This paper describes an embedded case study of "blended" teaching integrated with traditional lessons in a Student-Centered Active Learning Environment and social activities on the platform. The didactic phenomena were designed by creating learning environments, artifacts, and teaching/learning sequences in authentic educational contexts. We aim at improving the task design of a mathematics lesson with an impact on students' performance in mathematics. Quantitative results show considerable benefits in the evolution of the use and coordination of several systems of semiotic representation. As a result, a better predisposition to the study of the subject seems to appear; moreover, the satisfaction test shows the achievement of alternative teaching methodologies for most of the students.