I was horrified by the answer regarding zero as being neither even nor odd. Every integer is one or the other, and zero is definitely even. Furthermore, zero is not "nothing," it is a real number halfway between -1 and 1.
One wonders whether the correspondent's students will someday believe that -1, pi, and e don't exist because they can't draw "tail/no-tail" pictures of them!
Please, dump the silly manipulatives and journals, and start teaching math!