The cell dublicates the DNA 'double diploid', since it now has 4 copies of each chromosome. Your teacher would call this 'diploid', regardless of what the books say. Both your teacher and the books would agree. The nomenclature is just pretty poor it seems, the books are less clear nomenclature than your teachers. Describes a nucleus, cell or organism possessing a single set of unpaired chromosomes.
Gametes are haploid.
Meiosis reduces the starting number of 4n chromosomes in the parent cell to n in each of the 4 daughter cells. Each cell receives only one of each homologous chromosome pair, with the maternal and paternal chromosomes being distributed randomly between the cells. This is vital for the segregation of genes. This results in the recombination of genes. Meiosis occurs during the formation of gametes in animals, which are thus haploid and fertilization gives a diploid egg.