Your formula is returning the correct dates for each week number according to the WEEKNUM function, but you're likely finding that it is returning December for the first week of 2015 because the Monday of that week occurred on the 29th of December 2014. This is technically correct, so you may need to work around this with an IF function if you want it to always return January for the first week.
You can see an in-depth explanation of how to use the IF function in the video lesson: Expert Skills Lesson 3-5 Use the IF logic function.
I have attached an example workbook using your formula, along with an IF function applied to return the desired month. It also shows your formula applied to all weeks in 2015 and 2016, proving that the result always matches the result of the WEEKNUM function:
You might notice that I've also removed the CHOOSE function from your formula and replaced it with a custom format (mmm) that simply displays the Month part of the date. You can see an explanation of custom formats and how to apply them in the video tutorial: Essential Skills Lesson 4-4 Create custom number formats.
I hope this is the result you were looking for, but please feel free to reply if you need any more help with this.
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