Somebody commenting here asked the above question a couple of times. I did not respond, because the question itself seems to me to be manifestly absurd. If the child rejects adult-led education, then you are doing something wrong. The child's best interests are not served by abandoning all attempts to direct the course of the education if this happens, but by asking yourself how you can improve the education which you are providing. Let's look at a practical example to see what I mean by this.
I am not a great fan of the idea of the global warming scare. The temperature of the planet has always fluctuated and the ice caps have grown and melted over time. However, if children are going to learn about this hypothesis, they should at least understand what it is they are being invited to believe. What most of them seem to believe, as a result of poor teaching in schools, is that the ice at the north pole will melt and that this will have the effect of raising sea levels and flooding coastal areas elsewhere in the world. They believe this because they are taught ineffectively by ignorant people who don't really understand the subject themselves. This is poor quality adult-led education as delivered in schools.
So, let's have a science lesson. Your child has not asked for a science lesson, but you feel she should have one anyway. Gosh, I hope she doesn't reject my adult-led learning! The reason that children cannot be expected to understand the mechanics of global warming and climate change is that they have had no direct experience of ice caps and tropical oceans. The thing is so far removed from their everyday life that it is pure abstraction. Tell your child that you are going to make some polar ice melt and ask them to guess what will happen. They don't need to do anything. You are not asking them to open a book or pick up a pen; just watch you make a fool of yourself. Take a large glass jug and fill it with water. Then put in a handful of ice cubes. This is our ocean and ice cap. Mark the level of the water on the side of the jug and ask your kid what will happen to the water level when the ice melts. Will it go up, down or remain the same. Der! it will go up of course. Why is my mother wasting my time asking silly questions? Of course, the water level remains the same. If your child shows any interest in why this should be, you can explain the mechanism involved and they will then see that if all the ice at the north pole melted, it would make no difference at all to sea levels.
Now you can demonstrate the real mechanism which could be implicated in rising sea levels. Fill the jug with boiling water and again mark the level. Ask your child what will happen as the water cools. The level falls. Explain that hot water takes up more space than cold water and that if the sea level did rise as a result of global warming it would be as a result of this thermal expansion and nothing to do with melting ice. If you are lucky, he will ask why hot things take up more space than cold things. This gives you a chance to explain that all matter is made up of little particles that are jiggling about. The more they jiggle about, the more room they need. Heat is just the molecules jiggling about more and more, thus needing more room.
You can go on to do things like put a glass of earth and a glass of water on a sunny windowsill and see which heats up more quickly and which retains the heat more effectively. This has implications for the whole global warming business. You can put a large glass bowl upside down on a sunny lawn and then see how dramatically the temperature inside will rise. You have demonstrated the greenhouse effect.
None of this science requires your child to ask any initial questions; you have chosen to teach science today, not her. If it is done in a lively way as a series of games, I cannot imagine any child free of pathological abnormalities of mind who would not be interested in watching what you are doing. They have all heard about global warming and are worried about the ice melting and the implications for polar bears; of course they will be interested. You can also grab their attention by explaining that everything they are hearing about the melting of the ice caps is quite wrong and this can start a wider discussion about the extent to which they should trust newspapers and textbooks. For the child who has been put off learning by a school, this will really catch his attention.
The above science lesson is suitable for any child over the age of eight or nine. I simply cannot imagine a child who would not gain something from it, always provided that you do not present it in terms of; 'Now we are going to learn science'. As part of a series of games in the kitchen, the kid will not even think of the word 'science'; it is just something really interesting that his mother is showing him. And it allows him to steal a march on his schooled friends by telling them that they have been taught a pack of nonsense in their lessons!