ABSTRACT

This chapter presents manipulatives-approach based on what is called 'a domain-specific theory for realistic mathematics education'. It introduces this theory briefly first, then It presents description of a realistic course for developing long division. The chapter refers the mathematical activity of 'looking for problems' which implies a mathematical attitude, which encompasses knowing the possibilities and the limitations of a mathematical approach, knowing when a mathematical approach is appropriate and when it is not. The bottom-up character of the realistic approach is expected to guarantee insightful mathematical knowledge and the realistic concept of generalising is presented as a bottom-up alternative for the top-down concept of transfer. Realistic mathematics education is rooted in Freudenthal's interpretation of mathematics as an activity. Freudenthal takes his starting point in the activity of mathematicians, whether pure or applied mathematicians. The chapter focuses on the adequacy and the efficiency of various solution procedures.