There is increasing social and political pressure to prepare teachers of the future with strong technology‐enhanced learning design capabilities, yet little is known about how teachers in training actually go about technology‐enhanced learning design processes. This study involved an in‐depth analysis of three groups of three pre‐service teachers as they completed a five‐week collaborative technology‐enhanced learning design project. Recordings of all in‐class group discussions and out‐of‐class use of social media were analysed in order to understand the focus of the novice teachers' technology‐enhanced learning design processes. Post‐project interviews were also conducted to determine the reasons for the novice teachers' design approaches, and to better understand what constrained and supported their design efforts. A key finding of the study was that, despite the intentions of the pre‐service teacher education program, participants rarely mentioned or thought about pedagogy during their collaborative design activities. In addition, tutor support, technological capabilities and group collaboration were identified as strongly influencing the technology‐enhanced learning design process. The implications of the study are discussed in terms of furthering the capabilities of novice teachers as designers of TEL interventions.

Analysing pre-service teachers' learning design conversations in relation to Technological Pedagogical and Content Knowledge (TPACK) framework to understand their learning design practices has remained unexplored. This paper presents findings from a study of pre-service teachers' design discourses that identified how TPACK elements were used during their collaborative design of technology-enhanced lessons. Through thematic analysis of 81 design conversations in two cycles, it was found that pre-service teachers discussed design related issues, TPACK elements, and context in their design conversations with dominant references to design-related issues, substantial occurrences of single TPACK elements, and lower frequencies of integrated TPACK elements and context. Practical recommendations and a Design-TPACK or 'D-TPACK' framework were proposed to support pre-service teachers' learning design practices.

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Integrated teaching is a modern, learner-centered trend. Today, Vietnam is strongly innovating from teaching academic knowledge to integrated teaching. Integrated teaching helps learners to develop their competencies. This method makes students to be active and creative. Students have more motivation in learning. Integrated teaching means helps us to find the relationship between these knowledge, methods and other ones. The above things are illustrated by teaching geometric extremes. This is a practical problem in Hau Giang, Vietnam. Teacher gives questions and students answer them. These questions are pedagogic. In addition, the article gives some results of empirical investigation confirming the superiority of integrated teaching compared to traditional teaching. The article proposes a number of research results on the concept of integration and features of integration. Some features of integration are subjective, association, useful combination, expression of introvert and extrovert orientation, creating a unified block, in a certain context.

The law of Cosines is an essential theorem in mathematics in particular and in science in general. The Cosine Rule allows us to calculate the length of one side of a triangle when we know two sides and the angle between the other two sides. This theorem is one of the first theorems when people want to build trigonometric systems. Because of such importance, many people studied the Law of Cosines. In Vietnam, they taught the Law of Cosines in the 10 th -grade Geometry program. It appears in Basic and Advanced sections, after having learned some concepts about vector operations. Although it is a famous theorem, there are not many documents mentioning how to teach the Law of Cosines effectively. We need to understand the relationship between mathematics and other fields expressed by the Law of Cosines, as well as to apply the method of problem-based learning in teaching this theorem.