respect expansion joints. I am sure that the remedy for this project depends alot on the region, but mine for example, the joints are working all the time and they need their space to continue to work. The joints in the side walk and streets are constantly moving regardless of the age and the season. So to compromise the joints could cause some problems.
In my area, I repeat, in my area, I would fill in the area with a flexible caulk that will give and take. Then I would go over the crack with a Membrane made especially for this project. This membrane overlaps the crack about two feet on each side. the membrane acts as a rubber band and will allow the crack to open and close and also allows the tile to stay put. Again, as Dodgeman stated, the mastic has to be a flexible mastic too.
Now, a vinyl tile would be ideal as it would give and flex, but ceramic will not budge but only crack when under pressure.
If my area had basements, I would strongly suggest the following, install the membrane and then only use vinyl square tile and to install the tile over the crack and make it so that the tile can be replaced easily if when the summer shrinks the soils and the foundation falls. Then in the winter it would close back up.
I have one big crack in my closet wall above a door that I can actually tell the season by. I have stopped trying to patch it as it will NOT allow that to occur. The summer its as wide as the thinckness of a silver dollar and the winter its so tight you cannot even see the crack. I have tried all sorts of caulk and nothing will stand up to it. We even have jacks all around our foundation every 8 feet and on a slab foundation of course.
Be advised, this is only a regional remedy and course of action.