Duval-Smith and the prosecuting committee agreed on a summary of facts.
The summary said the boy, "child A", demonstrated "challenging behaviour from time to time".
At about 11am on May 11 last year, the summary said, "when the class was having circle time, child A was repeatedly lunging into the centre despite Mr Duval-Smith asking him to stay in his place.
Duval-Smith reached forward to move child A back and put his hand on child A's hand. The boy spat on him.
"[He] took child A out of the circle and to the bathroom. He told child A to wash the spit off. Child A said 'No'.
"Mr Duval-Smith reports at that point he lost control of himself and hit child A firmly on the back of his head with an 'open handed hit'. Child A cried as a result.
"[He] said his intention had been to support child A to 'make it right' by helping clean away the spit. His striking the child was in response to child A refusing to do this. 'The moment of hitting the child happened with feelings of frustration and anger at his refusal to do as I asked.'
"A co-worker stated she heard the hit from the circle area in the other room, and that it sounded like a clap of hands.
"Mr Duval-Smith acknowledged the action he took was not an acceptable way for a professional person to respond, and he was remorseful that he had failed the child's trust, himself, and the teaching profession."
He immediately apologised to the boy and comforted him. He also promptly reported the incident to his colleague, his employer and the boy's mother. The next day he told the Education Council.
As a result of the incident he resigned from the centre three days after it happened.
He had found working at the centre stressful, partly due to the boy's challenging behaviour around "boundaries". It was his responsibility to supervise child A for a large part of the time.
"He confirmed that he worried a lot about keeping child A safe. Child A's mother stated that her son really liked Mr Duval-Smith but 'pushed' him and Mr Duval-Smith reacted by becoming authoritarian."
The police had formally warned Duval-Smith for "assault", stating that his "actions amount to an application of force", the summary said.
The tribunal, chaired by Theo Baker, said in its verdict, "The respondent's conduct and attitude following this incident persuades us that cancellation [of his teaching licence] is not necessary in this instance, and a rehabilitative approach is required.
"We appreciate that child A displayed some challenging behaviours. The respondent will need to implement appropriate strategies for dealing with such events."
Duval-Smith was ordered to pay 40 per cent of the costs of his prosecution.