From Mathematical Education to Educational Mathematics

Author: Zhang Jingzhong
Publisher:
Publish Date: 2005-01-01
Features: Why is it "Educational Mathematics" rather than "Mathematics Education"? Mathematics education relies on mathematics science to provide materials. The pedagogical processing of these materials to form textbooks is the task of mathematics education. However, mathematics education does not undertake creative work in mathematics. For educational needs, the re-creative organization of mathematical research results to provide materials suitable for pedagogical processing often requires mathematical innovation. This falls under the task of educational mathematics. Therefore, we believe that Euclid, Cauchy, and the Bourbaki group were educational mathematicians. Their works have been repeatedly processed by mathematics educators into various textbooks, which are still in use today. From Euclid to Bourbaki, they were engaged in re-creative activities at the forefront of mathematical development. Today, in middle and high schools and universities, facing the valuable legacy left by masters like Euclid and Cauchy, we seem to be in the "rear area" of mathematics. In the rear area, besides "pedagogical processing," is there nothing left to do? If there is nothing to do, does "educational mathematics" have no place in the broad field from middle school to university? The reality is not so. The valuable legacy left by the predecessors is not perfect. In mathematics courses from middle school to university, there are recognized difficulties. How to address these difficulties has always been considered the task of mathematics education. These difficulties demonstrate the shortcomings in the work of the predecessors. Pointing out these shortcomings and re-creating them mathematically rather than pedagogically is one of the current tasks of educational mathematics. The author of the book From Mathematics Education to Educational Mathematics has been dedicated to this research. This book introduces the author's explorations since 1975. We hope that after reading this book, readers will have the impression that educational mathematics is concrete and practical mathematics, not vague discussions. However, as a discipline, it is still a young sapling, or even just a newly sprouted seed.
When we were in middle school, we all studied plane geometry, a valuable legacy left by the predecessors represented by Euclid. For over two thousand years, generations have devoutly followed in Euclid's footsteps, with no one raising objections! Academician Zhang Jingzhong discovered that Euclidean geometry has a troublesome problem: it remains at the level of "one problem, one method," lacking a set of powerful and universal problem-solving methods. The method of drawing auxiliary lines often leaves people at a loss. Academician Zhang Jingzhong dared to challenge the traditional geometric treatment model that has stood for thousands of years. After years of dedicated research, he pioneered a new approach and system centered on area. This new system has a clear focus, allowing students to start from this center and reach every corner of plane geometry, making geometric problems follow a clear path, fully demonstrating the superiority of the "area method." Over more than 20 years of teaching practice, it has been proven that the "area method" can save time and improve students' problem-solving abilities; especially its advantage in solving mathematical olympiad problems is particularly evident, and it has been widely mastered by many middle school teachers and students.