I have been 'lurking' and following this thread with great interest since the beginning. Thank you Robert for all your insights. One of the main impacts on me has been to make me better able to understand the need to prioritize maths and make choices about future education. I am based in the UK so don't follow all of the discussions about US curriculae though.
I was really interested to read of the 20 hours a week that you devoted to maths. This makes a lot of sense to me following the 10,000 hours to reach expertise rule from many different sources, which would suggest that at this rate it would take about 10 years to become an expert in maths - it sounds like that roughly is a match for your journey? Would you agree?
I'm interested on your take on other curriculae that are available. It strikes me that 10,000 hours on any half decent curriculum in maths (or anything else) is likely to take most people to a pretty high level. Do you have any opinion on approaches such as Singapore math (where they have a far higher achievement in math across the whole population compared to most other countries) or Rightstart, for example? I can see that Saxon has worked fantastically well for you, so I understand why you would advocate this as one of the best routes to follow. I'm wondering if it is a less good fit for some children, whether you see it as a stand alone choice or one of many possible good options.
I like the way that you raise these issues so clearly and eloquently. My oldest is 3.8 years and not quite ready for following a formal curriculum although we do a lot of preparation and maths development work using various materials including different types of abacus. Like you as she gets older I will be afterschooling her and I can see that the reality is that there is limited time to do music, sport, maths, reading, languages etc etc. So there are some hard choices to be made. Like Manda and Tamsyn, I also place value on some non-maths subjects (music in particular) and sport / exercise is to me an essential part of a healthy lifestyle. So I think we will struggle to find 20 hours for math (I hear you sigh and shake your head disapprovingly
!!!). I do have a rationale though. Many careers also place a high value on a range of skills and expertise and I would like to equip my children to have both academic, communication, leadership and other skills for their future lives. For example, in my field (medicine) it is essential to have a very broad range of these and to be able to demonstrate them on a CV for admission to university as well as the requisite academic requirements.
However, where we can hopefully agree is that maths is super-important to focus on, starting from early in the child's education, and that if we are to choose academic subjects to pay attention to, then this is the big area to go for. This is the one message I have taken from this thread. We will aim for 10 hours. I hope this is achievable.
I'm interested in your comment about the importance of learning to read (I agree). Once a child can read (which does not necessarily take a long time, especially if starting early as many of us have done here), then what do you see as the next steps? Do you mean learning to read is the process of systematically learning to decode words using phonics instruction or do you also refer to the later skills of increasing fluency in reading more complex text, fictional and non-fiction etc?