Digital transformation in education is an inevitable trend and has been increasingly promoted in Vietnam over the past few years. The application of digital games in mathematics instruction not only alleviates students’ stress and pressure but also fosters engagement and motivation in the learning process. This paper clarifies key concepts related to digital games as well as presents a set of principles and a design process for digital games using the web-based application Pink Cat Games. Based on a proposed four-step process, the paper illustrates the design of a digital game integrated with the mathematics curriculum for second grade. The findings of this research are to provide practical guidance for teachers in designing digital educational games, thereby augmenting the effectiveness of their pedagogical practices.

Mathematics education contributes to the formation and development of students' key qualities, general abilities and mathematical abilities. In particular, the ability to solve mathematical problems is one of the core elements of mathematical ability, helping students develop key knowledge and skills and creating opportunities for students to experience and apply practical mathematics. The study proposes some measures to foster students' mathematical problem-solving capacity in teaching the topic "Algebra" (Math 10). Teaching practice shows that the proposed measures are appropriate and feasible, initially contributing to improving the quality of teaching and meeting the goals of educational innovation specified in the General Education Program math pass 2018.

Fractional differential equations are an important branch of mathematics and have been considered under many different fractional derivatives. Among them, differential equations with Riesz-Caputo fractional derivatives have also attracted the attention of many researchers. Studying differential equations that may have singularity coefficients is more difficult than usual because they require several complex techniques. In the present paper, we consider a nonlinear pantograph differential equation where the source function may have a temporal singularity. Using the contraction principle, we prove that the problem has a unique solution under some appropriate conditions. Furthermore, we define a new type of Ulam-Hyers stability and show the main equation of the problem is stable in the mentioned sense. To obtain the main results, a new inequality is proposed and proved. Some examples are constructed to confirm the validity and feasibility of the theoretical results.