Abstract:

In the 21st century the integration of digital technologies in the classroom is an essential part of the teaching practice of different subjects. In mathematics teaching, technologies are crucial, because of the essential learning and transversal mathematical skills that should be part of the students' curriculum in all the school years. In this context, mathematical reasoning, which can be improved using digital technologies, computational thinking, critical thinking, and programming can be highlighted. No matter which theoretical model is used, teachers need to know how to integrate technology in a meaningful way in the teaching process, i.e., in a way that will produce an effective knowledge in students. Considering the various theoretical models in the literature with applicability in educational contexts, teachers should have as a theoretical background one or more of these models that focus on the one side, on issues related to their behavior, behavior decisions, and intentions and, on the other side, in the learning environment they intend to achieve, according to their level of technological knowledge and the content they intend to teach. Despite the large variety of technology integration models, many questions remain about the dimensions and criteria used to assess the quality of them. The aim of this paper is to analyze some these models: TPACK (Technological Pedagogical Content Knowledge, TIM (Technology Integration Matrix), TRA (Theory of Reasoned Action), TAM (Technology Acceptance Model) and IO (Instrumental Orchestration). This analysis is carried out considering six quality criteria, defined in recent studies, which are intended to assist the technology user in choosing the most appropriate model according to the objective that is expected to achieve. The quality criteria are clarity, compatibility, student focus, effectiveness, role of the technology and scope. We aim to answer the question: Which model of technology integration can best fit into the mathematics teacher's teaching practice considering its quality criteria?

We analyze the applicability of each model in mathematics teaching, arguing with the defined criteria, which model of technology integration is the most appropriate to help mathematics teachers in their teaching practice, so that they can make the most of the chosen technology, according to the intended learning outcomes. The description of these models and their comparison will allow teachers to reflect on their professional practice, methodologies, planning and development of specific tasks considering the characteristics of students and the learning environment.

With this study we conclude that, in teacher practice, the five technology integration models analyzed are complementary, because they focus on different dimensions of teaching: teachers' behaviors, intentions, context, knowledge and practices. The teacher can use TIM as a tool in combination with the other models to improve their professional development and teaching practice. Despite the different theoretical assumptions, the TPACK and IO are both equally important in the mathematics teacher's teaching practice because the focus is on the teacher in a technological environment. In fact, TPACK is related to the teacher's knowledge base while IO is directed towards the teacher's performance in the classroom. TAM and TRA are fundamental to evaluate teachers' intentions and behavior when integrating technology.

Keywords:

Technology Integration, Quality Criteria, Instrumental Orchestration, Mathematics Teaching.