Current Situation and Development of Chinese High School Mathematics Textbooks from the Perspective of HPM Theory--Taking Function as an Example

Jiaxin LI

Nanjing Normal University, Nanjing 210046, China

ABSTRACT. To cater to the trend of the integration of mathematics history into mathematics education from the perspective of HPM theory, this paper starts from Chinese high school mathematics textbooks (Human version, Jiangsu version and Hunan version), analyzes the current situation of the mathematics history knowledge existing in the function part and its integration forms, and puts forward suggestions for future development.

KEYWORDS: HPM theory; mathematics history; mathematics textbook; function

Introduction to HPM theory

HPM theory originated from International Study Group on the Relations between History and Pedagogy of Mathematics established at the second international mathematics education conference held in Exeter, UK in 1972. Since its establishment, HPM has specifically referred to the study on the relationship between mathematics history and mathematics education and is an important part of mathematics education research. [1]

The purpose of HPM theory is to promote the comprehensive improvement of mathematics education level through the perfect integration of mathematics history and mathematics education.It not only improves teachers mathematical literacy, but also enables students to understand the generation and formation of mathematics while mastering mathematical knowledge and thoughts, enhance their enthusiasm in learning mathematics, and realize the cultural value and scientific value of mathematics as well as its great role in promoting the development of social civilization.

The French mathematician Poincare once said: “If we want to predict the future of mathematics, then the appropriate way is to study the history and current situation of the subject.”[2]Since the advent of HPM theory in 1972, the integrated development of mathematics history and mathematics teaching has become an

important topic of research around the world. However, it was not until the beginning of this century that China emphasized the significance and value of mathematics history in the Curriculum Standards for Ordinary High School Mathematics (Experiment) [3].

At present, there are four forms in which mathematics history is integrated into mathematics teaching, which are additive, replication, adaptation and reconstruction^[1].The four methods will produce different effects according to the degree of integration and the application conditions, and the specific use is determined by teachers to make the corresponding curriculum design arrangement for the corresponding students. However, at present, the supplementary form is more frequently used, and teachers use the form of telling a short story to popularize the knowledge related to mathematics history, while the adaptive form and the reconstructed form are less, which can promote the self-construction of students by reshaping the historical scene and other forms.

The present situation and development direction of HPM theory in mathematics textbooks

Current situation and analysis

The functional knowledge in the compulsory textbooks of Human version, Jiangsu version and Hunan version is all based on collection, but the degree of correlation is different. Jiangsu version is more concise and clear, and puts all the knowledge of function into a single chapter. Human version and Hunan version choose cantors definition of correspondence relation in set theory and put together the concept and basic properties of function and set. For other knowledge of function, Human version is divided into two chapters: basic elementary function and application of function, while Hunan version is put together uniformly.

By comparing the three versions of textbooks, this paper makes the following statistics on the emergence and elaboration forms of mathematics history in functional knowledge:

Table 1 Analysis of mathematics history in the three versions of textbooks