The duchess, 38, embraced Denise Evans-Alford and Kevin Alford, who were teachers at St Andrews School. She was seen telling the two: “I want to instil in my children what I learned at St Andrews.” Kate and Prince William are currently on a visit to Wales.
Kate stopped to say hello to the teachers outside Joe's Ice Cream Parlour on Mumbles Road, near Swansea.
A large crowd gathered to meet William and his wife, who are parents to George, Charlotte and Louis.
Kate wore a long Navy coat from high street fashion chain Zara.
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Speaking afterwards, the steel worker, who also runs the Sa1ute military charity, said: "It was fantastic to meet them. I'm so grateful for the time they gave to speak to all of us."
He was on the first day of a two-week sailing holiday with his wife and two young children and had to be towed back to Swansea by the lifeboat.
"It took two-and-a-half-hours to get back as on the way back the lifeboat had three other shouts and they let us go," said Mr O'Dwyer, from Port Talbot.
"We had to put the sails up and they came back and got us. Our holiday was cut short and we had to go camping for two weeks instead."
After departing Mumbles pier, William and Kate were greeted by crowds cheering and waving Welsh flags as they arrived at Joe's Ice Cream Parlour on the nearby sea front.
They met directors of the family company, which is in its fifth generation, before being served with ice cream by staff.
William had told managing director Adrian Hughes that he liked chocolate ice cream and so was served two varieties, one vanilla in a cone with chocolate sprinkles and one chocolate in a cup with a wafer.
Kate had a vanilla ice cream in a cup with a wafer, the same served to five nursery children she and William met in the shop.
She pointed to her ice cream and said "snap" to the children before confessing that she did not think she would be able to finish all of her larger portion.
The parents of the children, from Oystermouth Primary School, said they had all completed the duchess's survey on the early years.
Later, the duke and duchess will meet workers, company directors and trade unions at Tata Steel in Port Talbot.
William and Kate will join a discussion with Tata executives and union representatives before spending time with employees in the plant's Hot Strip Mill and training academy in Port Talbot.