With the faster pace of China’s opening to the outside world, the contacts between Chinese enterprises and Portuguese speaking countries are becoming more and more frequent. Under this trend, how to further improve the quality of Portuguese classroom teaching is related to the development of students, enterprises and the long-term development of the whole country. This paper mainly focuses on the two aspects of “the main problems existing in Portuguese classroom teaching” and “the improvement countermeasures of Portuguese classroom teaching”. Combined with the current situation of Portuguese teaching, this paper puts forward targeted reform measures, in order to further optimize the Portuguese teaching system, with “student development”, “enterprise development” and take “national development” as the ultimate goal to cultivate a large number of high-quality Portuguese talents to the society.

Nowadays, international exchanges are becoming more and more frequent in the world. As a global language, English can establish a communication bridge between different countries and nationalities, and its importance is obvious. Since 2001, China has gradually added English education to the curriculum plan of primary schools in various regions. Later, with the deepening of the industry’s understanding of English teaching, the education reform has also followed up. It can be said that the level of educators and educates is rising spirally. However, there are still many restrictive factors in the current situation of primary school students’ learning English, among which the more prominent factors are the strength of English teachers and the evaluation mechanism for students’ learning achievements.

Employment guidance is an important way for employment education in colleges and universities, and it is also an important educational process. Strengthening the employment guidance in colleges and universities is necessary to alleviate the structural contradiction of employment and serve the talent cultivation of schools, as well as to enhance the employability of college students and serve the growth and success of young students. This paper focuses on the problems of employment guidance in colleges and universities in the new era, and proposes countermeasures to solve them in four dimensions: system construction, precise service, regional coordination and employment capacity enhancement.

Objective To understand the status quo of problem behavior of children in Henan Province, and to explore the applicability of the Conners Parent Symptom Questionnaire (PSQ) norm test in 3-6 years old children. Methods A total of 775 children aged 3-6 years old in Henan Province were selected to measure their problem behavior by using PSQ. The difference and consistency of the detection rate of Chinese and American norms were analyzed, and the difference between the average score of problem behavior of children in Henan Province and the average score of each factor of the two norms was studied. Results (1) The impulsive-hyperactivity index of boys was significantly higher than that of girls; Children's learning problems show a significant age difference, and the older the children, the higher the score of learning problems; Non-only children show more impulsive-hyperactivity, hyperactivity problems than only children. (2) There are significant differences between the Chinese norm and the American norm in the detection rates of learning problems, impulsive-hyperactivity, anxiety and hyperactivity index. (3) The PSQ scores of children in Henan Province were significantly different from most factors of Chinese and American norm PSQ. Conclusion There are differences in the problem behavior of young children in Henan Province in terms of gender, age, and whether they are only children. The consistency of Chinese and American PSQ norms is poor, and they are no longer applicable to young children in contemporary Henan Province.

The PBL teaching method emphasizes using specific problems as a guide in practical application, guiding students to achieve better teaching implementation results in practice. The integration of cross-border e-commerce and English teaching is a practical English course content in the teaching of English majors. In the current stage of English course teaching, it is an important method that is innovative and targeted to improve students' English course learning effectiveness. In the specific application process, the application of PBL teaching method requires teachers to provide important support for improving the teaching effectiveness of cross-border e-commerce English courses under the PBL model by building educational and teaching training bases, actively providing sufficient practical education guidance platforms, and emphasizing the innovation and richness of teaching evaluation links.

The work is devoted to the numerical solution of the initial boundary value problem for the heat equation with a fractional Riesz derivative. Explicit and implicit difference schemes are constructed that approximate the boundary value problem for the heat equation with a fractional Riesz derivative with respect to the coordinate. In the case of an explicit difference scheme, a condition is obtained for the time step at which the difference scheme converges. For an implicit difference scheme, a theorem on unconditional convergence is proved. An example of a numerical calculation using an implicit difference scheme is given. It has been established that when passing to a fractional derivative, the process of heat propagation slows down.