The terror atrocities in Paris last week has underlined the importance of teaching British values of tolerance and free speech to young people, Nicky Morgan said.
The education secretary said the attacks by Islamic extremists in the French capital were an example of what happens "when people don't appear to respect some of those values".
Ministers announced in the wake of investigations into the Trojan Horse scandal in Birmingham that all schools in England will be required to ''actively promote'' British values.
Ms Morgan made the comments in an interview with Parliament’s House magazine, in which she said the attacks on the offices of satirical publication Charlie Hebdo and a Jewish supermarket had shown the need to teach students about the importance of "core values".
"One of the other things we are asking of schools is the whole teaching of British values. This applies to all schools, it's about these core values," she said.
"We've seen what can happen last week when people don't appear to respect some of those values, things like tolerance and mutual respect. In the light of recent events ... It's very, very important.
"I know this is being discussed in governing boards up and down the country. Many schools do this without necessarily badging it as such. And others are having to think 'how do we bring this in?'"
She said citizenship and social education classes were "very important" and added "we must have core common values, that builds us as a country".
Ms Morgan said: "These British values have been defined in various strategies, by the Home Office, and we are asking schools to think about how they promote them. Ofsted will be looking at them when they visit schools
"It's about that shared history or heritage which I think makes us really strong as a country. We have freedom of speech and liberty in this country, we may not have had a revolution in the same way they perhaps had in France but I do think there are things that are precious and if we don't guard them and if we don't appreciate them ... Sometimes we think it's not very British to talk about them – but I think it's now clear that we do need to talk about them."