In the teaching of graphic design, students' learning state and learning effect are poor due to the lack of attractiveness of teaching materials. In order to fully display the graphic design knowledge contained in totem patterns, a model based on the pattern elements of totem patterns was constructed. Through Marvelous Designer software, the display of totem visual effects under different pattern element configurations was realized, providing a basis for the comparative explanation of graphic design teaching. When designing the teaching content, based on the totem art culture, it has constructed three parts of teaching methods of plane composition, teaching contents of plane composition and teaching concepts of plane composition, which correspond to the material selection, composition and freehand brushwork skills of totem patterns in modeling creativity and expression techniques, and the range of material selection, composition form and connotation of plane design teaching, the specific application is realized through knowledge transfer.

This study investigates pedagogical content knowledge (PCK) among teachers teaching mathematics at the preschool level in Colombia, highlighting the importance of integrating mathematical knowledge with innovative and effective pedagogical strategies. Using a mixed exploratory and transactional methodology, the perceptions and practices of 82 teachers were examined, focusing on their understanding of mathematical content, pedagogical skills, and knowledge of children’s cognitive development. The findings reveal a significant gap in teachers’ understanding of these concepts, indicating a critical need to strengthen PCK among teachers. To this end, training should be provided to enable teachers to foster meaningful and contextualized mathematical learning in preschool students. The study suggests reviewing teacher training curricula and fostering the development of pedagogical strategies that prioritize conceptual understanding and mathematical reasoning. Additionally, it identifies critical areas for improvement and offers concrete recommendations for transforming mathematics teaching in preschool education. To enhance the quality of mathematics education, several measures are proposed: ensuring continued availability of training programs for teachers, encouraging collaboration between educators, adopting constructivist approaches, and helping teachers understand the value of mathematics learning outside the school.

Rapidly changing business environments and fierce competition are making it increasingly difficult for modern companies to maintain competitive advantage and accomplish business longevity. This study can fill the research gap in mission research and longevity research, and provides implications on what form and content of mission should be selected when determining the direction of a company’s corporate strategy. Although a company’s mission is a communication tool that represents the company’s strategic priorities and unique values, it has rarely been considered an important factor in business longevity. This study conducts a content analysis of the mission statements of 43 companies in the Henokiens Association to clarify the linkage between a company’s mission and business longevity and the configurations of long-lived firms’ missions. Our results show most long-lived firms have clear missions and perceptions of familism expansion. The firms’ past, present, and future additions to their concern for products, business growth, unique philosophy, and stakeholders are highlighted in their mission statements. Therefore, the main theoretical contribution of focusing on the corporate mission as a factor of business longevity in this study is not only a new approach to the longevity factor, but also the discovery of new values of the mission in strategic management research. The practical contribution of this study is that it reveals that companies seeking long-term competitive advantage in the market need to design, possess, and share a high-quality mission from a long-term perspective and instill the ideology of extended familyism. It can also provide hints about strategic priorities for small, family-run businesses facing threats to their survival.