But, in her first media interview since taking up her post, Mrs Swan made clear that her experience in England will only partly inform her approach to the job -although she believes the partnership and collaboration she promoted in Derby are the way to go in raising pupil attainment.
Mrs Swan acknowledged that underperforming Falkirk has "some significant problems" to overcome but added that, while raising the authority's game was a challenge, it was not an insurmountable one.
Her arrival just over a month ago comes in the wake of the early retirement of Graeme Young following a critical report by inspectors last April. HMIE highlighted exam results below that of comparator authorities, "important weaknesses" in some of secondary schools and a lack of focus within the education service itself.
Mrs Swan, who was assistant director of education at Derby City Council with responsibility for school improvement and inclusion, said that, while political and educational structures are different in Scotland, the fundamental issues are the same.
"Children are children and the things that teachers want to speak about are the same," she said. "In parent forums, the issues are the same. There is an awful lot that is very familiar and the challenges are pretty similar."
Previous experience south of the border has seen her work with foundation schools and a city technology institution. Foundation schools are grant-maintained, financed directly by the Government and not accountable to local councils. City technology colleges are also not run by the authority but they do contribute to its overall performance statistics.
School management was also different in that governing bodies had completely different budgetary and governance procedures and, instead of an education committee, Derby operated under a cabinet system more generalist than specialist in its approach.
Mrs Swan said she was therefore used to "a more complicated process of getting agreement and signing up to strategies or developments", and favoured an approach that allowed all parties to find a common agenda.
Already she has held a meeting with the eight secondary heads in Falkirk to persuade them to sign up to her partnership vision. She argues: "If you have strong collaboration where everyone owns the problem, I believe that is quite successful, particularly with school improvement."
The preoccupation will not be exclusively with exam results, however.
"Focusing exclusively on attainment is not as effective as focusing on a holistic approach," she said.
In Mrs Swan's view, therefore, the emphasis has also got to be on teaching and learning methods, how schools deal with more vulnerable groups of pupils, school leadership and management, the relevance of the curriculum and how to give children more responsibility for their learning.
Alex Easton of Falkirk High, one of the longest serving headteachers in the authority, said: "She wants to set up a partnership model between all the schools with coherent planning for the secondary sector - like a subset of the education services plan.
"She got a really strong, positive reaction. I feel it was a very good, optimistic start."
Mrs Swan also indicated that Falkirk saw "real potential" in the Scottish Executive's schools of ambition programme. The authority would be indicating its interest, although it is still working out the finer details.
"These sorts of initiatives are helpful, but the key thing is being very clear at the beginning how you exit from them," she said. "If you become dependent on that level of funding and it then disappears, there can be problems."
Despite her previous background in England, Mrs Swan appears to be fully signed up to the Scottish consensus. "The educational entitlement of all children is extremely important," she says. "I would be professionally and personally unhappy about a system that put more emphasis on one group than another.
"The challenge for the comprehensive system is to give a full entitlement for all children and help them achieve their outcomes. I think it is possible - you have to commit towards that."
Mrs Swan confessed she was still "reserving judgment" on some of the reforms south of the border. Having spoken to friends who had moved from England to work in the Scottish system, she was attracted by an environment where "as a professional educator, you have a voice and you get a chance to participate in developing a national strategy.
"I am not entirely convinced it is as easy to do that in the English system."