Converting Month Numbers To Month Names For Pivots

My data sheet has a Month column, and those months are simply numbers one to twelve. They are formatted as plain old numbers. The data is coming from somewhere outside Excel.

How the numbers look in the data sheet doesn't matter. But I use this data to generate pivots, wherein the months are the columns. I want it to say Jan, Feb, etc. across the top of the pivot.

I realize that I could just loop through the raw data and convert the numbers to text. However, I want the pivot table to recognize this data as dates, so that I can do date-related stuff, such as the date grouping described on p. 85 of Jelen's Pivot Table Data Crunching book.

If I go into the raw data and try to convert the cells to the mmm format, they all convert to January.

I'm aware that formatting doesn't translate from raw data to pivot table anyhow. But it's not clear to me how I can use the date field grouping functions without somehow showing Excel that these are dates. Or is the pivot table smart enough to realize that just by the names, even if they are formatted as text?