The goal of this exploratory study was to uncover the construction processes which occur when pupils are taught to work with models in primary maths education. Two approaches were studied: 'providing models' versus 'designing models in co-construction'. A qualitative observational study involved two groups of pupils of a primary school in the Netherlands. A series of lessons involving problem-oriented tasks was given. For this article's purpose, we studied the learning processes of one pupil per condition in detail. Interpreting the results it is assumed that upper-grade pupils may be able to design models in co-construction as long as they receive sufficient teacher guidance. © 2002 Published by Elsevier Science Ltd.