From the overall distribution, except for the next semester of grade six, the People's Education Edition did not arrange the history of mathematics in the next semester of grade one, two and four, and the Jiangsu Education Edition did not arrange the history of mathematics in the first semester of grade one, two, three and five. However, from the first grade, the textbooks of the West Normal University began to infiltrate the history of mathematics, and each volume was arranged, showing a certain continuity, which made the history of mathematics stand out and show its uniqueness and integrity.
The value of mathematics history to mathematics teaching was recognized by some western mathematicians as early as19th century. 1972, at the second international conference on mathematics education, the international research group on mathematics history and mathematics teaching was established, referred to as HPM for short. For more than 30 years, with the deepening of HPM research, the combination of mathematics history and mathematics teaching has become a trend of international mathematics curriculum reform. It is inevitable for the history of mathematics to enter the primary school mathematics classroom, but this inevitability is quite different from the reality. In addition to the original teaching design, add a little knowledge of the history of mathematics to add some cultural color to the classroom. Does this method fully demonstrate the educational value of the history of mathematics? In a word, how the history of mathematics enters the primary school mathematics classroom has become an urgent topic arising from the two-way interaction between theoretical deduction and practical reflection.
2. The content and design of mathematics history in primary school textbooks.
The types of mathematical history in primary school mathematics textbooks mainly include anecdotes of mathematicians, stories of mathematicians solving problems, historical materials of relevant mathematical knowledge, classical mathematical problems and so on. Mathematicians' stories have also been selected to introduce three versions of textbooks to varying degrees. Among them, the textbooks of Normal University have specially added titles with prominent themes, such as the famous mathematicians Hua, Gauss and Zu Chongzhi, the father of Pi.
The selection, distribution and length of the content of the history of mathematics in primary schools reflect the external characteristics of the content of the history of mathematics in primary school mathematics textbooks, while the specific arrangement and design of the history of mathematics reflect its internal characteristics, that is, how to design the history of mathematics in primary school mathematics teaching can better play its educational and teaching functions.
At present, there are two main design modes of the history of mathematics, namely, "reading the history of mathematics with materials" and "introducing the history of mathematics with exercises". We think we can add two design modes: "Learning content leads to the history of mathematics" and "Learning content leads to the history of mathematics". The essential difference between the two is that the content of the history of mathematics has been invited to the core of the knowledge system of mathematics in primary schools, rather than being marginalized from the learning content. The mode of "learning content leads to the history of mathematics" takes the learning content as the main line and the history of mathematics as the annotation and explanation of the learning content, which can enrich the connotation of the learning content, add gorgeous colors to the learning of mathematics knowledge, and let children experience the sense of history and beauty of mathematics while learning mathematics knowledge. The model of "the history of mathematics leads the learning content" is to use the history of mathematics to lead the learning of mathematical knowledge, so that children can be placed in the historical situation and integrated with the text to form a historical understanding of mathematical knowledge.
Children in the lower stage have weak autonomous reading ability, and the study of mathematics history depends more on the guidance of teachers. Therefore, the design mode of mathematical history should be conducive to teachers' better design and implementation of teaching. The design mode of "Exercise content leads to the history of mathematics", "Learning content leads to the history of mathematics" and "Mathematics history leads to learning content" can do this, and the page can be slightly smaller. In the middle stage, four design patterns can be comprehensively used, and the patterns of "exercises lead to the history of mathematics", "learning leads to the history of mathematics" and "mathematics leads to learning content" can be gradually adopted. High-level students can gradually adopt the mode of "reading history of mathematics with materials" for layout design, and the number of pages should be sufficient. With the improvement of students' socialization, the infiltration and acceptance of mathematical history among low-level students can play an excellent role as long as teachers can guide them correctly. Of course, in the form of reading materials, it is best to clearly indicate the title to highlight the theme. In addition, relevant bibliographies and websites can be provided appropriately to help students expand their learning space.
Third, the significance of the history of mathematics in primary school textbooks
Considering the characteristics of primary school students in all aspects, the presentation forms of mathematical history should be as rich as possible to arouse students' interest in learning mathematics well from an early age. For example, some comic books can be added appropriately to make the history of mathematics more readable. If possible, you can also shoot relevant videos and attach them to the back of the book in the form of CDs, so that students can get in touch with the history of mathematics more vividly and intuitively and have a deep impression on it.
Both traditional mathematics textbooks and current textbooks contain a small amount of materials on the history of mathematics, or introduce new contents with interesting mathematics topics, or insert a portrait of a mathematician and briefly introduce his life, or attach reading materials to the text. Mathematics textbooks can use historical mathematics stories as problem situations, introduce new contents, and encourage students to love mathematics and study hard. For example, Archimedes was still obsessed with mathematical research when he died, and Euler still made a lot of achievements through memory and mental arithmetic after he became blind. But in addition to this simple patchwork processing, more mathematical historical materials (especially mathematical thinking methods) should be organically infiltrated into the curriculum.
Studying the history of mathematics is for the value orientation of mathematics teaching, and for history and teaching are two completely different value orientations. Most of the history of mathematics we see now is based on history, so we pay more attention to the authenticity of historical facts, and the research content is more important mathematical events and figures in the history of mathematical development. The purpose of studying the history of mathematics in teaching is to clarify the ins and outs of knowledge and the evolution trend of mathematical thought from a historical perspective, to better grasp the intelligence of mathematical knowledge in teaching and to ensure that our mathematics education can be profound. Therefore, reading the history of mathematics for teaching is based on "people" in reality and pays attention to "people" and "things" in history. By comparing different mathematical events in history, we can refine the law of the development of mathematical thoughts and constantly optimize our own mathematical concepts (for example, according to the fact that many important concepts in mathematics are intuitive, concrete and unsystematic when they are born, and then establish the concept that children treat mathematical knowledge as an extremely important teaching skill); Through the historical evolution of a certain knowledge, we can extract the order of gradual improvement of human cognition (for example, the development history of reading algebra can be summarized into three stages: literature algebra, abbreviation algebra and symbol algebra). We should be good at grasping the appearance of history and ask questions from the perspective of epistemology (for example, the process of knowing numbers is long, but why is it more tortuous and difficult for human beings to know negative numbers than to know natural numbers and fractions? Through the detours that human beings have gone through in history, the setbacks and puzzles of mathematicians, the obstacles for human beings to know a certain knowledge are extracted (these setbacks are precisely the cognitive difficulties of students); We should capture educational historical stories and events from the perspective of "giving children correct mathematical concepts and good learning emotions". The materials on which the research is based are not original mathematical historical materials and cultural relics, but various versions of mathematical history works; The research method should focus on the same event, study different versions of the history of mathematics, enrich the connotation of this mathematical event from different works on the history of mathematics, refer to the biographies of mathematicians in the history of mathematics, describe the thinking process of typical individuals in history in detail, and use various materials to confirm and complement each other, thus "restoring" the ancient people's mathematical thinking methods and thinking promotion process.