  Geometry problem solving presents a formidable challenge within the NLP
community. Existing approaches often rely on models designed for solving math
word problems, neglecting the unique characteristics of geometry math problems.
Additionally, the current research predominantly focuses on geometry
calculation problems, while overlooking other essential aspects like proving.
In this study, we address these limitations by proposing the Geometry-Aware
Problem Solver (GAPS) model. GAPS is specifically designed to generate solution
programs for geometry math problems of various types with the help of its
unique problem-type classifier. To achieve this, GAPS treats the solution
program as a composition of operators and operands, segregating their
generation processes. Furthermore, we introduce the geometry elements
enhancement method, which enhances the ability of GAPS to recognize geometry
elements accurately. By leveraging these improvements, GAPS showcases
remarkable performance in resolving geometry math problems. Our experiments
conducted on the UniGeo dataset demonstrate the superiority of GAPS over the
state-of-the-art model, Geoformer. Specifically, GAPS achieves an accuracy
improvement of more than 5.3% for calculation tasks and an impressive 41.1% for
proving tasks. Notably, GAPS achieves an impressive accuracy of 97.5% on
proving problems, representing a significant advancement in solving geometry
proving tasks.
