Mathematical composition model reference, when it comes to examination papers, I believe everyone is familiar with it. In our life, we have come into contact with some papers to some extent. Many times, writing a paper is not easy. Writing a paper needs to refer to many documents. Next, I will share with you the model essay reference of the math test paper.
Mathematical test paper model reference 1
Thesis topic: Cultivating students' autonomous learning ability and improving the effect of primary school mathematics classroom teaching.
Under the guidance of the new curriculum concept, the primary school mathematics classroom presents a new atmosphere full of educational opportunities and challenges. Under the cultivation of primary school students' all-round development ability, the cultivation of primary school students' autonomous learning ability, communication and cooperation ability and innovative thinking ability has become the focus of education, which requires teachers to have teaching wisdom and profound understanding of students. In this educational atmosphere, students' creative imagination, creativity and inquiry thinking can be cultivated, and their knowledge can be improved in the process of autonomous learning.
Keywords: autonomous learning ability; Innovative thinking; Primary school mathematics
Under the brand-new educational concept, the educational perspective has changed from "asking me to learn" to "learning to learn". In the process of cultivating primary school students' ability, teachers pay attention to the cultivation of primary school students' all-round quality, including autonomous learning ability and innovative thinking ability, so that primary school mathematics teaching classroom presents a learning process of active participation, and mathematics classroom shows the light of wisdom under students' subjective behavior. This requires teachers to adopt methods and strategies suitable for primary school students in the teaching process, pay attention to the process of students' learning rather than the results of learning, give play to the nature of primary school students' independent exploration and free discovery, and promote students' healthy and all-round development.
First, the present situation and reflection of mathematics teaching in primary schools
Because of their age and personality characteristics, primary school students show a strong curiosity about fresh and vivid things, and most of them have a strong thirst for knowledge, self-esteem and competitiveness. In the teaching process, teachers should cultivate students' autonomous learning ability according to their age characteristics and personality. However, there are still some shortcomings in primary school mathematics teaching, which need our reflection.
(A) too much introduction of situational teaching, the loss of teaching objectives
Some math teachers use situations too much in class introduction, which distracts the attention of primary school students. For example, in the classroom introduction, the teacher had a whim and used Pleasant Goat and Big Big Wolf as the classroom introduction situation. The students opened their eyes and ears, and developed their imagination of fighting wits, but forgot that the teacher was having a math class. Another example is: In the math calculation of "addition and subtraction" in senior one, the teacher wants to introduce "spring outing" into the math class as a situation, but when using the situation, too much scenery is introduced, which makes students indulge in the imagination of scenery, deviates from the teaching goal of the math class, and thus misses the purpose of math teaching.
(B) The adult imagination of primary school students lacks novel attraction.
When creating situations in the teaching class, math teachers use the eyes and perspectives of adults to imagine, ignoring the innocent eyes of children, and the simple situation creation is unremarkable and lacks challenges. For example, in the lesson of "multiplication formula of 7" in primary school mathematics teaching, the teacher introduces questions in class with "how many days are there in a week", which is not fresh for students and lacks memory of multiplication formula.
(C) the weakening and lack of "mathematics taste" in classroom teaching
In the primary school mathematics teaching class, teachers use various situations to create lead-in teaching, but fail to introduce situations into the learning of mathematics knowledge in time, which weakens the "mathematics taste" that mathematics should have and reduces students' interest in autonomous learning. For example, in the teaching of mathematical knowledge of statistics, teachers let students discuss and record in the form of group teaching, but students stay in the comparative discussion of the weights among group members and do not really enter the learning of mathematical statistics.
Second, the concept of autonomous learning and its importance
In mathematics teaching in primary schools, students should take active creative activities under the guidance of teachers to realize the benign development with students as the main body. Students can learn independently and selectively through various ways and means, and creatively integrate and internalize what they have learned, so as to reach the level of autonomous learning ability. The importance of primary school students' autonomous learning is mainly reflected in the following aspects.
(A) improve the quality of mathematical knowledge absorption
Autonomous learning is an active way and a way to cultivate students' autonomous habits. On the premise of arousing their desire for knowledge, it is transformed into the internal driving force of cognition, stimulating the internal motivation of learning, internalizing it into learning habits, and truly improving the initiative of absorbing mathematical knowledge.
(2) To lay a foundation for the subsequent study of mathematical knowledge.
The primary school stage is the initial stage of mathematics knowledge learning. At this critical stage, it is necessary to cultivate students' habit of autonomous learning, make use of their spontaneous interest in mathematics learning and their ability of independent discovery, and master the strategy of learning mathematics knowledge, so as to lay the foundation for subsequent higher-level mathematics learning.
(C) the cultivation of self-discovery and self-learning ability
Most pupils have a pair of curious eyes. They are curious about the world around them and have the ability to discover independently. In this process, the more they explore their self-discovery ability, the stronger students' self-learning ability, and the habit of self-learning will easily lead to knowledge transfer.
Third, autonomous learning in primary school mathematics classroom teaching strategies
The classroom teaching of primary school mathematics autonomous learning gives full play to students' subjectivity and aims at cultivating students' independent inquiry, practical ability and innovative thinking ability. In a good teaching atmosphere and autonomous participation environment, we can realize various forms of autonomous learning, acquire mathematics knowledge in different activities, and master the general rules and learning methods of primary school mathematics knowledge learning.
(A) the effective introduction of mathematics classroom, to stimulate students' independent participation.
Appropriate and effective introduction of mathematical situations is an effective way to conduct efficient mathematics classes. We should create a good atmosphere in the process of classroom lead-in and stimulate students' autonomous learning of mathematics knowledge in a relaxed, happy and intelligent way. The specific method is as follows.
1, using life as the teaching situation to transfer mathematics knowledge. Life is seamless, life is the most profound experience of students, and "mathematics in life" and "life in mathematics" are closely linked and closely related. Students perceive the value of mathematics in the experience of life and feel the mystery of mathematics in the on-site experience. The higher the life-oriented degree of mathematics situation, the easier it is for students to activate their inner life experience and the deeper their grasp of mathematics knowledge. For example, in the teaching of "Understanding RMB", students are grouped to buy RMB, and different items are labeled with different prices, and then students in groups are asked to buy fake RMB with different denominations, so that students can experience the changes of numbers during the purchase process. [ 1]
2. Take the game as the teaching situation to stimulate students' awareness of independent participation. The game link is the link that primary school students are most willing to participate in and interact with. Mathematics teaching can appropriately introduce games, so that primary school students can enhance their interest in learning mathematics knowledge and feel the successful experience of mathematics exploration. For example, the addition practice in primary schools within 50 years is not simply for students to do addition, but in the form of "postman delivering letters" to increase students' learning autonomy. Teachers can prepare mailboxes marked with different two digits in advance, prepare envelopes for different addition exercises, select several students as "messengers and postmen", and match these envelopes with mailboxes, so that students can master mathematics knowledge in their scrambling choices, which is like an invisible magnet.
3. Introduce stories to guide students to learn independently. Pupils like stories, so we can use stories to increase their interest in mathematics in teaching, guide students to imagine with creative thinking and carry out autonomous learning. For example, in the teaching of "number within 10" in senior one mathematics, in order to let students learn the related concepts of number, stories can be introduced for image learning. In the kingdom of numbers from 0 to 9, the number 9 finds itself the biggest, so it is very arrogant and proud. It said to the other numbers, "You are all very young, younger than me, so you must all listen to me." In order to eliminate its arrogance, other numbers agreed to let the number 1 and 0 form a new two-digit number. When the number 9 saw it, it lowered its head and realized its mistake, so it stopped being arrogant and became good friends with everyone. In the process of teacher telling stories, students also begin to think and imagine numbers, realize the cardinal number and ordinal number meaning of numbers within 10, and carry out autonomous cognitive learning. [2]
As a public course in engineering colleges, advanced mathematics plays an important role in cultivating students' thinking and training mathematical thinking. After entering the new century, people pay more and more attention to the concept of quality education. If the traditional teaching methods are still used, students will lose their enthusiasm and interest in learning advanced mathematics. Mathematical modeling based on modern educational technology builds a bridge between practical problems and theory. In the actual teaching process, senior mathematics teachers start with after-class experiments, integrate mathematical modeling ideas into higher mathematics teaching, and use mathematical modeling to solve practical problems.
First, the status quo of higher mathematics teaching
(A) outdated teaching concepts
As far as the current higher mathematics education and teaching is concerned, senior mathematics teachers attach too much importance to students' computing ability, thinking ability and logical thinking ability, and all teaching activities are based on textbooks. As a dynamic and novel subject, due to the backwardness of educational concepts and ideas, there are no application examples interspersed in classroom teaching, and students do not know how to solve problems in their work, so their work efficiency cannot be further improved. Not only that, old teaching concepts and ideas make students gradually lose their interest and motivation in learning.
(B) traditional teaching methods
Excellent teaching methods play an important role in students' learning process and directly affect their academic performance. Generally, teachers of advanced mathematics teach in the order of textbooks, that is to say, teachers "from definition to theorem" and "from exercises to exercises". This stereotyped teaching method can not create an active learning atmosphere for students, and students' ability to study and think alone is further reduced. This requires teachers to create a harmonious classroom atmosphere and use novel teaching methods to let students actively participate in learning in the classroom.
Second, the role of modeling in higher mathematics teaching
Mathematical modeling plays an important role in cultivating students' imagination, observation, ability to find, analyze and solve problems. In recent years, there have been many competitions and teaching and research activities with mathematical modeling as the main body in China, which have played an important role in improving students' interest in learning and stimulating their enthusiasm for active learning. Introducing mathematical modeling into higher mathematics teaching can also cultivate students' fearless quality and practical work spirit, and play an outstanding role in coordinating students' learning knowledge and practical application ability. Although most colleges and universities in China have set up elective courses or training courses in mathematical modeling, due to the great difference between the requirements of the courses and the students' cognitive level, the courses cannot be popularized as popular education. Now colleges and universities are actively looking for a carrier to cultivate students' comprehensive quality, enhance students' innovative spirit and creativity, and let students meet the needs of society for compound talents, and the best carrier is advanced mathematics.
Advanced Mathematics is a basic course for engineering students. Because of its compulsory nature, it has a wide influence to introduce mathematical modeling into advanced mathematics classroom. Infiltrating the idea of mathematical modeling in higher mathematics teaching can not only restore the original appearance of mathematical knowledge, but also cultivate students' ability to apply mathematical knowledge in daily life. Mathematical modeling requires students to simplify, abstract and translate some real-world information, use mathematical language and tools, and show the internal relations in the form of figures and tables to improve students' expression ability. After learning mathematical modeling in practice, it is necessary to test the real information to determine whether the final result is correct. Through the practice in this process, students can actively and objectively use mathematical methods in the process of analyzing problems, and finally get the best way to solve problems. Therefore, it is of great significance to introduce mathematical modeling into higher mathematics teaching.
Thirdly, the concrete measures of applying modeling thought to higher mathematics teaching.
(A) the application of modeling ideas in the formula
Formulas play an important role in advanced mathematics textbooks, and are also one of the contents that students are required to master. In order to further improve the teaching effect of teachers, teachers should not only improve students' computing skills, but also combine them with modeling ideas to make problems easier to solve and the classroom atmosphere more active. In order to make students understand the modeling ideas used in formulas more thoroughly, teachers should also teach with examples.
(2) The method of using mathematical models when explaining exercises.
Textbook examples are solved with the idea of modeling. The teacher explained the example well and told the method of solving problems by mathematical modeling, so that students can clearly understand how to use mathematical modeling in the process of solving problems. After completing each chapter, make full use of time to answer questions for students, choose appropriate examples according to the professional situation and students' level, complete the whole process of modeling and problem solving, and improve the efficiency of students' problem solving.
(C) organize students to actively participate in mathematical modeling competition
Generally speaking, students' competitive consciousness and independent thinking ability can be well exercised in the competition. This requires schools to make full use of resources, widely publicize, let students actively participate in competitions, and exercise their practical ability in practice. Use mathematical modeling to solve problems in daily life, let students think alone, then realize their own shortcomings in the process of competition, and then study hard, correct mistakes and improve their abilities in the future.
Four. Concluding remarks
Advanced mathematics mainly cultivates students' ability from theoretical study to solving practical problems. Applying the idea of modeling in advanced mathematics can make students fully understand the knowledge of advanced mathematics, further reduce the learning difficulty, and improve their application ability and exploration ability. At present, there are still some shortcomings in introducing modeling ideas into higher education, which requires in-depth research and exploration by higher mathematics teachers in colleges and universities, as well as good cooperation from students in order to further improve the teaching quality in the future.
References:
[1] Xie, Yang. Integrating Mathematical Modeling into Higher Mathematics Teaching [J]. Journal of Qiqihar Teachers College, 2014 (02):19-120.
[2] Li Wei. Exploration and Practice of Integrating Mathematical Modeling into Higher Mathematics Teaching [J]. Educational Practice and Reform, 2012 (04):177-178, 189.
[3] Yang Sixiang. On the infiltration of mathematical modeling in higher mathematics teaching [J]. Journal of Changchun Institute of Education, 2014 (30): 89,95.
[4] Liu. Integrating Mathematical Modeling into Advanced Mathematics Teaching [J]. Journal of guiyang university, 20 13 (03): 63-65.
Talking about the Spreading Ways of Mathematics Culture in Senior High School
A, combined with the history of mathematics, held a cultural lecture
The education of mathematics history plays an important role in understanding mathematics. The history of mathematics is not only a chronological record of mathematical achievements, because the development of mathematics is by no means smooth sailing, and more often it is full of hesitation, wandering, difficulties and twists and turns, and even facing crisis; The history of mathematics is also a record of the struggle of mathematicians to overcome difficulties and crises. The lecture introduces important mathematical ideas, excellent mathematical achievements and related personnel, so that students can understand every hard course in the process of mathematical development, which is helpful to cultivate students' perseverance, unremitting will and integrity. For example, by holding cultural lectures, students are introduced to the origins of "three crises in the history of mathematics", "Hundred Cows Theorem" and "Goldbach conjecture and progress". Introduce some mathematical prizes and famous problems in the field of mathematics to students, such as Fields Prize, Wolf Prize, Hua Prize, Paulia Prize and Gauss Prize. This kind of quiet education will stimulate students' personal development aspirations. In addition, major events in the history of mathematics are introduced, such as the controversy and cost caused by the appearance of irrational numbers, the argument between infinitesimal zero and nonzero, Cantor set and so on.
Second, combined with teaching content, interspersed with mathematical stories
Mathematical stories are fascinating, which can stimulate students' emotions and interests and promote them to be positive. Teachers should pay attention to collecting math stories related to math content and insert them into classroom teaching when talking about related content. By showing students the background of mathematical knowledge, mathematical thinking methods and mathematicians' scientific spirit of pursuing truth, we can let mathematical culture enter the classroom, and we can seize the opportunity to inspire and motivate students through mathematicians' stories and educate them on humanistic values. In the introduction of new courses, we can provide some historical and realistic "questions" from the development and perfection of concepts, theorems and formulas, anecdotes of famous mathematicians, the origin of concepts, the discovery of theorems and the tortuous course of mathematical progress in history. A wonderful lead-in can not only enliven the classroom atmosphere, stimulate students' interest in learning, reduce the difficulty of mathematics learning, but also broaden students' horizons. Cultivate students' all-round thinking ability and flexibility, and make mathematics a lively and interesting subject instead of a boring one. For example, when talking about Euler's formula, introduce Euler's legendary life, Euler's whimsy in solving this problem, especially his contribution after blindness, and infect students with the personality charm of mathematics masters; When we talk about analytic geometry, we introduce the main contributions of Descartes and Fermat in the establishment of this discipline. Students can understand the historical background of analytic geometry, the growth experience of mathematicians, feel the persistent beliefs of famous mathematicians and learn valuable mathematical spirit. When talking about related contents, this paper introduces the struggles and mathematical achievements of modern mathematicians in China, such as Hua, Chen Jingrun, Su, Yang Le, etc., so that students can feel the hardships of mathematicians and inspire national pride.
Third, combined with real life, for example to solve mathematical problems
As a tool discipline, mathematics is closely related to daily life. Mathematics teachers must consider the connection between mathematics and life, connect mathematics with real life, and mathematize the problems in a certain life, so as to sublimate the application of mathematical knowledge, help students acquire vital mathematical knowledge and guide students to observe the world from a mathematical perspective. Furthermore, let students realize the importance and necessity of learning mathematics, and quote examples close to students' life in teaching activities, so as to create mathematical problem situations close to students' cognitive level and real life, and let students realize that mathematics is around us. For example, when talking about the summation formula of equal ratio series, we can enumerate its application in the purchase of houses by loans. Explain the abstract concepts of mapping from life examples that students are familiar with, such as "barcode" and "fingerprint", and guide students to find the mapping in life. Keys correspond to locks and student numbers correspond to students. When talking about probability, list its application in lottery and so on. When talking about "exponential function", let students know how archaeologists use the proportion of alloys to measure the age of bronzes; When talking about hyperbolic equation, students can experience the application value of hyperbolic equation by combining hyperbolic cooling tower in industrial production, hyperbolic channel built in Beijing and the landmark Eiffel Tower in France. In addition, which is more profitable, installment payment, math scores and myopia lenses, bank deposit or insurance, house mortgage, stock market trend chart, price analysis table and other issues closely related to people's lives. By answering these questions, students feel that mathematics is useful. They learn to look at the problems in life from a mathematical perspective and analyze them with a mathematical mind.
Fourth, combine other disciplines to enjoy the essence of culture.
The development of science and technology has ushered in the mutual penetration, intersection and integration of various disciplines. Especially in contemporary times, the influence of mathematics has spread throughout all fields of human activities. Mathematics teachers should pay attention to the connection between mathematics and other disciplines, try to find the combination point between mathematics and other disciplines in teaching activities, and realize the migration of mathematics to non-mathematics fields, so as to enjoy culture to the maximum extent, taking people as clues, mathematics themes as clues, history books as clues and mathematics as clues. We can open the contents of closed textbooks, break closed concepts, formulas and rules into several "small plates", design some open questions for students to explore, broaden the knowledge of books outside books and integrate with other cultural knowledge. Practice has proved that students will show great interest and enthusiasm when teachers talk about "living mathematics" or link mathematics with philosophy, aesthetics, economy and other cultures and arts, for example, speaking. When explaining the content of trigonometric function, we can introduce the origin and development of trigonometry and explain its role in practical activities such as navigation, calendar calculation and astronomical observation. When talking about reduction to absurdity, tell students in detail how Galileo corrected Aristotle's wrong assertion that the falling motion of an object lasted for 1800 years. When we understand the concepts of elevation angle and depression angle, we can relate to "looking up, I found it was moonlight, and then sinking, I suddenly remembered home"; When we understand the positional relationship between a straight line and a circle, we can relate it to "the desert is lonely and straight, and the long river sets the yen"; When it comes to the concept of "three views", it can be associated with "seeing the mountain side as the peak, the distance is different, and I don't know the true face of Lushan Mountain, but toward which corner of the mountain"; When we understand random events, inevitable events and impossible events, we can associate them with idioms ("Waiting for a rabbit, dripping into ice, meeting unexpectedly" is a random event, "As you sow, you reap what you sow, you will catch turtles in a jar" is an inevitable event, and "Fishing for the moon in the water, eating cakes to satisfy your hunger" is an impossible event), so that students can realize that mathematics is different from other events.
Five, combined with extracurricular activities, group cooperation.
Because classroom time is limited and the content of mathematical culture is all-encompassing, it is not enough to teach mathematical culture only in classroom time. Extracurricular activities should also highlight mathematical culture, make full use of natural and social resources inside and outside the school, and use various channels such as the internet, newspapers and magazines to understand the rich content of mathematical culture, and extend it to students' extracurricular life in some form. Recommend valuable works related to mathematics by holding mathematical cultural knowledge competitions. For students to read after class, broaden their horizons in mathematics, and then let the dribs and drabs of mathematics culture moisten students' hearts like spring breeze and rain by writing post-reading, mathematics composition and organizing students' communication. Books include The Miracle of Mathematics by American mathematician Sioni pappas, Enlightenment from Mathematicians by Chen Shigu and Ge Mengzeng, and Contemporary Mathematical Elite (Fields Prize Winners and Their Achievements) by Li Xincan. The Mathematicians' Vision, New Concept Geometry, Random Talk on Mathematics and Mathematics and Philosophy written by Academician Zhang Jingzhong are easy to understand, and they are all good books to spread mathematics culture and show its charm in teaching. Students can also be grouped, and teachers can provide some references or topics for a certain content or topic, so that students can learn about the deeds of mathematicians at home and abroad from extracurricular books and the Internet in their spare time. Understand their success process, their contribution to mathematics, and their rigorous scholarship and daring to climb the peak of science, and then print out the collected stories and distribute them to students to exchange and experience mathematics culture. For example, the topic of "Discovery of Polyhedral Euler Formula" is advanced step by step from "intuition-verification-conjecture-proof-application", following the footsteps of the great mathematician Euler. We can not only master the ins and outs of Euler's polyhedron formula, but also understand the life of Euler's legend. We can also experience the hardships of discovery, learn the attitude of scholarship, master research methods and improve students' humanistic quality. In this way, students can increase their knowledge of mathematics culture in group cooperation, experience the fun of cooperative inquiry and make mathematics full of wisdom and life.
Six, combined with teaching evaluation, into the math exam.
Although the high school mathematics textbooks have been further improved, reflecting the content of mathematics culture to a greater extent, the experimental textbooks have the introduction of mathematics culture at the beginning and end of each chapter or module, but they are still reading materials. The teacher thinks that the students can understand, and the students think that there is no exam. In teaching, it is often "what to test, what to teach and what to learn". Teachers and students do not pay enough attention to this part, and usually pay attention to the assessment and evaluation of knowledge and skills. Pay more attention to explicit knowledge than tacit knowledge; In order to make teachers and students truly feel the importance of mathematical culture, we should promote the teaching of mathematical culture in senior high schools by evaluation, and we can root the relevant contents of mathematical culture in the college entrance examination questions, and properly involve common-sense mathematical culture in regular examinations. In this way, high school teachers will consciously combine the content of mathematics culture with the content of each module in high school as much as possible while teaching. Teaching mathematical culture step by step and systematically, the high school mathematics curriculum standard requires that we should not only pay attention to the transmission of students' mathematical knowledge, but also pay attention to the dissemination of mathematical cultural connotation, and establish a view of mathematical culture: give full play to the two functions of mathematics education, namely, the function of science and technology education and the function of cultural education. Different from the teaching of mathematical knowledge and skills, the expression of mathematical culture in mathematics teaching should be more diversified and flexible. The key lies in teachers, first of all, teachers should improve their own mathematical cultural literacy; Secondly, excavate the cultural connotation of mathematics and strive to create a mathematical cultural atmosphere; Third, improve the cultural taste of mathematics, and make efforts to integrate resources and optimize classes and activities. Teachers should be good at properly and skillfully infiltrating and spreading mathematical culture in all teaching links, let mathematical culture enter the classroom, and strive to make students really influenced by culture in the process of learning mathematics, so that students can become not only scientific people, but also cultural people, form and develop mathematical quality, and comprehensively improve their mathematical literacy.