In order to research tasks for mathematization in a technological environment, this study observed the processes where students constructed a mathematical entity from mechanical linkages through being asked questions by their teachers. From a Vygotskian perspective (Wertsch, 1991), the functions and restrictions of mediational means were focused upon. The process of students' construction was divided into four cognitive phases according to the representational phases of mathematization (Isoda, 1993). The process illustrated that obstacles to changing the cognitive mode from non-reflective cognition to reflective cognition (Norman, 1993) and the roles of mediational means changed as a result of the teacher's questions that aimed at overcoming the restrictions of the means from representation to interpretation. As for the tasks for mathematization, this case study implied the necessity of achieving synchronization between mathematical representation and physical objects.