He was joined on the visit by officers from Derbyshire police's Armed Response Unit who talked about their own backgrounds and discussed a wide range of issues from knife crime to the importance of reporting crime anonymously through www.fearless.org.
Mr Goodman said afterwards: "I am keen to meet as many people, groups and organisations as I can in my position as Chief Constable and particularly to engage with young people to find out more about their own issues and their experiences with the police.
"I did not have the best attitude towards education as a young man and I know that some of these young people have had their own challenges.
"I was therefore keen to start my young people's engagement programme here at Derby College – to share my own experiences to hopefully inspire them to aim high.
"I think it is far more challenging to be a young person nowadays than when I was growing up. Life was simpler then and young people now face more challenges and issues. It is important that we as a police service better understand their views and feelings."
Derby College Chief Executive Mandie Stravino, who welcomed the Chief Constable on his first visit to the Roundhouse, concluded: "We have a fantastic working relationship with Derbyshire police – particularly through their involvement in our Uniformed Public Services Employment and Skills Academy.
"It was an honour for our Transitions students to be chosen to launch this very important engagement programme.
"I am sure that the Chief Constable's honest and relaxed approach to talking openly about a wide range of issues will have a positive impact on these young people as they prepare for the next stage of their lives."