ped normally means for a child.. and -agogue means a leader.. hence pedegogue..
PEDA(a sweet)+GOt...student GOT a PEDA from TEACHER
ped+agog+ue--- pedantic means who is inclided towards academic learning, and agog means exicted, so pedagogue means a WHO TEACHES, as teacher are always excited to TEACH
split as ped(tree) + ago + gue(give) >> Trees teach us the 'value of giving' right from the time of youth. So trees are pedagogue