Catriona Stirling, 37, of Cumbernauld, made the discovery while her son was throwing stones into the water at Blackwaterfoot on the west coast of the island.
At first, she thought the black gleaming rocks were the remains of a meteor.
But it is now believed the rocks are pieces of pitchstone, a type of natural black glass that is found in several locations around the world, including Arran, the Rocky Mountains, Lake Taupo in New Zealand and Yellowstone National Park.
Ms Stirling said: "My son was in the water and I just saw these very shiny black rocks. I thought they might have been meteors. There are a few tests you can do to find that out but it didn't pass them all. I knew there was something different about these."
Ms Stirling, who said she had an inherited an interest in geology from her father, got advice from Glasgow Museums on her find, with it suggested they might be pitchstone which could be up to 350 million years old.
She added: "I can't believe it. It is amazing to think that these rocks could be that old."
Pitchstone is a variation of volcanic obsidian glass that was formed by volcanic activity around water.
It is formed when lava or magma cooled quickly to form a coarse crystal structure that can be quite silky to the touch.
The stone is usually black but brown, red, green and grey examples can also be found,
While usually found on Arran, a pitchstone ridge can be found on An Sgùrr on the Isle of Eigg.
Pitchstone from Arran was used to make tools, such as blades, during the Mesolithic and Neolithic periods and was later traded across the north of Britain.
Ms Stirling, a full-time mum, is due to take her finds to the Hunterian Museum at Glasgow University for final verification.