When the colourless solution is shaken it turns blue. What general explanation could there be for this change?      

Something in the solution is reacting with something in the air.

The solution contains the indicator methylene blue, which is blue when oxidised and colourless when reduced. It also contains an alkaline solution of glucose. Suggest in more detail why the solution turns blue when the flask is shaken.

The methylene blue is oxidised by oxygen in the air when the flask is shaken.

Why does the solution lose its colour when the flask is allowed to stand?

The glucose is a reducing agent and reduces the methylene blue to its colourless form.

What other observation supports your explanations?

The surface of the solution remains blue even when the flask is allowed to stand because it is in contact with the air.