to make a great effort of the mind in order to understand or find the answer to a difficult question
above the head
頭から突っ込む
頭からはねつける
頭からかっけなす
頭からどなりつける
with the head foremost
to lower one's head―bow one's head―(謙遜してなら)―humble oneself
of some idea, to appear for a moment in one's mind