How does stirring affect the rate of solution formation?
Stirring affects how quickly a solute dissolves in a solvent but has no effect on how much solute will dissolve.
The amount of solute that will dissolve is affected by temperature, more solute will dissolve at higher temperatures. This is called the solubility of the solute.
Stirring simply moves the solvent molecules around, allowing them to interact with the solid pieces of undissolved solute and transporting the dissolved solute away into the bulk of the solution.
In the absence of stirring, the concentration of solute will be highest, close to the pieces of solute, so more solute won't dissolve into the solution until the dissolved solute has been transported away by diffusion.