An approach to design of mathematical task sequences: Conceptual learning as abstraction

This paper describes an emerging approach to the design of task
sequences and the theory that undergirds it. The approach aims at
promoting particular mathematical concepts, understood as the result of
reflective abstraction. Central to this approach is the identification of
available student activities from which students can abstract the
intended ideas. The approach differs from approaches in which learning
to solve the problem posed is the intended learning. The paper illustrates
the approach through data from a teaching experiment on division of
fractions.