Paulia's mathematical education thought has two basic points: one is about the understanding of mathematical science. He believes that mathematics has duality, which is not only Euclidean deductive science, but also experimental inductive science in the process of creation and cognition. The other is about the understanding of mathematics learning. He believes that the law of biological heredity (also known as recursive law) can be applied to mathematics teaching and intellectual development. Therefore, in 1962, a paper entitled "Mathematics Teaching and Biological Inheritance Law" was published. 1965, in his book Mathematics disco-very, he further emphasized that the descendants of human beings should take several main steps to learn mathematics. Based on this idea, he deeply studied the papers of many famous mathematicians who made great contributions in the history of mathematics, such as Euclid, Archimedes, R. de Scutes, C. de Scutes, C. F. F. Gauss, especially L. Gauss, especially L. Euler, carefully analyzed the cognitive process of discovering mathematical theorems and their proofs by himself and his contemporaries, and observed the human thought of understanding mathematics.
1963, he wrote an article on Mathemati-Calmonthly in the United States, and put forward three famous psychological principles of mathematics teaching and learning, namely, the principle of active learning, the principle of best motivation and the principle of gradual progress. Paulia believes that teachers are only "midwives" in students' classroom learning, and his leading role is to guide students to discover as many things as possible. Guide students to actively participate in asking questions and solving problems. He believes that asking questions scientifically requires more insight and creativity, which is likely to become an important part of a discovery. Once students ask questions, they will be more focused and more active in solving problems. Teachers' teaching should be based on students' active learning, which is the principle of initiative. But he also believes that if learners lack the motivation to act, there will be no action. Paulia thinks that being interested in what she has learned is the best learning stimulus, and the happiness after intense thinking activity is the best reward for this kind of activity. This is the principle of the best incentive. According to the thought of the law of biological occurrence, Paulia divides the mathematics learning process into three different stages from low to high: (1) The exploration stage is the stage of human activities and feelings, which is at an intuitive level; ⑵ In the formalization stage, terms, definitions and proofs are introduced and promoted to the conceptual level; (3) In the assimilation stage, the learned knowledge is digested, absorbed and integrated into the learners' overall intellectual structure. Everyone's thinking should go through these three stages in an orderly manner, which is the principle of sequential stages.
He believes that in curriculum design and teaching, "the law of biological occurrence" can not only determine what contents and theories should be taught, but also foresee what order and appropriate methods should be used to teach these contents and theories. Accordingly, when 1965 "New Number Movement" was in the ascendant, he raised sharp objections. He said that this is tantamount to letting babies talk about modern mathematics such as set theory and group theory before learning traditional mathematics. Let him learn to walk again. Until 1977, when answering the question "What direction do you want mathematics education to develop in the next few years", he still strongly insisted that "the farther away from the new mathematics track, the better".