Based on the above reasons, this paper puts forward the practice of comprehensively applying various forms of mathematical history in mathematics teaching to improve students' mathematical view on the basis of combing the previous research on mathematical history. Specifically, on the basis of synthesizing the previous research results, the author puts forward the principles and factors that should be considered in the comprehensive application of various forms of mathematical history, and designs four available forms: integrating mathematical history into classroom teaching; Lecture on the history of mathematics; History of school-based curriculum of mathematics; Make a tabloid about the history of mathematics.
On the basis of the above theoretical research, the author has developed some concrete cases, including the teaching of negative numbers, the application of linear equations, the teaching of mathematical symbols and the cases of magic squares. ...
On the basis of case design, the author applies various forms of comprehensive application cases of mathematical history designed by himself to teaching, which proves that the comprehensive application of various forms of mathematical history has obvious effects on improving students' mathematical outlook.
First, the analysis of the current situation of senior high school students' mathematics view
Senior high school students' view of mathematics mainly refers to students' belief in mathematics itself, in mathematics learning and in themselves. [1] Because individuals have different knowledge backgrounds, or accept different philosophical concepts, or are influenced by different teachers, plus their own practical experience, they gradually produce and form their own different understandings and experiences in the process of mathematics learning.
(1) belief in mathematics itself
In the process of learning mathematics, students have different feelings and understandings of mathematics itself. Through the investigation of 6 14 senior high school students, it is found that about 52.5% of them "never thought about what mathematics is"; 24.9% people "thought about what mathematics is, but don't know what it is"; 7.8% people "have heard the teacher say what mathematics is"; 14.8% people "thought about what mathematics is, so they know what it is". But in their eyes, mathematics is mainly related to numbers and graphics; It is a discipline composed of concepts, formulas, theorems, rules and symbols. It is a subject with strong skills and methodology, but it is not easy to master; It is a subject about calculating and solving problems; It is a subject to explore the relationship between spatial form and quantity. ...
(2) Belief in mathematics learning
Davis et al.' survey (Li Shizhen 200 1, 2 17-222) shows that students hold different views on mathematics learning in the process of learning. The author found that high school students' mathematics learning beliefs mainly include:
(1) Learning mathematics means doing problems;
② Learning mathematics is to get good grades in the exam;
③ Learning mathematics mainly depends on memorizing, imitating and formulating formulas;
④ Learning mathematics is to cultivate a person's ability of calculation and thinking; Solid geometry mainly cultivates a person's logical reasoning ability and spatial imagination ability;
⑤ Learning mathematics means learning to use what you have learned to solve problems in real life.
(3) Belief in learning mathematics.
There are obvious differences in students' beliefs in learning mathematics. In the investigation, we found that:
(1) Full of self-confidence-some people are interested in mathematics and think that they have certain talents and advantages in mathematics, and they are confident and capable of learning mathematics well.
(2) Plain and confident-some people are interested in mathematics in general, and think that they don't have much talent and advantages in mathematics, but they can still meet the basic requirements as long as they work hard and study hard.
Lack of self-confidence-some people are not interested in mathematics and think that they have no talent for learning mathematics at all and have no ability to learn mathematics well. They often say that they have been poor at math since primary school, which shows that they can't learn math well.
(4) Types of mathematical views
According to the investigation and analysis, senior high school students' view of mathematics can be summarized as follows:
① Dynamic view of mathematics. In the eyes of students, mathematics is knowledge in the process of constant change and development, so there may be shortcomings and mistakes, and only through constant trial, correction and improvement will it be gradually improved. So learning mathematics is also a step-by-step and continuous improvement process. Be tolerant of your own confusion and mistakes, and know that only by taking a positive attitude can you learn math well.
② Static absolutist mathematics view. They regard mathematical knowledge as a collection of truths that have remained unchanged for thousands of years. It is a highly rigorous and extremely abstract knowledge system. So they emphasize acceptance and memory, imitation and training, and advocate that practice makes perfect; Or think that their memory ability is not good, their abstract ability is poor, and mathematics learning is bound to be difficult.
③ The mathematical view of instrumentalism. They think that learning mathematics is to learn the methods and skills to deal with and solve various (mathematical) problems. Therefore, they pay more attention to practical problems, advocate the close combination of mathematics and life, and pay more attention to accumulating materials related to mathematics.
④ View of mathematical culture. They believe that mathematics is a human culture that has a certain relationship with social nature, class consciousness and national spirit, and it is a specific knowledge system that reflects people's thinking methods, aesthetic consciousness and cultural values. Of course, this concept is less found and accepted among students.
The above concepts reflect students' knowledge and understanding of mathematics itself and their understanding and judgment of the value of mathematics from different angles. Of course, some ideas have a positive effect on students' learning, while others obviously have a negative effect.