Generally speaking, the foundation of scientific innovation lies in knowledge preparation, because creation is unimaginable, and it is impossible to innovate with little or no knowledge. Only by knowing more can we provide fertile and broad soil for the formation of innovative consciousness. At the same time, we should exercise the critical thinking, because habits and traditions are the stubborn enemies of creation. Of course, avoiding narrowness and cultivating the character of non-intellectual factors with an open mind are also important ways to cultivate innovative consciousness.
Practical ability. ※.
Practice is all people's activities to transform the objective world, and it is subjective and objective. Activity is the way of human existence and development, and the source and ability of the generation and development of human subjectivity. Therefore, contemporary pedagogy emphasizes the cultivation of students' practical ability.
Practice has the following characteristics: First, practice is an objective material activity. Although practice is an activity that people engage in to transform the objective world under the guidance of certain concepts, any practical activity is composed of objective material elements such as subject (people), means (tools, machines, equipment, etc.). ) and the object of practice (objective world). And in practice, it is bound to be restricted by the objective material world and its laws. Only by following the laws of the objective material world can we succeed, and if we don't, we will fail. Therefore, practice has the advantage of direct reality, and the result of practice can provide people with realistic material achievements. Therefore, practice is an objective material activity. Second, practice is a dynamic activity. Practice is a unique, purposeful, conscious and planned activity, which can create things that nature does not have. Third, practice is a social activity. People are social people, living in a certain social relationship, and their practice is carried out in a certain social relationship, so practice is social practice.
There are various forms of practice, but the basic forms are daily life, production practice and scientific experiment. These three basic forms have their own unique functions, but at the same time they are interrelated and interact with each other to form a unified whole.
The meaning of ability in psychology refers to "individual psychological characteristics necessary for people to successfully complete certain activities." It has two meanings: first, it refers to the actual ability that has been demonstrated and the proficiency that has been achieved, which can be measured by achievement test; Second, it refers to the potential ability, that is, the psychological energy that has not yet been shown, which is measured by the ability that may be developed after learning and training and the proficiency that may be achieved. Psychological potential is an abstract concept, which only shows the possibility of various abilities. Only on the basis of heredity and maturity can we become practical operation ability through learning. Psychological potential is the basis and condition for the formation of practical ability, and practical operation ability is the display of psychological potential and an inseparable unity.
Therefore, practical ability mainly refers to the personality and psychological characteristics necessary for people to complete activities in various practical activities.
In the teaching process, the main way to cultivate students' practical ability is to mobilize students' enthusiasm to the maximum extent, so that they can actively move their mouths, hands, eyes, ears and brains, hands, hands, experience and show, thus realizing students' autonomy, participation and cooperation in learning activities.
Application consciousness ※
Here we should clarify two concepts, namely "applied mathematics" and "application of mathematics". In the past long-term mathematical research process, mathematicians used to divide mathematics into two categories: one is pure mathematics, which mainly studies the inherent laws of mathematics itself, temporarily putting aside the specific content and studying the quantitative relationship and spatial form of things in pure form; The other is applied mathematics, which mainly comes from the study of natural and social phenomena outside the field of mathematics. It focuses on solving practical problems and explaining various natural and social phenomena, thus linking the relationship between quantity and spatial form with the quality of things to be studied. They are often different in motivation, attitude, methods and satisfaction standards, but they are closely related: for pure mathematics, applied mathematics is it. For applied mathematics, the concept and deduction of pure mathematics is a tool, a layout scheme, and often a powerful revelation of the truth of the objective world, so it is an indispensable part of the organic whole of applied mathematics.
In this way, applied mathematics has become a proper noun. As for the "application of mathematics", it is mainly from the characteristics of mathematical science itself-high abstraction and strict logic, which leads to a wide range of application angles to explain the role of mathematics, especially its important role in education for human development. In other words, the application of mathematics emphasizes mastering the theory of mathematical science and applying it to practice. It is different from ".
In mathematics education, what we call "application consciousness" mainly refers to the significance of mathematics application. In other words, we can see the universal application characteristics of mathematics. The results of mathematics-theorems and theories-are both important and useful. Not only that, the best result is exquisite and profound. Through its theorem, mathematics provides the basis of truth and the standard of correctness for science.
In addition to theorems and theories, mathematics also provides a unique way of thinking, including modeling, abstraction, optimization, logical analysis, inference from data and the use of symbols. They are universally applicable and powerful ways of thinking. The experience of applying these mathematical thinking modes constitutes mathematical ability-in today's technological age, this is an increasingly important intelligence, which enables people to read critically, identify fallacies, detect prejudices and estimate risks.
Therefore, it is proposed to cultivate students' awareness of mathematics application in mathematics education. At this time, the main meaning of applied consciousness refers to the psychological tendency to describe, understand, think and solve various problems with mathematical language, knowledge and thinking methods from the perspective of mathematics.
In the mathematics curriculum of primary and secondary schools, the methods of cultivating application consciousness can be carried out from three aspects: first, applying mathematics knowledge in mathematics class can directly stimulate students' learning motivation, and let students see the usefulness of mathematics knowledge through some simple applications; The second is to apply mathematics to the study of other disciplines, and let students deeply understand the role of mathematical scientific thinking methods in scientific development through the connection between mathematics and other disciplines; Third, apply mathematics to practical activities, solve real-life problems with mathematical knowledge, and cultivate students' application consciousness.
※ "Problem Situation-Modeling-Interpretation, Application and Extension"
Because mathematics reveals hidden patterns to help us understand the world around us, contemporary mathematics is far more than arithmetic and geometry, but a colorful subject. Data, measurement and observation data in contemporary mathematics processing science. It is inference, deduction and proof; It is a mathematical model of natural phenomena, human behavior and social system. The cycle from data to deduction to application appears repeatedly in all places where mathematics is used, from daily trivial matters such as planning long-distance travel to major management issues such as air transportation planning or investment business management. The process of "doing" mathematics goes far beyond simple calculation or deduction, and it involves pattern observation, guess test and result estimation. Therefore, mathematics is actually a science of pattern and order. The field of mathematics is not molecules or cells, but numbers, opportunities, shapes, algorithms and changes. Mathematics, as a science that studies abstract objects, relies on logic rather than observation results as its truth standard, but it also uses observation, simulation and even experiments as a means to discover truth.
In this way, through the in-depth analysis of various mathematical activities, we can find that it can be divided into at least three stages: (1) accumulating factual materials by observation, experiment, induction, analogy and generalization; (2) Abstracting the conceptual system from the factual materials, and establishing the mathematical theory deductively; (3) The application stage of mathematical theory.
Traditional teaching pays too much attention to the second stage of teaching, which leads to students being unable to apply what they have learned and not knowing the ins and outs of mathematical theory. In order to overcome these shortcomings, modern mathematics education and teaching advocates that the above three stages are equally important to students' mathematics learning. At the same time, according to constructivism, mathematics teaching should create problem situations for students. Let students accumulate rich and easy-to-understand factual materials. In this way, according to modern people's understanding of mathematical science, mathematics is a science of pattern and order, and it is proposed that mathematics teaching should cultivate students to learn various methods of establishing patterns. Of course, most people study mathematics not only to understand or understand mathematics, but to use mathematics. Therefore, it should be the ultimate goal of mathematics learning to explain, apply and expand the mathematical theory that one has learned.