The higher education responding to the fourth industrial revolution (referred as "university 4.0") in this study is identified as a model of innovation – driven smart university. Here, the innovation is the philosophy, object as well as solutions for growing university’s values; while the concept of smart means the infostructure and technical conditions for running the teaching and learning activities based on advancements of 4.0 technologies. The core features of the innovation - driven smart university are described in the so-called "543" model, which consists of: entrepreneurial education (model “5 in 1”); innovation – driven academic researches; innovative ecosystem (model “4 in 1”); smart university; operating mechanism (model “3 in 1”); int  ernationalization and community responsibilities. The framework with criteria for the "university 4.0" model in accordance with quality assurance and university ranking approaches has been developed. Indicators for meeting these criteria can be used by universities for benchmarking themselves to QS 4-star standards or Top 200 universities in QS Asia university ranking table. Keywords: University 4.0, smart university, innovation-driven university, innovative ecosystem, start-up, entrepreneurial spirit, cyber - physical system.

In Vietnam, primary school students explicitly learn the concept of fraction in Grade 4 and 5. Because this concept is introduced to them intuitionally, it is difficult for them to understand and apply it. Base on this point, we believe that the students will commit many errors when solving exercises related to this concept. The survey of 478 students showed that some remarkable errors were made by most students; when learning fractions, students still did not understand the nature of fractions as well as the equality of parts. Therefore, teachers should note the errors of students, and use the effective pedagogical measures to help them prevent, and correct the errors.

An important goal of teaching mathematics is to form and develop students' abilities to apply mathematical knowledge to solve problems arising from real life. This goal is also associated with the evaluation of specific mathematical competencies: mathematical thinking and reasoning, inference and proof, communication, modelling, problem solving and representation, using mathematical symbols and languages, using calculation tools. Among these competencies, modelling is the capacity mentioned by educators around the world and holds an increasingly important position in many popular mathematics programs of several countries. The objective of this study is to foster students' mathematical modelling competency through teaching sine and cosine theorems. The sample included 46 10th grade students at Phan Thanh Giang high school, Ben Tre province, Vietnam, and they were asked to solve numerous real-world problems associated with the theorems. The qualitative analysis method was used to evaluate students' performance in mathematical modelling competence. The results were found that most of the students made progress in mathematical modelling competency, from which they not only had the right motivation to learn but also supported them in realising the application of mathematics in practice.

Simulation-based teaching has been used in many training areas, including general education, the medical industry, military, aviation, and so on. The simulation-based teaching models are taken into account in models used for discovery learning. Hence, it is sometimes referred to as a method of teaching discovery based on simulation. This study restores the basic content of the simulation-based discovery, including the concept of simulation-based teaching, simulation-based teaching features, and some authors' findings that implemented simulation-based teaching. The study offers a simulation-based process of teaching mathematical concepts and applies them to teach the "circular surfaces" which is regarded as a quasi-experiment in 12th-grade Geometry with posttest only nonequivalent groups design. Based on the results of quasi-experimental teaching, we initially have drawn significant results as follows: 1) simulation-based teaching increases the learning interest of students compared to traditional teaching methods; 2) Because of the interest in learning together with self-discovery learning, the students' learning results in the experimental class are better than those of control class. One thing learned from practical teaching is that teachers applying simulation teaching need to use dynamic math software and spend a considerable amount of time in lesson design. This is one of the challenges for mathematic teachers in Vietnam.

No abstract