"That's as much as you're going to get," he quips, determined not appear triumphant.
Actually, Mr Jones has quite a lot to smile about at the moment. A letter he has just received from the school inspection body Ofsted is glowing in its praise of the strides that have been made to Smestow Academy since he took over as executive headteacher in 2019.
When he took the helm, there wasn't a great deal to be cheerful about. "The school was struggling," he admits.
The school in the Castlecroft area of Wolverhampton had just been issued with a stinging Ofsted report. Inspectors said the standard of teaching was "not good enough", and said Smestow "required improvement" in all five areas it was assessed on. Staff turnover, poor performance of pupils from difficult backgrounds and disruption in class were among the weaknesses highlighted.
Two-and-a-half years on, the picture is much rosier. While he is cautious not to be seen as complacent, Mr Jones has a spring in his step after a recent interim Ofsted inspection found the school was on course to be rated as 'good' when the next full inspection is carried out.
The report says that morale among both staff and pupils has improved considerably, with stable staffing levels and clear guidance about what should be taught.
"There is now a sharper focus on improving pupils' achievement through improving the curriculum," says the report. "They share your vision. They say 'Smestow is like a family'. Staff are excited about what the future holds."
Within months of taking over as executive head, Mr Jones faced the additional challenge of the school being plunged into lockdown, and having to switch to remote teaching for most pupils.
"That really reflects on the staff, who have worked much harder than we have any right to ask them, and the students who have borne much of the difficulties," he says.
"We have worked really hard with information technology in particular. We have used Sharepoint really well, we have moved to laptops, and we have provided wi-fi for those students who did not have it."
Smestow is not the stereotype struggling school. Located in comfortable, leafy suburbia, former pupils include television presenters Suzi Perry and Satnam Rana, machete heroine Lisa Potts and footballer Sam Winnall. But despite this facade, Mr Jones says 35 per cent of pupils qualify for the enhanced pupil premium funding, which provides extra money for youngsters from deprived backgrounds.
"While we're not in a deprived area, pupils come from all over the city to this school," he says.
The school is part of the University of Wolverhampton Multi-Academy Trust which also includes Wednesfield High School, where Mr Jones was head before taking over as executive head of the trust.
Over the past 18 months the trust has invested £1.6 million in the school. A new library has been created, equipped with both traditional books and electronic reading devices, the school has bought 300 new laptop computers, and every classroom has an interactive screen. The trust has also provided the school with three extra teachers.
Yet when asked what the most important improvement the school has seen during his time at the helm, he reckons it is the improvement to school lunches.
"I would say my proudest achievement is bringing all the catering in-house," he says.
"We now provide all the food internally, we have looked at the quality of the food, and raised the standard at a cost that is affordable. You can now have a main meal and afters for the price of a free school meal. If children aren't safe, if they haven't been well fed, if they aren't settled, then they can't learn."
All pupils are also now issued with a school uniform, free of charge, something else which he says plays an important role.
Work has also been done to improve the school environment.
"When I took over, one of the things the students wanted to tell me most about was the toilets. The toilets were 40 or 50 years old, and we have now rebuilt them," he says.
Mr Jones is proud of the range of 'enrichment activities' – Ofsted-speak for out-of-school clubs – which have been set up under his leadership.
"We now have over 60 things for the children to do, we offer Spanish, origami, extra maths, we support music, art and drama," he says.
The latest Ofsted report has identified clear improvements in teaching standards.
"Teachers value the simplicity of the revised teaching and learning policy," says the report. "Leaders provide teachers with clear guidance on where to access support if they need it. Pupils say that lessons are now more interesting, and staff are now more enthusiastic about the subjects they teach."
Mr Jones now awaits his school's next full inspection – which he hopes will be in 12-18 months time – to find whether its rating will finally be upgraded to good.
The teacher of 30 years has plenty of experience in turning round difficult schools. After arriving in Wolverhampton 13 years ago, he served as deputy head of the South West Bilston Academy and then as head of Wednesfield High, schools which have both had problems in the past.
"I enjoy trying to improve challenging schools, I don't think it's always really recognised," he says.
"If you're the head of an 'outstanding' school, everybody can see what you do, but I think it's really important to help schools by supporting them and developing them.
"We have fantastic students who deserve the best we can possibly give them."