Map environments provide a fundamental medium for representing spatial structure. Understanding how foundation model (FM) agents understand and act in such environments is therefore critical for enabling reliable map-based reasoning and applications. However, most existing evaluations of spatial ability in FMs rely on static map inputs or text-based queries, overlooking the interactive and experience-driven nature of spatial understanding.In this paper, we propose an interactive evaluation framework to analyze how FM agents explore, remember, and reason in symbolic map environments. Agents incrementally explore partially observable grid-based maps consisting of roads, intersections, and points of interest (POIs), receiving only local observations at each step. Spatial understanding is then evaluated using six kinds of spatial tasks. By systematically varying exploration strategies, memory representations, and reasoning schemes across multiple foundation models, we reveal distinct functional roles of these components. Exploration primarily affects experience acquisition but has a limited impact on final reasoning accuracy. In contrast, memory representation plays a central role in consolidating spatial experience, with structured memories particularly sequential and graph-based representations, substantially improving performance on structure-intensive tasks such as path planning. Reasoning schemes further shape how stored spatial knowledge is used, with advanced prompts supporting more effective multi-step inference. We further observe that spatial reasoning performance saturates across model versions and scales beyond a certain capability threshold, indicating that improvements in map-based spatial understanding require mechanisms tailored to spatial representation and reasoning rather than scaling alone.