Approaches form the foundation for conducting scientific research. Querying approaches from a vast body of scientific papers is extremely time-consuming, and without a well-organized management framework, researchers may face significant challenges in querying and utilizing relevant approaches. Constructing multiple dimensions on approaches and managing them from these dimensions can provide an efficient solution. Firstly, this paper identifies approach patterns using a top-down way, refining the patterns through four distinct linguistic levels: semantic level, discourse level, syntactic level, and lexical level. Approaches in scientific papers are extracted based on approach patterns. Additionally, five dimensions for categorizing approaches are identified using these patterns. This paper proposes using tree structure to represent step and measuring the similarity between different steps with a tree-structure-based similarity measure that focuses on syntactic-level similarities. A collection similarity measure is proposed to compute the similarity between approaches. A bottom-up clustering algorithm is proposed to construct class trees for approach components within each dimension by merging each approach component or class with its most similar approach component or class in each iteration. The class labels generated during the clustering process indicate the common semantics of the step components within the approach components in each class and are used to manage the approaches within the class. The class trees of the five dimensions collectively form a multi-dimensional approach space. The application of approach queries on the multi-dimensional approach space demonstrates that querying within this space ensures strong relevance between user queries and results and rapidly reduces search space through a class-based query mechanism.