A Theoretical Review on Solving Algebra Problems
It provides a theoretical foundation for reviewing algebra problem-solving algorithms, which is incremental as it builds on prior work to address gaps in scope and justification.
This paper tackles the lack of theoretical justification and scope in existing reviews of algebra problem-solving algorithms by developing a review framework based on State Transform Theory (STT), which structures algorithms according to states and transforms to accommodate relation-centric algorithms for word and diagrammatic problems.
Solving algebra problems (APs) continues to attract significant research interest as evidenced by the large number of algorithms and theories proposed over the past decade. Despite these important research contributions, however, the body of work remains incomplete in terms of theoretical justification and scope. The current contribution intends to fill the gap by developing a review framework that aims to lay a theoretical base, create an evaluation scheme, and extend the scope of the investigation. This paper first develops the State Transform Theory (STT), which emphasizes that the problem-solving algorithms are structured according to states and transforms unlike the understanding that underlies traditional surveys which merely emphasize the progress of transforms. The STT, thus, lays the theoretical basis for a new framework for reviewing algorithms. This new construct accommodates the relation-centric algorithms for solving both word and diagrammatic algebra problems. The latter not only highlights the necessity of introducing new states but also allows revelation of contributions of individual algorithms obscured in prior reviews without this approach.