Famous scientist Albert Einstein said: "ask a question more often than to solve a problem is more important.
Papers Category:Education Papers
- Disciplinary Education Papers
Post Time:2013-4-22 21:02:00
Solve the problem, maybe just a mathematical or experimental skills, and raise new questions, new possibilities, from a new perspective to look at the problem, but it requires creative imagination and marks real progress "from which we can recognize, to cultivate the students 'ability to ask questions, we should first develop students' awareness of the problem to start in higher mathematics teaching activities , only to make students aware of the existence of the problem, in order to inspire them to learn thinking spark students' awareness of the problem is more intense, their thinking is more active, more profound, more creative, with the deepening of curriculum reform , the creation of mathematical situations and allow students to learn mathematics in a vivid and specific situations, this teaching philosophy has been accepted by the majority of teachers and recognition, and to be applied in teaching practice can be said that the creation of situations has become a focus of higher mathematics teaching. We know that a lot of students in teaching advanced mathematics reflect the mathematical monotonous, boring, hard to learn, in fact, the creation of situations, to attract the students' active participation and active learning, from mathematics to find a lot of fun. stressed creation of situations develop students' enthusiasm and interest, to promote students through observation, continue to accumulate rich representation to enable students to practice feeling gradually realize that lay the foundation for knowledge, learn math, intellectual development.
Method of teaching in higher mathematics classroom the creation of a mathematical problem situations, for students to ask questions, teachers have to inspire students to think for students to create a good math problem situation, so that students in good psychological and cognitive environment generated the need of mathematics learning, stimulate the enthusiasm of learning to explore, mobilize the participating interest in learning good mathematical problem situation should follow the following principles.
The principle of the creation of a mathematical problem situation
1.1 in line with the principles of the students' zone of proximal development
Vygotsky's zone of proximal development theory ", that the student's level of development, there are two, one is the current level of the student, another student's level of development. Gap between the two is the zone of proximal development as a higher mathematics teachers should focus on the students 'zone of proximal development, based on a deep understanding of materials, the creation of students' prior knowledge associated background, close to the students the characteristics of the age and cognitive level math problem situation , in order to mobilize the enthusiasm of the students, prompting students to independently explore mathematical knowledge, its potential.
In higher mathematics teaching, mathematics problem situation but also according to the specific teaching content and the physical and mental development of the students need to set the prior knowledge as the basis of new knowledge as the goal, make full use of mathematical problem situations active classroom, teachers atmosphere to stimulate student interest in learning, to mobilize students learning initiative and creativity, thus contributing to the development of students' intellectual and non-intellectual factors. creation of mathematical problem situations, students must meet the mental level, the principle of moderation, the problem is too deep or too light is not conducive to the students' creative level of play.
1.2 follow inspired by the principle of induction
In higher mathematics teaching, the creation of mathematical problem situations in line inspired by the principle of induction, inspired induction principle is the people dialectical relationship based on the understanding of the process of law and the things the development of the internal and external factors. Teachers want to according to the actual situation of students, in and popular image on the basis of the combination of materials, the vivid and specific examples, the proposed mathematical thinking of the students play the role of enlightening, and inspire students to independently explore new knowledge and a strong desire to activate students' intrinsic driving force behind so that students in the inspired teacher induction, give full play to the initiative and actively participate in the process of exploration of mathematical situations.
In the process of higher mathematics teaching, teachers should be good creation has inspired induced mathematical problem situation, stimulate students' interest and curiosity, so that students in autonomous learning teachers create mathematical problem situation, and actively explore mathematical knowledge the formation process, and thus the book knowledge into their knowledge truly course is suitable.
1.3 follow the principle of combining theory with practice
The ultimate goal of college students to learn mathematics is applied to the actual mathematical knowledge source of life, mathematical knowledge should also be applied to life in higher mathematics teaching, teachers should create a real and effective mathematical problem situation, and guide students to use mathematical knowledge to analyze the problem to solve real-life problems, the mathematical problem of life, truly theory and practice. Meanwhile, students in the specific mathematical problem situation to learn mathematical knowledge, with a need to solve practical problems, not only can improve student learning initiative and enthusiasm, and allows them to better accept the need to learn new knowledge, learn more profound theoretical knowledge.
A problem situation to follow the above principles, then we follow the above principles on the basis of the application how to create situations? Following the creation of only in higher mathematics teaching, the initial use of several scenarios for a brief discussion.
The creation of a mathematical problem situation
2.1 The creation of the problem suspense scene
Suspense as a learning psychological mechanism, is puzzled by the students in contact with the object, but are eager to solve it resulting in a positive state of mind. It strong and sustained stimulation of the cerebral cortex, so that you moment both guess, the problem can not figure out, and not thrown open, fit, suspense settings, can stimulate students' motivation and interest, so that active thinking, rich imagination, retrospective memory, help students overcome difficulties perseverance. teachers in the classroom teaching, good at capturing the timing, proper use, the creation of suspense, can touch the students to explore the psychology of new knowledge to improve the efficiency of classroom teaching, for example, in the study of the function of the variable upper limit given integral ■ f (t) dt , such a question can be raised to allow students to thinking: What is the ① ■ f (t) dt from variable? ② ■ f (t) dt its derivative how to beg? better answer for the previous question, the latter issue in the taught , we can recall one yuan composite number
the derivative of y = (phi (x)), u = Phi (x) composite function key at the titles, remind students y = (phi (x)) can be seen as y = ■ f (t) DT students naturally come to a conclusion. thus, we can see that the principle set in the classroom teaching students already know as the context of the questions most students can inspire positive thinking mobilize the enthusiasm of students to learn. reposted elsewhere in the free papers Download Center http://eng.hi138.com
2.2 the creation of analog situations
The analogical reasoning having some of the same or similar properties, is based on two subjects Release When an object is still another attribute of another object may also have this property, or a similar way of thinking, i.e. from the sth recognize push to similar things.
Many of the concepts have similar properties, higher mathematics teaching these concepts, teachers can let students have learned the concept of property, and the creation of analog found situations, and guide students to discover, try to define new concepts. For example, in the number of guide teaches a multi-function two yuan function z = f (x, y) guide number as an example, we can contact and functions of one variable derivative up, in the lecture can be the first review about functions of one variable demand guide, in seeking binary function of the derivative of time, which one independent variable as a constant, another argument derivation process is similar to the functions of one variable so that new concepts can be assimilated easily in the existing cognitive structure and construction, so that students' thinking into the knowledge and the track at the same time lay the foundation for the understanding of the concept and further research.
2.3 the creation of intuitive situations
Based on a combination of abstract and concrete, abstract theories intuitive perceptions of students can not only enrich and deepen the understanding of the theory, and enable students to observe the process of analysis enlightened, emotions are running high, so as to develop students' The purpose of creative thinking as to explain the closed interval continuous function of the nature of zero theorem, a simple explanation Theorem students often experience is not deep, the meaning of the theorem also understand thoroughly, then teachers can give around common example will be explained, For example, we know that winter temperatures often below zero degrees Celsius, the spring temperatures gradually rise above zero degrees Celsius, the temperature rose from zero degrees Celsius zero degrees Celsius, the middle will certainly be 1.0 degrees Celsius, this is what we call zero degrees Celsius zero .
2.4 the creation of variant scenarios
Is the use of so-called variant scenario transform proposition, transform graphics arouse students' interest and desire to touch the students to explore the psychology of new knowledge to improve the efficiency of classroom teaching as taught in value theorem, Rolle's theorem By the end of , teachers can further pointed out that the three conditions of Rolle's theorem is relatively harsh, it makes the application of Rolle's theorem has been limited, If you cancel this condition interval endpoint is equal to the function value, then the curve is still there exists a point makes the connection still parallel with the two endpoints of the tangent to the curve after this point to change the graphics, you can easily get to the conclusion, then the conclusion is that the Lagrange mean value theorem. further if there are two functions to meet La Long-China value theorem, we can get two equations, then the ratio of these two equations is Cauchy Mean Value Theorem, so that after the transformation of the problem leads to a step-by-step content to be taught, students can easily accept new knowledge . The method of creating teaching situation is not isolated, but interacting with each other.
Teachers should be based on the specific circumstances and conditions, closely surrounds the teaching center creation suitable for the actual content of the students' ideological and health problems, but contagious teaching situation the same time, to make the students in mind and situational blend happily explore deep understanding and a firm grasp of the mathematical knowledge.
Course, create situations in higher mathematics teaching method, there are many, but no matter what kind of design scenarios, should be from the students' life experience and existing knowledge and background to stimulate students' curiosity, to stimulate students' interest in learning as the goal, natural and reasonable, in order to make the significant increase in student interest in mathematics and self-confidence, students' mathematical thinking and analysis of the problem, the problem-solving ability is improved. reposted elsewhere in the Research Papers Download http://eng.hi138.com