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Partisans of the constructivist approach to mathematics education, such as Brousseau or Chevallard, developed an accurate theoretical framework in which didactical systems are viewed in a systemic perspective. What they somewhat fail to draw, however, is a sharp distinction between role variables – concerning the roles played in the didactical interaction by the individual elements of the system (Student-Teacher-Knowledge) – and contextual variables – concerning the action on the learning process of the system as a whole.

Our research in progress on 2nd graders' word problem solving strategies applies the previous dichotomy to class management strategies adopted by teachers. Partial evidence collected so far points to the tentative conclusion according to which, contextual variables being equal, differences in teaching styles and methods may deeply reshape the role component of didactical systems. If we take into careful account this distinction, we can shed additional light into some hitherto unexplained phenomena observed in the literature.

“Signals and Systems” is an important professional basic course of electronic engineering and information science majors. Because of strong theory, much content, and abstract concepts, students generally feel difficult to learn the course, even cannot well understand and master analysis methods and basic theories. This paper discusses about teaching methods of strengthening connections among chapters, emphasizing principles, and combing with the practical engineering, which is helpful for students to understand the course and can improve the teaching effect.

This paper proposes improvements and learning reforms through research-orientated teaching based on the characteristics of the “water pollution control engineering” course. Through a series of hierarchical teaching measures, optimizing teaching contents, improving teaching methods and strengthening practice steps, the teaching characteristics were formed. In order to accomplish the goal of “student-centered”, several methods have been proposed which includes stimulating students’ learning motivation, cultivating students’ ability in research learning and arousing students’ interests in the scientific experiments. The results demonstrate that the implementation of both reformed teaching and learning of the research-oriented teaching practice concurrently, is beneficial to the improvement of the comprehensive ability of students.