Motivation is the cause of behavior, that is, the subjective reason for individuals to use a certain form of activity. Motivation can be divided into internal motivation and external motivation. The motivation of mathematical research is an intrinsic motivation, which is based on physiological needs and has been developing into a driving force to meet social needs and promote mathematical research. Mathematics learning motivation refers to a conscious behavior tendency caused by a certain need related to mathematics learning. It is the intrinsic motivation to encourage or promote students' behavior in order to achieve certain mathematics learning goals [1]. Educators believe that effective learning requires each learner to trace the main steps of the historical evolution of his subject [2]. Therefore, it is necessary to study mathematics learning motivation from the perspective of mathematics history.
1. Logical reasoning and practical application are the driving forces of mathematics learning.
The history of mathematical development includes two typical mathematical cultures: one is Greek mathematical culture which attaches importance to logical reasoning, and the other is China mathematical culture which attaches importance to practical application.
Mathematical historians divide ancient Greek mathematics into several stages: the first stage is from 600 BC to 323 BC; The second period is from 323 BC to the first 30 years, also known as the pre-Alexandria period; The third period is from 30 BC to 600 AD, also known as the late Alexandria. In the first two periods, Greek mathematical culture believed that the correctness of mathematical propositions could only be explained by geometric logical reasoning, and mathematics became the mainstream of mathematical research, and geometric logical reasoning was proved to be the measure of the correctness of mathematical results. This standard has gradually developed into an expectation or ideal of mathematical research. That is, the expected mathematical results can be demonstrated by logical reasoning in geometric form. In the "Late Alexandria", ancient Greek mathematics broke through the tradition of geometry-centered, and arithmetic, number theory and algebra gradually broke away from the bondage of geometry. During this period, under the influence of Roman practical thought, demonstration mathematics was no longer popular, for example, many propositions in Helen's measurement were not proved. However, logical reasoning in demonstration mathematics still plays an important role in mathematical research. For example, Diophantine's book Arithmetic deals with the problems of number theory and algebra by pure analysis [4]. Logical reasoning is separated from geometric argument, and the idea of solving problems with logical reasoning has developed into a new ideal of mathematical research, that is, I hope to solve mathematical problems with pure logical reasoning. Throughout the whole Greek mathematical culture, mathematical research has become a labor to meet the above two ideals. The idea of logical reasoning is essentially the basis of geometric argumentation and analysis to solve problems, and it is the most essential idea of the above two ideals, which meets the definition of motivation. Therefore, it is the motive of ancient Greek mathematics research and human motivation.
The overall development of ancient mathematics in China is reflected in the construction and perfection of algorithms [5]. The so-called "algorithm" is not just a simple calculation, but a general calculation method to solve a whole class of practical or scientific problems [4]. The purpose of arithmetic is to solve practical problems, which are endless. Therefore, ancient mathematics in China not only withstood the test of the abolition of "Shu Ming" by the rulers, but even developed. For example, the popularity of abacus in the late Yuan Dynasty and early Ming Dynasty. With the formation of China's mathematical culture, solving practical problems with mathematical knowledge has become an arithmetic ideal, that is, expecting mathematical achievements to be applied in practice. The mathematical research in ancient China became a labor dominated by this ideal, a labor to realize personal value and meet the social needs of curiosity. Practical application conforms to the definition of motivation, so it is the motivation of the development of ancient mathematics in China and the motivation of human beings to carry out mathematical research.
Therefore, logical reasoning and practical application are two driving forces for human beings to carry out mathematical research. According to the classification of motivation, it belongs to driving force and is an intrinsic motivation based on physiological needs. Mathematics learning can be regarded as a directional re-study process of existing mathematics achievements, and it is a special form of mathematics research.