You need both to do mathematics. But for teaching/understanding one should start with observe-model-test (concrete concepts/things and their relations) leading

You need both to do mathematics. But for teaching/understanding one should start with observe-model-test (concrete concepts/things and their relations) leading on to definition-theorem-proof (symbolic abstraction and manipulation). While the approaches are very different there is a synergy which is what motivates and grounds the latter in reality.