returning value if month is January

I have a list of data (1000 rows).
Each row has several columns containing information on a given transaction.

column F contains the date of the transaction (mm/dd/yyyy format.)
column M contains a dollar amount.

I have two formulas that I need to make that i am not sure how to handle.

1. I want formula that will count all the cells in column F that have a month of January and a year of 2006 and give me a total for the number of rows that contain this. I tried: =COUNTIF(F2:F1000,MONTH(1)) but it did not work.

2. I want a formula that will add up the sum ($) of all the cells in column M if the month in column F is January and the year is 2006.