[susan53]

She learns very fast is perfectly good English. Fast can function both as an adverb or adjective, just as chair can function both as a noun and a verb, and out as a preposition or adverb. It´s normal for words to have more than one function.

There´s nothing "colloquial" about it, either. Here are some authentic examples taken from formal, written texts :

... Siberia was also fast developing into a haven and a land of freedom
... rising prices of bread, milk and meat will worsen the already fast declining living standards of the population
... Unemployment has fallen in the county, although not as fast as in other parts of the region,
... my pleas for help were not heeded. I ran as fast as I dared along the Tottenham Court Road.
... With the West German economy growing fast already, the impetus from the East German migration...

I don´t know where this idea came from, but if the argument that fast isn´t an adverb (or more precisely an adverb of manner) is based on the argument that it doesn´t end in -ly, then this is irrelevant. There are several adverbs of manner which are not formed with -ly eg well, hard, late, straight - and several adjectives which are - eg friendly, likely, lively, lonely, lowly, .