A special award for a special person
She is not only the first recipient of the medal outwith St Andrews University, but also the first woman to receive it.
John Haldane, professor of philosophy and director of the Centre for Ethics, Philosophy and Public Affairs at the university, said that, under her "humane and generous direction", the school had served not only the Catholic population of the area, but many others, Christian and non-Christian.
The university had particular reason to be grateful since so many of its staff had chosen Greyfriars for their children's primary education because of the caring and respectful community that Miss McConnochie and her colleagues had created and sustained. The decision by some university staff to move to St Andrews had turned on the education provided by Greyfriars, said Professor Haldane.
For her part, Miss McConnochie said she felt deeply honoured. "I think I am just an ordinary person but I gave everything I could to the school," she said.
The medal was not simply a personal honour, but one for the whole school - staff past and present, parents and pupils - she added.
She began her teaching career in 1973 in a very different setting from St Andrews - at St Scholastica's Primary in Easterhouse, Glasgow. One of nine children, she was educated in Glasgow and did her teacher training at the former Notre Dame College.
After six years at St Scholastica's, she took the road to the isles - to Balivanich Primary on Benbecula in the Outer Hebrides - where pupils were a mixture of islanders and the children of RAF and army staff stationed on the island.
Eight years later, she was appointed headteacher of Greyfriars Primary in St Andrews - a post she held for nearly 20 years, from 1987 to 2006.
It was a very multicultural school, having at one point 23 nationalities on the roll: the newsletter was printed in 16 languages - something which, although increasingly common nowadays, was relatively rare then. This was in part due to the proximity of the university, but also because it drew its pupils from families stationed at RAF Leuchars. It also served the local farming, fishing and business community, giving it a "great social mixture", said Miss McConnochie.
Around half of the pupils came from a Catholic background, but some parents from other faiths chose it because they valued its religious background.
She was also one of the first headteachers 20 years ago to promote inclusion policies. An early beneficiary was Ryan Peterson, a former pupil who had Down's Syndrome and went on to win a gold medal for swimming in the Special Olympics.
Under her leadership, the school roll rose from 69 in June 1987 to its current roll of more than 200. She pays tribute to the support of other headteacher colleagues as well as Fife Council's education staff.
Summing up Miss McConnochie's contribution to primary education in St Andrews, Professor Haldane said: "Education is not a thing but a method of formation. But, as GK Chesterton once observed, we cannot create anything good in the sphere of education until we have first conceived it.
"Kathleen McConnochie has a conception of education as value-led formation; it is one she has practised throughout her career, the fruits of which many of us see in our own families."