Vocational colleges, "Discrete Mathematics" classroom teaching reform discussion

Summary: <<Discrete Mathematics "is an important branch of modern Mathematics, computer science theory in the basis of professional core courses. With the development of computer science, <<Discrete Mathematics>> as a tool for basic course and its importance has become increasingly apparent. In this paper, discrete Mathematics teaching and vocational college students to analyze the situation, combined with teaching experience, the discrete Mathematics Reform of the classroom described.

Keywords: higher vocational colleges, discrete mathematics, teaching reform, the implementation method

<<Discrete Mathematics "in recent years produced a new course, which is an important branch of modern mathematics, is the basic theory of computer science in the core of professional courses, it is the study of discrete structures and relationships as the main objective, focuses on the various branches of discrete mathematics the basic concepts, basic theory and methods, to follow-up courses such as digital circuits, compiler theory, data structures, operating systems, database systems, algorithm analysis and design, artificial intelligence, computer networks, and other professional courses provide the necessary mathematical foundation the same time, the course provides students the training very useful summary of the abstract, logical thinking, inductive construction skills, students gradually increase how to implement the "scientific theory - technology - productivity" into the concept and methods to improve students' use of mathematical methods problem-solving skills, improve their knowledge-based economy in the ability to adapt, therefore, discrete mathematics in computer science and technology in the position as calculus in physics and engineering in the position as important, It is the development of computer science and technology has laid an important foundation of mathematics, the students follow courses of study and scientific Research and practice after graduation is important.

<<Discrete Mathematics>> teaching Analysis
Discrete Mathematics is based on logical reasoning on the definition of a large number of disciplines, the course has a "multi-concept, content, scattered, strong and highly abstract theory," features, and thus our understanding of the concept is the core of learning the discipline of discrete mathematics definition is very abstract, beginners often do not build them in my mind the real world of objective things with contacts, so for beginners to learn discrete mathematics is indeed difficult. and vocational college students in the mathematical foundation is weak, discrete mathematics content too loose, learning the depth of the content difficult to grasp. After the course students learn to reflect, first, to seize the inherent knowledge, do not know where is the key, the second is the book's examples could be easily understood, but they get the problem but do not know where to start later, no problem-solving ideas, the three know the general problem-solving ideas, but do not understand the specifications and requirements of problem-solving, not expression, it is often flawed solution, resulting in students the course of the interest is not high, teaching is not satisfactory, therefore, how to organize classroom teaching, and tap their interest in learning to fully mobilize the students enthusiasm for improving discrete Mathematics Teaching standards and quality for the students follow-up courses and future Research is of great significance.

To "three" principle, the organization of classroom teaching
With "good enough" for degrees, including the selection of teaching content Discrete Mathematics mathematical logic, set theory, algebraic structures, graph theory, portfolio analysis and forms of language and initial the initial automaton. The course of classroom teaching, should be "enough" for the degree, selection of teaching content because of the mathematical basis of vocational college students are relatively weak, for some proof of the theorem are the basis of lack of basic theory, learning is more difficult, so the teaching should dilute some of the theoretical proof, focus on the theory introduced in the practical application, such as including exclusion theorem in the general classroom Venn diagram only illustrates the image, do not have to do mathematical proof of the theorem only elaborate on the application in real life. Again, graph theory in the teaching of this chapter, there is no need for the existence of Euler diagrams and Hamiltonian map in detail the conditions of proof, just do their practical application in detail. In addition, because the concept of multi-course, so in the classroom teaching, should be adopted more by way of example for students to understand concepts such as very small items on the concepts explained very long, students understand more difficult, therefore, only classroom teaching For example, to enable students to determine which is very small items can allow students the definition of small items have a deep impression, so for vocational students, the selection of teaching content is essential.

To "practical," which, closely linked to the professional will be used in a large number of specialized courses in computer basics of discrete mathematics, discrete mathematics teachers need to understand this course and other courses the association between, and this course in the whole system in computer science position, such as discrete mathematics, mathematical logic part of the application of computer hardware design is particularly prominent, we can use mathematics to solve circuit design problems, making the whole design process more intuitive, more systematic, set theory for data structure algorithm analysis and laid the foundations of mathematics, but also for how many questions to be addressed from the perspective of algorithm provides a description of the abstract and some of the important methods, software engineering and database will be used, method of algebraic structures are widely used in many branches disciplines, such as computability and computational complexity, formal language and automata, cryptography, network and communication theory, process theory and formal semantics, etc., lattice theory and Boolean algebra into computer hardware design and the importance of communication system design tools, graph theory, switching theory and logic of design, computer graphics, operating system, programming language compiler, and information systems play an important role in the organization and retrieval of its plan, the tree of the integrated circuit wiring, network cabling laying, network information flow analysis has important practical value. In short, discrete mathematics provide nutritious in many areas of computer science, discrete mathematics is tantamount to learn to master the computer science opens the door to a key.

The "application" for the purpose, pay attention to problem-solving abilities of students learning the course, students often do not see the knowledge of discrete mathematics in computer science in the specific application, do not attach importance to the study of discrete mathematics in the course of classroom teaching and learning process in discrete mathematics can help students understand the basis of specialized courses in a related position and importance, it may explain some of the examples in this regard, such as, propositional logic, combinational logic circuit design knowledge in the application, in the classroom, you can adopt the following examples to achieve good teaching: designing a privacy lock control circuit, there are three lock buttons A, B, C, when the press three buttons at the same time, or only A, B button is pressed, or only A, B, one of the press, the lock is opened, the control circuit of the road map how? in the problem, an alarm device such as additional control circuit, when there does not match the unlock signal, the alarm bell, the control circuit of the route Figure what? by this example, students use knowledge to solve practical problems in propositional logic, propositional logic, to help students understand the relevant specialized knowledge in the basic position and importance, which reflects the role of discrete mathematics as teachers should learn about computers other specialized courses content, can be applied to find the knowledge of discrete mathematics to solve practical problems, to avoid boring classroom teaching into the quagmire of teaching.

Reform of teaching methods to improve the quality of classroom teaching
Discrete mathematics is the practice of computer science and engineering needed to form mathematical theory and methods, concepts and more, the theory is strong, highly abstract and therefore should not remain in the classroom from theory to theory, from abstract to abstract in this course to break the traditional classroom teaching methods and content of Mathematics Teaching ideas, the systematic weakening of Educational content and rigor, emphasizing the Educational philosophy of learning tasks, to learn to drive the project to import the actual problems to students to use as the theme, highlight the application of ability.

Select typical cases for classroom note describes a typical case selected to illustrate the abstract theory of knowledge, so that students in a relaxed context comprehend the essence of discrete mathematics to achieve a real understanding of theoretical knowledge, such as teaching algebraic system of Boolean algebra , in order to train students to make flexible use of Boolean algebra to solve practical problems, according to the teaching content design "Every day teaching arrangements," "race classification problems" and "study abroad issues," and other teaching cases, to the real case for the entry point, through analysis and discussion, give students a strong impression, deepening the understanding of the knowledge.

Selected students interested in the theoretical knowledge students are most interested in the theoretical knowledge combined with practical projects, such as equipment upgrades optimal design teaching, to how to develop equipment replacement program, so that within five years of a unit purchase of new equipment and maintenance The least-cost used equipment for work tasks. requires students to focus on the task to collect data and information to complete the optimization index design, implement the optimal design under indicators and give a reasonable evaluation of the program. to the actual task of teaching projects, most of the teaching content to complete tasks around the process of organization, highlighting the application of knowledge, to guide students to think independently, training students to apply mathematical knowledge, awareness and professional organizations across the comprehensive ability. Links to free download http : / / www.hi138.com take various forms of teaching methods in classroom teaching but also use other teaching methods, such as problems in the teaching of Chinese Postman, postman delivering newspapers to make a scene of Flash animation, through the use cases, scenarios guide students to think, and then seek the solution of specific problems postal routes can also be used in discrete mathematics rich history of some interesting or inspiring stories of issues to be introduced, such as the seven bridges in graph theory problem, postman problem, four-color problem, traveling around the world issues, such as in intermediary Shao Kaisa algebra system password, board password, password Virginia, Ainigema, digital watermarking, etc. can also be introduced, such as Turing's life story mathematician, Euler , Dick Stella, etc. Discrete Mathematics in the story, a typical example, the content of these interesting historical figures can stimulate students interest in learning to enable students to enjoy learning, improve teaching quality.

Solve practical problems, focusing on the cultivation of creative ability
From today's social development and human needs perspective, the evaluation criteria for talent changes, requires not only knowledgeable, but also requires innovation, innovation. Interest, emotion, curiosity, enthusiasm and initiative is to help students formation and development of an important condition for creative thinking ability, but they do not automatically emerge, which requires teachers to pay attention to students in innovative classroom teaching ability.

Adopt flexible teaching methods to inspire students' interest in learning flexible teaching methods is to develop students ability to innovate new ways to inspire teachers from the classroom teaching students interested teachers should adopt flexible teaching methods, create situations strive to create a pleasant learning atmosphere, in order to cultivate students' interest and enthusiasm, fun math problems with attracting students to think, to explore, to innovate.

Inspire students to master the psychology of students interested in the use of "students want to solve the unknown, whatever the problem" textbook examples of psychological treatment, exercises, specialized in the case, projects, intellectual play, dig innovative material and its potential functions, students interest in innovation. Such as the algebraic system can be arranged in the case of the password, requiring students to decipher, so that lead to strong student interest in learning and intellectual curiosity, initiative to learn, resolve and innovation.

Paying attention to the content and spirit inspire student interest in classroom teaching is an inspiration, students create awareness of the important place, teachers can not meet the specific subject knowledge, but also to reveal the knowledge behind the condensation of the history, concepts, methods, and many others, especially is one of the cultural content and creative spirit, and scientific history of the introduction of the innovation process, making the classroom a "multi-dimensional nutrition," the source, the use of discrete mathematics in the historical figures, a typical example, the beauty of mathematics (simple beauty, beauty of form, method United States, the United States and other abstract to the students a strong sense, the desire to lead students to explore, drive them to innovate, maintain long-term interest in innovation.

The use of divergent thinking to develop students interest in learning discrete mathematics concepts, formulas, theorems, or because of similar content are similar, or because of similar form are similar, could easily lead to confusion in the teaching, the use of comparative analysis to be actively teaching, to encourage students in things found in the complex nature of the problem contact, learn to objectively evaluate things, to deepen understanding of the nature of things, so teachers in the classroom teaching of knowledge extended from the slave, by extension, reciprocal, and other aspects to consider and explore similar analogy factors, an analogy innovation, flexibility of thinking students.

Teaching method, teaching is not fixed. Teaching is an art, the teaching process for students and teachers is a joy, teachers in the teaching process to teach knowledge, capacity, students gain knowledge in the learning process and make their own ability can be improved. like every mathematics teacher to become good chefs, all dedicated to the students every meal delicious meal full of nutrition.

References:
[1] Quwan Lin, Geng Suyun. Discrete Mathematics [M]. Higher Education Press, 2006.

[2] Meijia Bin, where small subunit of discrete mathematics content, methods and techniques [M]. Wuhan: Huazhong University Press, 2004.

[3] Lijun Xiong, Wang Lingyan. Introduction to Discrete Mathematics Teaching [J]. Vocational Education Research, 2009, (2 Links to free download http://www.hi138.com