1. Significance of Mathematics History in Mathematics Teaching
1. 1 Use the history of mathematics skillfully to stimulate students' interest in learning.
Classroom teaching is an important part of mathematics teaching. Teachers teach mainly through classroom teaching, while students learn mainly through classroom teaching. Citing the stories of mathematicians who cooperated with the teaching content in the history of mathematics can arouse students' strong interest at the beginning of classroom teaching and make them concentrate on thinking about mathematics problems. This is a method to create the best teaching "situation" and quickly kick off classroom teaching. This method can stimulate students' interest in learning mathematics. Almost every part of the mathematics content in the textbook has fascinating historical allusions, such as negative numbers, irrational numbers, complex numbers, etc., and there are many interesting stories behind it.
Facts have proved that teachers who are rich in knowledge and persuasive in class are far more popular with students than those who are simple and boring and practical. When teachers teach some common mathematical concepts, theories and methods, if they can point out their sources, allusions and historical evolution, students will be interested. For example, if a teacher only gives proof of deduction when teaching Pythagorean theorem,
When teachers teach mathematics knowledge, if they can seize the opportunity to properly infiltrate some famous allusions, backgrounds or interesting things into students, when students know that the acquisition of mathematics knowledge is so tortuous and moving, they will broaden their horizons and have a deeper understanding of knowledge points. Knowing the ins and outs of knowledge will expand students' knowledge to varying degrees. If he knows that there are more than 300 proofs of Pythagorean theorem from ancient times to the present, even more.
1.2 Apply the history of mathematics to educate students on dialectical materialist world outlook.
The education of dialectical materialism and historical materialism is an important part of moral education. 1. It is the task of middle school mathematics teaching to cultivate students to establish dialectical materialism. 1. Dialectical materialism education combined with textbooks has certain limitations and lacks vivid and intuitive materials, while the history of mathematics is full of a large number of dialectical and unified examples. Just make up for this deficiency. For example, when talking about Pythagorean theorem, we can introduce that China mathematician Zhao Shuang summed up the dialectical thought of "combination of numbers and shapes" when the figure of Pythagorean square is less than or equal to or greater than. For example, 32+42 = 52 is the relationship between three numbers, which can correspondingly establish a tangible right triangle. This has a simple dialectical materialism thought, which embodies a viewpoint of dialectical materialism: the material world is unified.
In the process of perfecting the mathematical theory system, many dialectical quantities are good materials for educating students on dialectical materialism, such as constants and variables, positive and negative numbers, finite and infinite. All these will help us, as math teachers, dig deeper into the textbooks in the future, extract the knowledge behind the textbooks, and subtly spread it to students' dialectical materialism.
1.3 Patriotism education for students through the history of mathematics.
The history of mathematics is the struggle history of mathematicians, which shows the great personality and lofty spirit of mathematicians who have devoted themselves to truth. There are many reading materials in the new mathematics textbooks, which can help students understand the fruitful achievements of China's ancient mathematics research: for example, China's famous mathematical classic "Nine Chapters of Arithmetic", in which the concept and algorithm of positive and negative numbers are put forward for the first time, making the generation of algebra earlier than 2000 BC in the west; The famous Pythagorean Theorem was first put forward by Shang Gao, a mathematician in the Western Zhou Dynasty, so it is also called Shang Gao Theorem. Liu Hui initiated "secant technique" and scientifically obtained the emblem rate of 3. 14 (i.e. pi); At the same time, students can be encouraged to consult relevant materials on their own according to the teaching content. For example, with regard to "pi", students will surely know that Zu Chongzhi's excellent score in pi calculation is between 3. 14 15926 and 3. 14 15927. He is the first person in the world to make Pi accurate to six decimal places. For another example, Yang Hui's "Triangle Array" was discovered more than 500 years earlier than the French "Pascal Triangle". These outstanding mathematicians and their achievements have written brilliant chapters in the history of Chinese mathematics. This can not only transform students' national pride, self-esteem and self-confidence, but also transform them into the sense of responsibility and consciousness of studying hard for the cause of building the motherland. On the other hand, they can also cultivate students to be fearless and work hard. Dedication to study hard. There are many such examples in mathematics. Teachers can find many similar moral education textbooks as long as they dig up the textbooks skillfully. For example, when teaching "similar triangles Application", I adopted the "Four Tables Looking Far" in "Nine Chapters Arithmetic", which recorded how to use similar triangles's knowledge to solve problems in ancient times, killing two birds with one stone. When students experience the extension of mathematical knowledge, they will be surprised by the outstanding talents of our ancestors.
We have a glorious history of mathematics, and China is one of the main birthplaces of mathematics. The history of mathematics provides the foundation for patriotism education. We Chinese are the smartest, most industrious and most creative people. We should learn the history of Chinese mathematics, understand the history of mathematics, understand the advanced achievements in ancient times, enhance our pride and self-confidence, and enhance our confidence in catching up with and surpassing the advanced level in the world.
2. Infiltrate the method of mathematics history education
2. 1 get down to business with history
I think we all know the story of Indian King Shehan praising the inventor of chess, which is an interesting story. Take it as the beginning of the lesson "the first n sums of geometric series", and I think students will soon enter the best learning state. This is the role of a good start. We should be able to grasp students' attention and arouse their desire for knowledge, and use the history of mathematics to introduce it in an appropriate way in combination with teaching requirements.
2.2 citing the history of mathematics, highlighting the way of thinking
As we all know, it is better to teach people to fish than to teach them to fish. In mathematics teaching, it is more important to pay attention to method teaching: whether we can draw inferences depends on whether we master the thinking method. If we dogmatically teach students a way of thinking, they may not accept it, but there are many ways of thinking in mathematics history. How can we properly introduce the thinking methods of our predecessors to students? This requires our teachers to constantly learn and summarize.
Middle school students are reluctant to accept Pythagorean Theorem, and Zhao Shuang's Pythagorean Square Diagram makes the proof easier to understand. The proof method is: "The lattice string diagram can be multiplied by Pythagoras as Zhu Shi 2, multiplied by Zhu Shi 4, and the difference between Pythagoras and Pythagoras can be multiplied into the middle yellow real, plus the difference real, and also become the string real." It is expressed in letters:
2ab+(b–a) 2 = C2 means a2+b2 = c2.
The ingenious combination of geometry and algebra embodies the thinking method of combining numbers and shapes. This way of thinking will always get unexpected results when solving some difficult problems.
We should pay attention to the exploration of mathematical methods in the history of mathematics, and infiltrate them into mathematics teaching appropriately so that students can accept them intuitively.
Problems that should be paid attention to in infiltrating the history of mathematics.
3. 1 has various forms and is flexible.
Take junior high school mathematics textbook of new curriculum standard of People's Education Press as an example. The content of the history of mathematics is presented in the column of "Reading and Thinking" as an elective course. These contents can be used as extracurricular reading materials for students to learn by themselves, and teachers can also use them flexibly in teaching as materials to improve students' interest in learning and inspire students' mathematical thinking.
In addition to teachers' flexible mastery of the history of mathematics in mathematics textbooks, teachers should also give full play to their subjective initiative, and appropriately and timely infiltrate students with some contents of the history of mathematics that are related to what they have learned, but are not presented in the textbooks. The example of summation of geometric series we just quoted was introduced at the beginning, which attracted students' attention and completed the content of this section well. If an evocative ending is set, I think it may open up a broad road for interested students. For example, Chen Jingrun teacher Shen Yuan ended the lesson with a mathematical conjecture: "The queen of natural science is mathematics, the crown of mathematics is number theory, and Goldbach conjecture is the jewel in the crown." Perhaps it was such a strange ending that Chen Jingrun took off this pearl of mathematics.
We should not only make full use of the limited classroom time, but also rationally develop and utilize extracurricular time, so that students can broaden their knowledge of mathematics.
3.2 Infiltration should be comprehensive
We have a glorious history of mathematics, which is an important part of China's splendid ancient culture. The great contribution of ancient mathematics is not only the excellent material for patriotism education today, but also the noble character of ancient mathematicians, such as seeking truth from facts, daring to uphold the truth and dare to climb the peak. It can also inspire future generations to revitalize China and strive for the great rejuvenation of the Chinese nation. However, since the mid-Yuan Dynasty, ancient mathematics in China has gradually declined. It has been overtaken by western mathematics. There are few achievements in modern times. Therefore, to understand the history of foreign mathematics, science has no borders. On the whole, it will definitely promote the education and teaching of mathematics.
3.3 Correct introduction of historical materials
As a math teacher, we should adopt the attitude of historical materialism when introducing mathematical historical materials. We must follow the historical records, and we can't change the age at will to weaken the achievements of foreign mathematical history just because we want to highlight the history of Chinese mathematics.
Take Liu Hui's The Circumcision as an example. We all know that it is the concrete embodiment of China's earliest extreme thinking method, so we can't tell students that it is the earliest in the world, because Archimedes discovered it about 400 years before Liu Hui. Their achievements are the wealth of the world, and we should all respect them. This requires us to read a lot of relevant materials in our daily work so as not to mislead students.
3.4 should be closely combined with teaching materials.
Infiltrating mathematics history education is not simply for history. The purpose of properly combining the knowledge of mathematics history into textbooks is to promote mathematics teaching. After all, our mathematics textbooks mainly teach mathematics knowledge, and the infiltration of mathematics history should be just right, not systematic, to prevent the result of usurping the role of master. The teaching of this kind of content is best to achieve the realm of moistening things and being silent.
These are my views on the education of the history of mathematics. It is the concrete embodiment of the educational function of the teaching material to tap the educational resources of the history of mathematics in the teaching material. Focusing on the current situation, we should pay attention to strengthening the study of the history of mathematics, collecting the data of the history of mathematics, and properly applying them to practical work, constantly improving the classroom teaching of mathematics in senior high schools, improving the teaching art, making good use of it in mathematics teaching and giving full play to its role in teaching. It can make the teaching content vivid and infectious, fully mobilize students' learning enthusiasm, make students truly become the masters of learning, and have a multiplier effect on improving teaching quality.