I also am the father of 3yo and 1yo daughters. One of the things I try to do is let their critical thinking or rationality actually have a payoff in the real world. I think a lot of times critical thinking skills can be squashed by overly strict authority figures who do not take the child's reasoning into account when they make decisions. I try to give my daughters a chance to reason with me when we disagree on something, and will change my mind if they make a good point.
Another thing I try to do, is intentionally inject errors into what I say sometime, to make sure they are listening and paying attention. (e.g. This apple is purple, right? ) I think this helps to avoid them just automatically agreeing with parents/teachers and critically thinking through on their own what makes sense. Now my oldest is quick to call me out on any errors I may make when reading her stories, or talking in general, even when I didn't intentionally inject them.
Lastly, to help them learn in general, make their learning applicable to the real world. As an example, both of my daughters, when learning to count, got stuck at around 4. To help get them over that hurdle, I started asking them questions like, "How many fruit snacks do you want?" and then giving them that number. That quickly inspired them to learn bigger numbers.
This sounds like solid parenting; my only concern is that you might not be taking the psychology of children into account. Children sometimes really do need an authority figure to tell them what's true and what isn't; the reason for truth is far less important at that stage (and can be given later, maybe even years later).
One issue that could arise is that if you don't show authority then your child may instead gravitate to other authority figures and believe them instead. A child may paradoxically put more faith in the opinions of someone who insists on t...
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