PA28180
I know the Nut Tree quite well from the air and I80. Good pizza at the new amici's there.
The problem you state is probably because the CFI didn't know JACK ...a damn shame. Was he using uncontrolled airport radio work? Were you?
The best uncontrolled airport entry in my view was taught by the local examiner, bill gianotti, fly over the field at 2000' agl, circle the field to read the wind sock, the tpa and get a lay of th land. Then fly perpendicular to the downwind until clear, descend while turning opposite to downwind, continue the turn until established ont he 45 entry to downwind...at the correct altitude and making radio reports throughout.