Are representations to be provided or generated in primary mathematics education? Effects on transfer

With regard to transfer, is it better to provide pupils with ready-made representations or is it more effective to scaffold pupils' thinking in the process of generating their own representations with the help of peers and under the guidance of a teacher in a process of guided co-construction? The sample comprises 10 classes and 239 Grade 5 primary school students, age 10-11 years. A pretest-posttest control group research design was used. In the experimental condition, pupils were taught to construct representations collaboratively as a tool in the learning of percentages and graphs. Children in the experimental condition outperformed control children on the posttest and transfer test. Both high- and low-achieving pupils profited from the intervention. This study shows that children who learn to design are in a better position to understand pictures, graphs, and models. They are more successful in solving new, complex mathematical problems.