How does day length change with latitude in the Northern Hemisphere during this time of year?
Since the shortest day in the northern hemisphere is 21st December, the days are getting longer.
Day length is increasing very slowly. For example, at 40N (Philadelphia or Beijing), the day length is increasing 1 to 2 minutes per day. Later on, as we near the equinox, the daily increase in day length at 40N will be closer to 3 minutes per day, but then as we approach the solstice, the daily rate of increase will slow down again (and be zero at the summer solstice). Oh sorry - you asked how day length changes with LATITUDE...that's easy, the days are shorter as the latitude increases, until you get a certain point above the Arctic Circle, and all points north of that certain point will have a winter day length of zero.
The daylight lasts longer each day until summer solstice.