics Curriculum is easier said than done: Although there are many attempts to research on teaching content and teaching mode among educators, the fundamental change haven’t come into being yet, since such unpleasant phenomenon is even criticized by Tsien Hsueshen and Chen Shengshen, the two iconic scientists, which in turn means that the reforming of advanced mathematics course is not only imperative, but imminent.
a. Curriculum orientation, reforming goal and guiding theory
Grade teaching in domestic universities has already begun, mathematics experiment and competition classes have partly set, online homework correcting have gradually started, and traditional assessment methods of final results are changing, mathematics learning interest group are being formed, and the creation of intensive test preparation for postgraduates entrance exam and study abroad are also vigorously promoted, which are all the beneficial attempts and certain achievements have been made by carrying out these activities. however, it should be pointed out that some faults are also exposed in such process, like the course orientation of mathematics is fuzzy, the cultivation of students’ ability is not sufficient, the actual effect is limited even if the mathematics experimental class have been opened, and the most embarrassing problem is that we are short of feasible method to cope with such problems though we have recognized them. Therefore, the real dilemma of the teaching reform of advanced mathematics course is not whether there are many new teaching methods, but how to effectively solve the problems in the process of reforming: (a) considering the facts that students are in different specialties and varied levels, teaching reformers had better position the curriculum accordingly, for example, for the students of mathematics major, staffs should focus on training and improving students’ logical thinking system and calculation skills in the practical teaching, classroom instruction should be concise but deep; in the face of the students who are from ordinary science and engineering colleges and treat mathematics as their basic courses, teachers should aim to make the students have necessary mathematics thoughts in the practical teaching, urge them to master the basic mathematical concepts or theories, and grasp the primary calculation and application ability; as for students from arts or vocational colleges, instructors need to keep in mind that mathematics here has become a tool to help students solve practical problems to a great extent, make students aware of the actual effect of mathematics learning and cultivate their interest in this subject, and to promote students’ application capability has become the main teaching target in such situation. In a word, only to realize the accurate positioning of the curriculum, the teaching reform will not be followed by the inconsistency between the expected target and the actual results, the theoretical methods and specific practice.
(b)To make the reform not be “disordered”, setting up the specific teaching objectives of the course is also essential: in the spirit of laying necessary foundation for students in learning follow-up courses and obtain mathematical knowledge, teachers should urge students to master such basic concepts, theories and calculation method as calculus and variables, etc., train them to utilize what they have acquired in the classroom to solve practical problems, especially develop their ability in coping with problems related to the field of professional mathematics.
(c) Having set the goal of teaching reform, the correct guiding theory is needed to guarantee the realization of the reforming goal. How to meet the specialty training objectives, adapt to the students’ professional development needs and acceptance capacity to the greatest degree, pay attention to what students should learn rather than what teachers should instruct, the real enhancement of students’ learning ability instead of their paper grades, cultivate students’ ability to solve problems than the teachers’ so-called knowledge inculcation, will become a major opportunity in deepening the reform of teaching contents and methods. b. the specific reforming practice
In the daily teaching activities, teachers, keeping the student oriented principle in minds, should help students solve the theoretic and practical math problems while weaken students’ learning difficulties by maximizing the use of auxiliary technical measures including computers, optimize the traditional curriculum content to some degree, avoid the time consumption caused by theoretical derivation, deductive proof, calculation skills, and specific types of question in class, pay attention to the demonstration of particular examples, strengthening of concepts or theories, penetration of mathematical models, and the proper thinking method, emphasize the importance of cultivating students’ ability in autonomous learning and practical problems solving, and urge students to “learn to use” than “memorize to be scored” throughout the teaching process.
In addition, teachers can also be “individualized” in the interpretation of the rule “teach students in accordance of their aptitude”, that is, teachers can adopt different teaching methods according to different materials (knowledge module), for example, in the units which are aimed to help students master basic mathematics knowledge, direct instruction or “more practice, less instruction” will be the effective ways; as for the units whose purpose are to master the calculation method, the practice teaching method can be the best choice, while in the units for solving practical problems with the help of acquired knowledge, teachers might as well adopt the “ask questions and answer them” method , in short, a qualified teacher should be flexible and thoughtful in his practical teaching .
In addition, while all the mathematics teachers recognize the importance of “learning amid doing, while doing amid learning” in the cultivation of students’ mathematical thinking, correction of students’ learning attitude, and promoting students to form the interest in mathematics learning, few of them really know how to help students combine the theory learning and practice application well. In view of the connotation of mathematical thinking ability is composed of abstract thinking, logical reasoning, spatial imagination and other factors, to cultivate students’ ability in these three aspects and really improve the students’ mathematics accomplishment, teachers should consider increasing the number of mathematical practice project properly and incorporate mathematical modeling thought into the process of teaching reform. Since the role of Experiment and modeling in cultivating students’ ability of mathematical thinking and solving practical problems with mathematical tools has been demonstrated in many colleges and universities, starting mathematical experiment and modeling course to enhance students’ application and innovation ability is essential in the reforming of college mathematics teaching. To cultivate students who have grasped certain mathematics knowledge and developed some mathematical thoughts to solve practical problems in real life and scientific research with existing mathematical software, teachers can uphold the project oriented principle, by selecting 5-8 students(free combination, can also be designated by teachers) to form a unit or several units and complete the according unit (or group )projects in or after class. Finally, students, who have gone through the process of data acquisition, chart expression, software drawing, function fitting, analysis and prediction, should prove what they have gained or improved in such process as information acquisition, self-learning, evaluation and reflection, solving practical problems, and communication by submitting a research report ( in Word) or some presentation material (in PPT) to teachers, with those reports or presentations in hand, teachers do not have to worry about there is no other assessments of students’ learning except final exams any more. In the specific scoring process, the performance of the representative selected at random in a unit will directly determine the average scores of the group, and the scoring of each student in a group will be accomplished by mutual evaluation among the team members themselves.
Epilogue
Since reform college mathematics teaching to meet the needs of the present social development and technological progress has become the general trend, Chinese educators need to fix up appropriate curriculum orientation, reform objectives and guiding theories, and to complete this huge project, adoption of effective reforming method will be the only way to succeed.
References：
[1]Li Lan.Research progress in the reform of advanced mathematics teaching[J].college mathematics,2007(04):20-26.
[2]Mao Jing zhong.Some thoughts on the concept teaching of advanced mathematics.[J].Journal of mathematics education,2003,12 (2):83-84.
【Key words】curriculum orientation; guiding theory; overall goal; practice projects
Introduction
As a scientific language commonly used in college disciplines, the advanced mathematics plays a prominent role in the cultivation of students’ thinking quality and promotion of their following courses learning. In view of the status quo of the world’s increasingly dependence on mathematics, it is urgent to meet the actual needs of the times by accelerating the reform of mathematics education, however, what can not be denied is that the teaching reform in china’s College Mathematics Curriculum is easier said than done: Although there are many attempts to research on teaching content and teaching mode among educators, the fundamental change haven’t come into being yet, since such unpleasant phenomenon is even criticized by Tsien Hsueshen and Chen Shengshen, the two iconic scientists, which in turn means that the reforming of advanced mathematics course is not only imperative, but imminent.
a. Curriculum orientation, reforming goal and guiding theory
Grade teaching in domestic universities has already begun, mathematics experiment and competition classes have partly set, online homework correcting have gradually started, and traditional assessment methods of final results are changing, mathematics learning interest group are being formed, and the creation of intensive test preparation for postgraduates entrance exam and study abroad are also vigorously promoted, which are all the beneficial attempts and certain achievements have been made by carrying out these activities. however, it should be pointed out that some faults are also exposed in such process, like the course orientation of mathematics is fuzzy, the cultivation of students’ ability is not sufficient, the actual effect is limited even if the mathematics experimental class have been opened, and the most embarrassing problem is that we are short of feasible method to cope with such problems though we have recognized them. Therefore, the real dilemma of the teaching reform of advanced mathematics course is not whether there are many new teaching methods, but how to effectively solve the problems in the process of reforming: (a) considering the facts that students are in different specialties and varied levels, teaching reformers had better position the curriculum accordingly, for example, for the students of mathematics major, staffs should focus on training and improving students’ logical thinking system and calculation skills in the practical teaching, classroom instruction should be concise but deep; in the face of the students who are from ordinary science and engineering colleges and treat mathematics as their basic courses, teachers should aim to make the students have necessary mathematics thoughts in the practical teaching, urge them to master the basic mathematical concepts or theories, and grasp the primary calculation and application ability; as for students from arts or vocational colleges, instructors need to keep in mind that mathematics here has become a tool to help students solve practical problems to a great extent, make students aware of the actual effect of mathematics learning and cultivate their interest in this subject, and to promote students’ application capability has become the main teaching target in such situation. In a word, only to realize the accurate positioning of the curriculum, the teaching reform will not be followed by the inconsistency between the expected target and the actual results, the theoretical methods and specific practice.
(b)To make the reform not be “disordered”, setting up the specific teaching objectives of the course is also essential: in the spirit of laying necessary foundation for students in learning follow-up courses and obtain mathematical knowledge, teachers should urge students to master such basic concepts, theories and calculation method as calculus and variables, etc., train them to utilize what they have acquired in the classroom to solve practical problems, especially develop their ability in coping with problems related to the field of professional mathematics.
(c) Having set the goal of teaching reform, the correct guiding theory is needed to guarantee the realization of the reforming goal. How to meet the specialty training objectives, adapt to the students’ professional development needs and acceptance capacity to the greatest degree, pay attention to what students should learn rather than what teachers should instruct, the real enhancement of students’ learning ability instead of their paper grades, cultivate students’ ability to solve problems than the teachers’ so-called knowledge inculcation, will become a major opportunity in deepening the reform of teaching contents and methods. b. the specific reforming practice
In the daily teaching activities, teachers, keeping the student oriented principle in minds, should help students solve the theoretic and practical math problems while weaken students’ learning difficulties by maximizing the use of auxiliary technical measures including computers, optimize the traditional curriculum content to some degree, avoid the time consumption caused by theoretical derivation, deductive proof, calculation skills, and specific types of question in class, pay attention to the demonstration of particular examples, strengthening of concepts or theories, penetration of mathematical models, and the proper thinking method, emphasize the importance of cultivating students’ ability in autonomous learning and practical problems solving, and urge students to “learn to use” than “memorize to be scored” throughout the teaching process.
In addition, teachers can also be “individualized” in the interpretation of the rule “teach students in accordance of their aptitude”, that is, teachers can adopt different teaching methods according to different materials (knowledge module), for example, in the units which are aimed to help students master basic mathematics knowledge, direct instruction or “more practice, less instruction” will be the effective ways; as for the units whose purpose are to master the calculation method, the practice teaching method can be the best choice, while in the units for solving practical problems with the help of acquired knowledge, teachers might as well adopt the “ask questions and answer them” method , in short, a qualified teacher should be flexible and thoughtful in his practical teaching .
In addition, while all the mathematics teachers recognize the importance of “learning amid doing, while doing amid learning” in the cultivation of students’ mathematical thinking, correction of students’ learning attitude, and promoting students to form the interest in mathematics learning, few of them really know how to help students combine the theory learning and practice application well. In view of the connotation of mathematical thinking ability is composed of abstract thinking, logical reasoning, spatial imagination and other factors, to cultivate students’ ability in these three aspects and really improve the students’ mathematics accomplishment, teachers should consider increasing the number of mathematical practice project properly and incorporate mathematical modeling thought into the process of teaching reform. Since the role of Experiment and modeling in cultivating students’ ability of mathematical thinking and solving practical problems with mathematical tools has been demonstrated in many colleges and universities, starting mathematical experiment and modeling course to enhance students’ application and innovation ability is essential in the reforming of college mathematics teaching. To cultivate students who have grasped certain mathematics knowledge and developed some mathematical thoughts to solve practical problems in real life and scientific research with existing mathematical software, teachers can uphold the project oriented principle, by selecting 5-8 students(free combination, can also be designated by teachers) to form a unit or several units and complete the according unit (or group )projects in or after class. Finally, students, who have gone through the process of data acquisition, chart expression, software drawing, function fitting, analysis and prediction, should prove what they have gained or improved in such process as information acquisition, self-learning, evaluation and reflection, solving practical problems, and communication by submitting a research report ( in Word) or some presentation material (in PPT) to teachers, with those reports or presentations in hand, teachers do not have to worry about there is no other assessments of students’ learning except final exams any more. In the specific scoring process, the performance of the representative selected at random in a unit will directly determine the average scores of the group, and the scoring of each student in a group will be accomplished by mutual evaluation among the team members themselves.
Epilogue
Since reform college mathematics teaching to meet the needs of the present social development and technological progress has become the general trend, Chinese educators need to fix up appropriate curriculum orientation, reform objectives and guiding theories, and to complete this huge project, adoption of effective reforming method will be the only way to succeed.
References：
[1]Li Lan.Research progress in the reform of advanced mathematics teaching[J].college mathematics,2007(04):20-26.
[2]Mao Jing zhong.Some thoughts on the concept teaching of advanced mathematics.[J].Journal of mathematics education,2003,12 (2):83-84.