X, Y, and Z better than story problem when learning math

William Atkins
Friday, 25 April 2008 20:13

Science - Health

The paper (pdf file) “Do Children Need Concrete Instantiations to Learn an Abstract Concept?” is another study performed by the three Ohio State researchers.

In this study, they performed similar experiments on sixth grade students in the Columbus, Ohil area. The results of the paper appear on the Ohio State University website.

The abstract to their paper states, “The effects of relevant concreteness on learning and transfer were investigated. Sixth grade students learned artificial instantiations of a simple mathematical concept. Some students were presented with instantiations that communicated concreteness relevant to the to-be-learned concept, while others learned generic instantiations involving abstract symbols.”

“Results suggest that relevant concreteness may have some advantage over generic for learning. However, relevant concreteness hinders transfer of conceptual knowledge to novel isomorphic situations, while generic instantiations promote transfer.”

The conclusion of this paper, “The results of this study demonstrate that children do not need a concrete instantiation to acquire an abstract concept.”

In addition, “The results of this study have important implications for teaching. If indeed the goal of teaching abstract concepts, such as mathematical and scientific concepts, is transfer, then elaborate teaching of concrete instantiations is not likely to help attain that goal.”

“Moreover, generic external representations such as traditional symbolic notation can be well learned by children and will increase the likelihood of transfer.”

“In conclusion, while the ease of learning can make relevantly concrete instantiations appealing for teaching, these instantiation are unlikely to promote transfer. Generic instantiations, on the other hand, can be learned by children and once learned they can give children the power to gain knowledge of novel analogues."