Who decided there are 88 constellations, and is the Big Dipper one of them?

The 88 constellations were settled by astronomers, not by the stars. In 1922 the International Astronomical Union, the body that agrees names and rules in astronomy, accepted a list of 88, and in 1928 it adopted official boundaries so that together they cover the whole sky. The list is roughly based on the Greek constellations of Ptolemy's Almagest from the 2nd century, with additions covering the parts of the southern sky unknown to Ptolemy.

So where does the Big Dipper fit? It is a famous shape, but it is not on that list. It is an asterism: a pattern of seven bright stars inside the official constellation Ursa Major, the Great Bear. In Britain and Ireland the same seven stars are the Plough. An asterism can be any recognisable star pattern, so it is a broader idea than a constellation.

The sky is not drawn on the stars themselves. The stars in a pattern are not necessarily related, and their grouping can be just a matter of our perspective. Different cultures drew different pictures, and Ursa Major itself has been seen as a bear, a plough, a wagon or a ladle.

There is a practical bonus. Draw a line through the two stars at the front of the Dipper's bowl, Merak and Dubhe, and extend it, and it leads you to Polaris, the North Star.