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The Swans will look to extend their unbeaten run to nine games in all competitions when they host Burnley this weekend.
Carvalhal has won 11 points in his six Premier League games in charge to lift the Swans out of the relegation zone.
And Ayew, who hopes to make his second Swans debut on Saturday after rejoining the club in January, believes the manager’s style has boosted confidence in SA1.
“He has played a huge role in helping the team turn results around,” Ayew said.
“He has style and a way of working and he believes in his plan. That is important for players. If you feel the boss knows his plans and is confident, it pushes you to follow the steps.
“We are all really behind him and we need to keep that mentality going and do everything to make sure we keep getting positive results.”
Last Saturday’s 1-1 draw against Leicester at the King Power Stadium meant the Swans climbed out of the relegation places.
But the picture in the bottom half of the table is remarkably tight, and Ayew insists the fight to stay up is only just beginning.
“We are still in a challenging position and I am not scared of challenges,” he added.
“There are a lot of clubs in a similar situation to us so we must stay focused, be positive and keep fighting.
“We need to make sure we stay strong, but I have a lot of confidence in the squad and the manager. If we are on top form there will not be any reason for us not to stay up.”