Self-Regulation

Abstract

This chapter elucidates the importance and centrality of self-regulation in the context of the prevailing new conception of school mathematics as a major objective of mathematics education and as a crucial characteristic of effective mathematics learning. However, this importance contrasts sharply with the many observations that demonstrate that students of different ages show serious shortcomings in various self-regulatory aspects of a mathematical disposition, more specifically, in their metacognitive and metavolitional skills. In addition, they are affected by naive and incorrect beliefs about mathematics, mathematics learning, and problem solving that are not conducive to the development of self-regulation skills. Evidence shows these weaknesses should not necessarily occur and develop in students, and that if they do, they probably can be remedied. Indeed, a series of design experiments, in which new research based learning environments are implemented in real classrooms indicate that such interventions can have significant favorable effects on students' cognitive self-regulation skills, as well as on their mathematics related beliefs. A comparison of the instructional models that underlie the interventions in those experiments leads one to the identification of a rather coherent set of principles for the design of powerful learning environments. These principles relate to the nature of the tasks and problems presented to the pupils, the kinds of powerful instructional activities embedded in the learning environment, and the sociomathematical norms that determine the classroom culture and climate.