Shaw, 20, has been regarded as a prodigy ever since he made a record score of 546 in a Harris Shield elite division match.
In the two-match series against the Kiwis, Archer took only a couple of wickets at an average of over 100.
Archer's bouncer evaded Kane's helmet by a whisker.
Root is confident that Archer will come back strongly after a lean series in New Zealand.
Archer was racially abused by a member in the crowd during the first Test.
All the statistical highlights from the drawn Hamilton Test match between New Zealand and England.
Root became the Player of the Match in the Hamilton Test for his double ton.
England's Adil Rashid and Moeen Ali are currently out of contention with both struggling for form in the longest format.
Kane Williamson didn't give any chance to England thereafter and notched up his 21st Test century.
New Zealand wins two-match Test series against England by 1-0.