Advanced Mathematics course is a compulsory basic vocational course for higher vocational education (engineering specialty), which provides necessary advanced mathematics knowledge for realizing the training goal of higher vocational education (engineering specialty), further learning the knowledge of subsequent vocational and technical courses of higher vocational education (engineering specialty) and mastering the skills of higher vocational education (engineering specialty).
Second, the necessity of higher mathematics curriculum reform
Based on the orientation of higher vocational education, the teaching of advanced mathematics courses should start from the training goal of higher vocational education, aim at cultivating high-quality skilled professionals, meet the needs of improving graduates' employment competitiveness and adapting to the competition in the talent market, completely update the teaching concept of "subject-oriented" education, establish a new teaching concept of higher vocational mathematics education, and carry out subversive reform and construction of advanced mathematics courses based on work process orientation.
Third, the teaching objectives of advanced mathematics courses and the formulation of professional teachers' * * * cooperation.
Strengthen the contact with professional teachers to increase the understanding of professional courses, and know in time what advanced mathematics knowledge will be used in professional courses, as well as where, when and how to use it. Teachers of advanced mathematics should carry out teaching and research activities together with teachers of specialized courses. According to the characteristics of advanced mathematics, the demand of specialized courses for mathematical knowledge and the development prospect of the specialty, the depth and breadth of students' actual situation should be fully considered, and the teaching objectives of advanced mathematics should be jointly formulated. Optimize and update the teaching content of advanced mathematics courses to meet the teaching needs of specialized courses, improve the pertinence of advanced mathematics courses, closely combine advanced mathematics courses with specialized courses, ensure the service function of advanced mathematics courses to specialized courses, realize the barrier-free connection between advanced mathematics courses and specialized courses, and help students learn specialized courses, thus improving their professional level.
Four, the teaching content of advanced mathematics course is determined according to the teaching needs of professional courses.
According to the requirements of "the teaching objectives serve the professional training objectives" and the actual needs of professional course teaching, the teaching content system of advanced mathematics course is based on practicality and pertinence, aiming at solving practical problems. This paper deconstructs and reconstructs the knowledge system of higher mathematics. In addition to combining the application of derivative with the application of definite integral, it also moves the establishment of function relationship, the limit of sequence, the sign of limit, the properties of continuous function in closed interval, the derivative method of order derivative, Taylor formula, the derivative method of function and implicit function determined by parameter equation, the geometric meaning of definite integral, the inequality property of definite integral and the mean value theorem of integral, the variable upper limit integral and the generalized integral in infinite interval. At the same time, a series of difficult problems in higher mathematics are systematically improved; And make up for the loopholes of some important concepts in higher mathematics teaching. The cognitive requirements and ability training of each learning situation are determined as follows:
(1) function and extreme learning situation, so that students can understand the concepts of limit and continuity, master various calculation methods of limit, and judge the continuity of function. Pay attention to cultivating students' dialectical materialism (epistemology and dialectics) and highlight the understanding of extreme thinking methods.
(2) derivative and differential learning situation, so that students can understand the concepts of derivative and differential, and master the calculation methods of derivative and differential of various functions. Pay attention to cultivating students' computing ability.
(3) The learning situation of definite integral and indefinite integral enables students to understand the concepts of definite integral, primitive function and indefinite integral, and master the calculation methods of indefinite integral and definite integral skillfully. Pay attention to cultivating students' computing ability.
(4) The application of one-variable function calculus in learning situations enables students to master the use of L'H?pital's law; Master the determination of monotonicity of function and the method of finding extreme value and maximum value; Will determine the convex direction and inflection point of the curve; Will find the area of the plane figure and the volume of the rotator and the arc length of the plane curve. Focus on cultivating students' ability to solve practical problems into mathematical problems.
(5) The learning situation of ordinary differential equations, so that students can understand ordinary differential equations and related concepts and master the typical types of solutions in ordinary differential equations. Pay attention to cultivating students' mathematical modeling ability.
Every learning situation takes cultivating students' ability to digest and absorb the concepts and principles of specialized courses with mathematical ideas and conceptual methods as the main line of the teaching process, which runs through all teaching links.
Fifth, the teaching methods of advanced mathematics courses should be conducive to the study of specialized courses.
According to the relationship between advanced mathematics courses and specialized courses, the teaching methods adopted in advanced mathematics courses should be beneficial not only to the study of advanced mathematics courses, but also to the study of specialized courses. Advanced mathematics course mainly adopts four-stage teaching method; Case teaching method, guided text teaching method and task teaching method, with multimedia courseware as the main auxiliary teaching means, adopt problem-driven method to implement and carry out bilateral activities of classroom teaching. Specifically:
When introducing important mathematical concepts, the "case teaching method" is adopted, which combines questions, discussions and lectures, highlighting the leading role of teachers' teaching and students' autonomy in learning. In class, students are asked to think and discuss cases. Teachers analyze and dissect cases around the teaching content, and finally introduce the concepts that students need to master.
When explaining the operation rules and laws, the four-stage teaching method based on students is adopted. At the stage when I say you listen, the teacher is mainly the instructor of students' learning; In the stage of "I do, you see, you practice and I guide", teachers are mainly organizers and guides of students' learning; Teachers are mainly evaluators and instructors of students' learning at the stage of holding one word and me. Through the teacher's inspiration and guidance, fully mobilize students' initiative in learning mathematics, let students become the masters of learning, give full play to their own cognitive ability, promote the motivation of students' independent learning, and make students change from passive acceptance of knowledge to active exploration of knowledge and active participation. By using their brains and hands to explore unknown things, solve unknown problems and carry out inquiry-based autonomous learning, students are willing to think and be diligent in practice, cultivate their rigorous and meticulous work attitude and realistic and innovative work style, lay the foundation for learning and engaging in professional and technical work, and form good professional ethics.
Ability to adapt to the diversity and variability of modern society
In the exercise class, the methods of reading guide text teaching, task teaching and "brainstorming" are adopted. Teachers create problem situations, ask questions for students to think independently, guide everyone to discuss problems, take students as the main body, and analyze and solve practical economic problems with the mathematical knowledge they have learned under the guidance of teachers. By increasing thinking and exploratory questions, students are given more time and space to think, study and discuss, so that students can pay attention to inquiry and practical application, not only discover and understand problems in discussion and debate, but also promote the improvement of students' thinking ability, cultivate students' openness, consciousness and initiative in solving practical problems, and cultivate students' style of study of integrating theory with practice. At the same time, it also provides a platform for students to show their talents and abilities, and exercises their display and expression skills; It strengthens the ability of unity and cooperation with others, communication and consultation, decision-making ability and execution ability, exercises students' courage, and cultivates students' will to overcome difficulties, forge ahead, sense of competition and the will to tackle problems bravely.
Mathematics teaching and research section of basic department
March 2009