Teaching the history of the founding of the US, and the reasons for the first 10 amendments, IS teaching secularism.

No, it’s not really an ideal in and of itself it’s just the absence of several bad ideals, which should be evident in any public school curriculum to begin with. The public school I went to did a pretty good job of keeping all their course material secular, as required by law. My science teacher taught evolution and was visibly mad at the ridiculous religious ideals that claim to challenge it. My favorite social studies/history teacher would answer “What!?” Anytime someone said oh my god lol. I’m sure I had a couple Christian teachers but they kept it to themselves. Secularism has to be the basis of all education, and evident in all aspects of public law, not just one class about it. It should be an important focus when teaching American history and the founding of the nation, but that’s about the only time it needs to be mentioned by name more so than practiced.

hell yes

Are you familiar with the After School Satan (ASS) clubs put on by The Satanic Temple? They teach rationalist ideas and about critical thinking and science.

If they are providing other living philosophies in such classes, then by all means.

I know it's a good deal different in the UK, there's seems to be a lot more pressure and overt Christianising (probably a made up word) of every facet of life in the US but, and this would also apply to the UK although tricky in church schools, teaching critical thinking and how to think would, I would hope over time envelope the secularism you seek.
Getting religious schools or institutions to teach secularism is a bit like turkeys voting for christmas/thanksgiving but you never know, as more and more people question the validity of religions and what they represent maybe we can move forward with something more humanitarian.

While students should be taught the constitution in civics class the subject should be taught in the social science curriculum as well. So I would say both.

Students should be taught that the founders of this nation understood that theocracy is the enemy of democracy. And for that reason they articulated the separation clause in the very First Amendment. Student should also receive rigorous instruction in the life and physical sciences, which roundly refute literal interpretations of the Bible in matters of the nature of the universe and the origin of species. Once these lessons are thoroughly understood, the students will know that secularism is a cornerstone of multiculturalism and the antidote to religious war.

Teach secularism ???? What exactly would the curiculum involve?

The US constitution gets taught, right? That's a secular document. I think that would be a great time to talk with children about the glory of separation of church and state.

Honestly I don't think it should.
Instead children should be taught how to think for themselves, Critical thinking, the Scientific method and such.

As a former social studies teacher, I would say no. Civics and government classes should be secular only in the sense that they do not deal with religion or rejection of religion at all, except for freedom of religion (including freedom from religion) as a constitutional freedom included in the Bill of Rights. They should focus on the functions and structure of government and on the rights and responsibilities of citizenship in a democracy.

In my opinion, nothing but scientifically verifiable facts should be taught in any school, parochial or otherwise; especially during the early grades. There is enough inevitable confusion for children to deal with and we should not compound the problems by asking them to believe things that don't make sense. If children have a solid foundation of scientific knowledge, everything else might make more sense and allow him or her to move on to something else.

I'll go with civics, but critical thinking is important.

A good grounding of various philosophies in high school would be a great idea -- including secularism. Social studies might be a good place for it. School should prepare the young for the world and they will be exposed to various philosophies. Of course, if parents took the time to expose their children to various philosophies that would work as well.

I'd be happy if they just taught Civics.