I'll teach them about the true, true nature of truth, about logic and evidence, and about facts and information. I'll also teach them that they should be skeptical, and that they need to learn to differentiate truth from falsehood. I don't know exactly what I'll teach my kids. I'll probably teach them to trust, and to not believe everything they are told or do. I'm just not sure which lessons I will teach.
What I do know
I seriously practiced astrology between the ages of 12 to 16. Specifically from this book [1].
How did I start believing in it?
My dad believed in it and went to an Indian astrologer and the guy gave me a reading and got my character spot on. Because of that, I became really enthusiastic. However, since I knew that my family let me down before when it came to matters of knowledge, I decided to do my best to quickly debunk it as fast as possible.
I got into palmistry and numerology. It took me 4 years to debunk.
The reason it took 4 years: well with palmistry, it's tough to know where to start. Furthermore, life events play out on a life scale, so the instant feedback is zero. At the time, I eventually ruled it out by association, a very weak argument indeed. Nowadays, I rule it out by logic, but I still can't empirically rule it out (not that I care).
Numerology was actually doable and that took me 4 years. It took so long because there's an insidiuous effect going on. With most numbers (check the source [1]), the descriptions are relatively positive and when you're capable of always giving quite a positive reading, then people tend to agree with you! In fact, a psychologist tested this on a 100 college students. He wrote the same positive personality description for all of them and got 4 out of 5 stars! While I couldn't find the source of that, I could find the source on something very similar [2].
Eventually I noticed that numerology had an accuracy of 50%, I reasoned that's basically a coin flip's worth of chance (remember, I was 16, I didn't understand what base rate meant) and if numerology would be true, I'd expect a 95% accuracy. Also, in hindsight there were some very strong indicators of it being bullshit. I used the system to pick my friends this way for a while and that didn't go too well (not too bad either).
I've wasted a lot of time on it and I'm sad that this is the stuff I spent my time on, and that this is the stuff my dad found important. When I'll be a dad, I'll teach my kids about math, music and the world. I'll teach them about numerology and palmistry as a cautionary tail and how to distinguish true knowledge (math) from nonsense such as astrology (in a scientific sense, I agree that it's useful for simply talking, etc.).
The irony is, whenever I give readings to people (once per year on average), they tend to become almost immediate converts despite me saying it's bullshit. That's something to think about. Even more ironic is that ever since that period in my life, I behave as my birth date would stipulate. Since whatever you believe in -- between the ages of 12 and 16 -- stays forever with you.
(Obviously, there's a good explanation for that and it doesn't involve planets. It definitely involves the effects of a self-fulfilling prophecy)
[1] https://archive.org/details/in.ernet.dli.2015.70770
[2] https://en.wikipedia.org/wiki/Barnum_effect