She and the Duke of Cornwall were on their first official joint visit to the county since taking on their new roles.
Jim Embury, now a volunteer at the National Maritime Museum in Falmouth, was among the crowd gathering to greet them.
The Duchess said "Oh my goodness!" and hugged Mr Embury, before adding: "I do recognise you."
She asked: "Are you based here now? And you are volunteering here? Wow. That is such a small world.
"I'm trying to teach my daughter all the things you probably taught me."
Speaking after the meeting, Mr Embury said he taught Kate history in the mid-1990s.
Asked what sort of pupil she was, he replied: "I have to say fantastic.
"It was a great class and she was a great participant and a great kid. It was 25 years ago."
Also in the crowd was a protester holding a blank sheet of paper, who shouted "No more monarchy!" at the couple.
The man, who did not want to give his name, was held back by police who he said "were worried that people were going to get annoyed and attack".
Speaking afterwards, he added: "It is the 21st Century. We don't need a monarchy - it's ridiculous."
At the museum the royal couple met volunteers working on boats including the Kiwi, a 14ft sailing dinghy presented to the Queen and Duke of Edinburgh as a wedding present.
They tried their hand at riveting on a Helford Delta Class boat dating back to the 1940s, made of mahogany and oak.
William said: "It's probably safer if you show us - we don't want to be the ones who put a hole in it."
As they lined up to have a go, he told his wife: "Make sure you do the right one; it's a bit like that Only Fools And Horses sketch with the chandeliers."
The couple met people supported by Young and Talented Cornwall, which provides financial support to young people in the county.
Poppy Luxton, 16, who is being funded through the scheme for her sailing, said: "They were saying how their children go sailing on the dinghy... She was saying she really thinks sport and getting outdoors is great for children."
William and Kate discussed the benefits of music with Imogen Dowse, 18, a cellist and singer, who performed as the couple walked through the museum.
Miss Dowse, a chorister at Truro Cathedral, said: "We spoke about how music has life-changing benefits on mental health and educational development. They are trying to get their children into playing musical instruments... I recommended the cello."
In November, William made his first official visit to Cornwall since taking the title Duke of Cornwall.
William, who is still Duke of Cambridge, became the heir apparent, and the Prince of Wales, after the death of his grandmother and the accession of his father Charles to the throne.
Kate is now known as the Princess of Wales and the Duchess of Cornwall and Cambridge.
Duchess of Cornwall does the hokey cokey