hey!! i'm pretty sure your teacher was a little confused with the terms
Species richness is a measure of the number of individuals of a particular species that is present.
Species richness is a measure of the number of different species. So the textbook is correct, maybe just clarify with him. He might have been confused with a species' abundance, in which case it would me a measure of a number of individuals of a particular species present.
species diversity is the number of different species present.
This definition isn't wrong, but it's not complete. Your textbook definition is better but I don't like its wording. If you flick through majority of past exam papers, I think you'll find the best definition. It should go along the line of "the variety of species in a paticular area, measured by the number of species (species richness) and the abundance of each individual species (species abundance)"
One thing to also consider is that species richness alone or species abundance alone can be measures of species diversity, but when defining this term have to mention both.
cheers!