If I had been a year older I probably would have gone to a girls' grammar school in Worcester rather than Dyson Perrins High School, a co-ed secondary modern turned comprehensive in my home town of Malvern. For 1974, the year when I moved up to "big" school, saw the end of the 11-plus in Worcestershire and the introduction of comprehensive education.
The school is named after its benefactor Charles William Dyson Perrins, whose grandfather had co-created the Lea amp; Perrins Worcestershire sauce recipe. Yet despite such entrepreneurial connections, it had low expectations of its pupils. The teaching wasn't bad; it just failed to nurture the academic ambitions of pupils.
As committed socialists, my parents believed in the comprehensive system and chose Dyson Perrins because of its caring ethos, personified in its headteacher. Mr Bormond was the best sort of caring head: very gentle and immensely kind.
I did well in tests and remember clearly a girl in the lunch queue complaining that it was unfair and I should give someone else a chance. My socialist background had instilled in me values of equality and fairness, which made me uncomfortable about being challenged in this way. Mr Bormond was sympathetic and eventually I realised I couldn't fail to do my best just because others weren't doing as well.
In 1976, Mr Bormond retired and a new head, Bill Lucas, swept in, larger than life, full of vigour and enthusiasm. We called him Batman because he would swoop along the corridors in his academic gown.
As a 13-year-old, I remember feeling that his style was anachronistic. I now realise he was trying to raise expectations.
Unfortunately his academic expectations didn't filter down to all the staff, who until then hadn't experienced many pupils wanting to go to university. When I wanted to apply for Oxford, it was my father who helped me to prepare.
He identified Hertford College, where I applied to read philosophy, politics and economics. On the interview panel was economics fellow Roger Van Noorden, who, even at my interview, was so dedicated to teaching that he led me through my knowledge rather than trying to catch me out. Professor Van Noorden would always go the extra mile for students and held Saturday morning classes for people such as myself without A-level maths.
I am now an honorary fellow at Hertford College and last year was seated next to him at the annual fellows' dinner. Even then, he still drew me out as he had done in tutorials - gently challenging the Government's approach to the global financial crisis. Sadly three weeks later he suddenly became ill and died, which is a massive loss. He will remain a reminder to me that universities need to value high-quality, caring teaching as well as research.
Former Labour MP Jacqui Smith served as home secretary from 2007 to 2009. Before moving into politics, she worked as a secondary school teacher. She was talking to Sara Parker.