On the Approaches of Solving Arithmetic Problems
Jing Xia, Xinguo Yu · 2021
It becomes a hotspot research problem again in the past decade to develop algorithms for solving arithmetic problems after several decades. Currently, one challenge prob-lem is to establish a theory that can not only explain the existing algorithms but also can guide the further research. Facing this challenge, this paper conducts a preliminary study on establishing the theory of solving problems. This study is going to propose the approaches of solving arithmetic problems based on the existing algorithms and then to assess the proposed approaches. To reach the above-stated research goal, this paper implements multiple divided tasks. First, it proposes a state-action mining method to establish an algorithm framework that abstractly captures the main states and main actions of connecting these states. Second, it proposes approaches of solving arithmetic problems by finding sharing states and sharing actions of the relevant algorithms. Third, it proposes a confusion scheme to assess the performance of approaches against different types of problems. The types of problems are defined according to the description indicator and the knowledge indicator of problems. This paper forms a new paradigm of defining and assessing the approaches and intends, which will be used in evaluating developing new algorithms and in identifying new research problems.