Static and dynamic equivalence form part of the underlying architecture of the ENCAL computer-based learning system.
ENCAL differs from the CENTS system of Ainsworth et al.
With the ENCAL design, the third and most abstract way of representing a problem statement is through the use of algebra and a calculator.
shows the current ENCAL interface which incorporates the three external representations (i.e., iconic, datatree and calculator).
A coded summary of the results and the performance coding meanings from the ENCAL evaluation is shown below in Tables 1 and 2 respectively.
These results suggest that ENCAL has a very beneficial effect on performance.
ENCAL has been designed to facilitate translation (i.e., re-representation) from textual word problems to iconic, datatree, and calculator graphical representations and thus overcome the translation problems highlighted by Lesh, et al.
In particular, ENCAL facilitated deeper mathematical understanding through the translation process from the problem statement, to an intermediate re-representation of the problem, to computation.
However, a drawback of ENCAL is that it does not keep previous representational states for reference once a representation has been modified by a user.
ENCAL enables users to translate (i.e., re-represent) information: (a) between the three external representations; and (b) from the external representations into meaningful mental schemata--e.g., the icons support Johnson-Laird's (1983) mental models ideas.
The results of the ENCAL experiment tended to reflect this position.