To refresh your memory, the standard IUPAC periodic table looks like this:
Now this one's just fine for most purposes, but it gets a bit confusing when you're dealing with electronic configurations of elements. for the first three periods (rows), you can tell which shell the outer electrons are in because it's the same as the number of the period, so for instance, phosphorous's outer electrons are in the third shell, because it's on the third period.
unfortunately for my students, and chemistry students across the world, once you get to the fourth period, things go a bit wonky. For instance, iron (Fe) has it's outer electrons in the third shell, despite the fact it's on the fourth row. in fact all the element in that part of the periodic table (the d-block) have electrons in the shell one LESS than the period they're in, so ruthenium (Ru) has it's outer electrons in the fourth shell.
When we get to the f-block (the bit hanging underneath which actually belongs between barium/radium and lutetium/lawrencium) things get wonkier, since the outer electrons are now in the shell TWO less than the period, so uranium has its outer electrons in the fifth shell, not the seventh.
the new form of periodic table is the only one i've ever seen which is simple, lists the elements in order of atomic number AND allows a student to easily figure out the electronic configuration. it does this by cleverly adding a 3-D "step" at the junctions between the blocks. it's also vertical, which is unusual too.
Here is a version from the website:
Now the diagram contains some extra stuff that's beyond the scope of this discussion, but i'd be happy to explain it if anyone's interested. What's cool is that the numbers at the bottom represent the shells, rather than just an arbitrary label for which row the elements are in.
slightly freaky is that the blocks actually fit inside a tetrahedron, due to some math i don't totally understand yet. There's a bunch more discussion at this website (external - login to view) but basically it means that finally the periodic table doesn't just suggest at the relationships between the elements, it actually embodies them in its shape, perfectly.