Can my school see my internet history?

I have an iphone and i was wondering if i use my Wi-Fi at my house or my 3g network and deleted my history & went on private browsing on my phone, if the school could see my history. Our school has Wi-Fi so when i go to school and use my phone (w/ teachers permission) can they see what i've done on my own Wi-Fi at home even though it is deleted?

No, They can monitor your traffic on current connections, but unless you are transmitting your entire history when you're connected to the school Wi-Fi, (or they have installed some special apps on your phone) it won't track back to your home