Reminds me of one of my favorite quotes from the quotes thread.

At home there was a game that all the parents played with their children. It was called, What Did You See? Mara was about Dann’s age when she was first called into her father’s room one evening, where he sat in his big carved and coloured chair. He said to her, ‘And now we are going to play a game. What was the thing you liked best today?’

At first she chattered: ‘I played with my cousin . . . I was out with Shera in the garden . . . I made a stone house.’ And then he had said, ‘Tell me about the house.’ And she said, ‘I made a house of the stones that come from the river bed.’ And he said, ‘Now tell me about the stones.’ And she said, ‘They were mostly smooth stones, but some were sharp and had different shapes.’ ‘Tell me what the stones looked like, what colour they were, what did they feel like.’

And by the time the game ended she knew why some stones were smooth and some sharp and why they were different colours, some cracked, some so small they were almost sand. She knew how rivers rolled stones along and how some of them came from far away. She knew that the river had once been twice as wide as it was now. There seemed no end to what she knew, and yet her father had not told her much, but kept asking questions so she found the answers in herself. Like, ‘Why do you think some stones are smooth and round and some still sharp?’ And she thought and replied, ‘Some have been in the water a long time, rubbing against other stones, and some have only just been broken off bigger stones.’ Every evening, either her father or her mother called her in for What Did You See? She loved it. During the day, playing outside or with her toys, alone or with other children, she found herself thinking, Now notice what you are doing, so you can tell them tonight what you saw.

She had thought that the game did not change; but then one evening she was there when her little brother was first asked, What Did You See? and she knew just how much the game had changed for her. Because now it was not just What Did You See? but: What were you thinking? What made you think that? Are you sure that thought is true?

When she became seven, not long ago, and it was time for school, she was in a room with about twenty children – all from her family or from the Big Family – and the teacher, her mother’s sister, said, ‘And now the game: What Did You See?’

Most of the children had played the game since they were tiny; but some had not, and they were pitied by the ones that had, for they did not notice much and were often silent when the others said, ‘I saw . . .’, whatever it was. Mara was at first upset that this game played with so many at once was simpler, more babyish, than when she was with her parents. It was like going right back to the earliest stages of the game: ‘What did you see?’ ‘I saw a bird.’ ‘What kind of a bird?’ ‘It was black and white and had a yellow beak.’ ‘What shape of beak? Why do you think the beak is shaped like that?’

Then she saw what she was supposed to be understanding: Why did one child see this and the other that? Why did it sometimes need several children to see everything about a stone or a bird or a person?

Doris Lessing, "Mara and Dann"

I have edited your title to "Raising numerate children" since numeracy, rather than general rationality, is the subject of your post. You are welcome to edit the title again, but more specific titles are usually better.

The question of the subject is too dense and should be partitioned. Some ideas for auxiliary questions:

• Do there exists attempts at classifications of parenting styles? (So that we may not re-invent tread tracks)

• Is parenting or childrearing an activity that supports the existence of relevant goals? Do there exist relevant values? Or is parenting better approached as a passive activity sans evaluation with no winners or losers? (So that we may affirm this question is worth answering)

• Given affirmative answers to the above questions (and having achieved some epistemic rationality in this domain), and assuming a choice of parenting style(s) and/or values, what specific steps can be taken to activate those values in meatspace (so that we may gain instrumental rationality in this domain)?

• The above kind of direct onslaught will likely lead to overzealous suggestion, so we can also consider stepping back and asking: what are some strategies for generating candidate actions without concurrently assuming premature preferences? [1]

• Potential answers to the above queries will always be accompanied with degrees of uncertainty. How do we determine when to stop researching and move towards implementation? How does the domain of parenting differ here from the general solution (productivity / to-do systems like GTD or strategical thinking )?

• Are there tangible contributions that can be made in the general case? If we went through this much work and make significant progress in answering some of these questions, and we have been surprised by some of the answers, is it our duty to make an attempt to inform other parents? What are the best ways of doing so? Joining a local club or school district assembly? A blog? Submitting to an editorial? Your lullaby above is wonderful and could make some serious universe-changing modifications to reality (e.g., a child grows up to assume a mathematical or scientific vocation) but we do not feel the wailing alarm in our head that assigns it the appropriate significance. Effective parenting is one of the most accessible optimization processes Joe Schmoe has access to, so how can we make meta-improvements on a large scale?

If you are serious in your attempt to answer the original query, I recommend selecting one of the above questions or something even finer-grained and re-submitting to Discussion. (By the way, I am interested.)

[1] Say that a naive answer is the banal "brainstorm," to make a list of relevant large-scale projects to relevant values (e.g., figure out a consistent system of reminding my kids to be compassionate to those around them (name 3 examples of specific compassionate actions) if we value empathy and mindfulness). Then a follow-up question is to locate where your candidate actions are in behaviorspace for this domain: collate several "brainstorm" lists by independent parents who seem to have similar values and styles. Are there academic resources? Potential analytics to be done? Are there quantitive variables that correlate to success? Can we data-mine historical sources over these variables? (e.g., if we are determining whether to raise kids vegetarian or omnivore, what do long-term studies in the literature say about follow-up health?)