Hi people,

When I hear the term "Higher Order Thinking Skills" it makes me cringe.  The term, I believe, was popularized in the 1960s and just about everything from that time frame has been a disaster for the country, with the exception of the space program, and that was due to people educated well before the 1960s.

My first thought with the term "Higher Order Thinking Skills" (abbreviated as HOTS for now on) is that it is a term used by the education establishment to make parents feel inferior or incompetent when discussing the education of their kids.  As far as I can tell, what the establishment says is that you can either have "Rote Memorization" (RM) or HOTS, but not both.  RM includes things like learning addition/multiplication tables, doing math by hand, and, I guess, phonics.  To them, calculators take care of all RM math tasks, so why bother teaching kids that material.  For reading, they look at phonics as stupid, because they all read by sight, like us too (hence the push for "Sight Words"; how we got here doesn't seem to matter to them).

In the case of math, I didn't stumble on to Saxon until David was 6.5 years old (with Saxon 54), and he still managed to get 8 years ahead of his age level in short order.  That gave him several years prior to Saxon to get through the RM part.  My point is that there is room for both and I think one can safely say that RM skills are very, very good to have, since you won't have a calculator with you every moment of your life and you don't want your kid to look illiterate when he needs a calculator to add 12 and 17.  On top of that, there's no assurance that a calculator will always be permitted in every scenario of your kid's life.  For example, the college where my mother taught, New Jersey Institute of Technology, terminated the use of calculators on math tests while she was there.  The kids there simply did not know arithmetic and the college did not want to be handing engineering degrees to them, setting them into a profession where mistakes cost lives.  As to those kids, well, New Jersey introduces calculators in math classes in Kindergarten (or at least did, at the time), so I just feel sorry for the kids.

As to HOTS overall, I kind of look at it as a side effect from using a good curriculum...not a primary purpose.  I think that I mentioned this earlier, but in David's case, I had to make a call as to whether to stall his RM development in favor of HOTS, or to ignore RM.  Specifically, he had no clue what 3 plus 4 meant, and as hard as I tried to teach him (i.e., apples, oranges, things like that) it was was hopeless.  I finally concluded that he would be better off if he could manipulate numbers first, and then figure out what it all meant later.  Likewise with reading - I didn't care if he understood the words, because I knew that he had plenty of time for learning that.  All I wanted when he was little was to simply be able to read the words.  I feel that I was right on both counts.

(usual disclaimer:  These are my opinions, based on my experience, feel free to ignore them if you don't like them)

Interesting tidbit today at work:

So far, at work, and beyond, there have been a grand total of two people that have asked how David managed to get so far ahead for his age, while hundreds of people (at least) know of him.  The rest, I speculate, figure that Einstein or someone like him transplanted some brain matter into David, and therefore there is no way that their kids could ever hope to achieve the same.  The two people are a Chinese immigrant in New Jersey and a Russian immigrant here in Houston that I work with (I've mentioned the Russian before, here).

Anyway, the Chinese immigrant got a bit weird and my wife is no longer in contact with her, but the Russian woman, that I work with, seems to understand the importance of parents providing primary instruction and has talked with me a bunch about David.  So I ran into her today and she quickly mentioned that, now, 11 more people in her Russian group (I assume mothers of young children) are now using Saxon Math.  She said that was because I told her about it, and then the other 11 parents saw it, and immediately concluded that was exactly what they were looking for (keep in mind, they all, likely, speak and understand English fluently).  So they saw Saxon Math and, I suspect, the way they were taught came to mind, and they knew that Saxon was the way to go.  In Russia, they didn't waste time trying to convince kids of that Che and Mandela were great mathematical minds - instead they just taught math.

I plan to ask more questions the next time I see her.  This country may yet be saved, but it will only be due to parents that take the primary education (reading and math) of their kids into their own hands.

As far as keeping track of the Saxon work, I had David do the work on loose leaf paper and then put it into a binder when he finished a section.  That seemed to work well.  With more than one kid, then obviously more than one binder.

I agree that once a kid is proficient on math facts Saxon will pick up from there, with Saxon 54.  As others said, Saxon covers a lot more than just number manipulation, it basically covers everything.  I think that I said earlier on this thread that, after David had been through a few books, I went to a bookstore and looked at a study guide for one of our state tests (Texas).  I was blown away by it, because it looked like John Saxon had simply copied his book - I couldn't find one question in that guide that was missed by Saxon.  And keep in mind that I had been desperately searching for something that could actually teach David math, and I looked at a lot of stuff before I stumbled into Saxon.  Just about everything talked about how much fun their particular approach was.  That sent my defenses because I know that learning math is not fun - or at least fun in the way they conveyed.  It is tedious and tiring.  About the only way it can be "fun" is the joy when the kid accomplishes something...but that still isn't fun until it's over - so still not fun while they're learning.

The saddest thing for this country was how the Big Education tore down Saxon prevented it from taking over in math - they had to know what was possible, which is why that bunch had to do what they did.

As far as Glenn Beck - I don't follow him, but on stuff I've heard him talk about, I have yet to see where he's been wrong on just about anything.  The reason that I don't follow him is that it's too depressing - depressing that he's almost always right, and depressing that he's been marginalized at the same time.

We had a fun time with the Monte Hall problem yesterday.  Here's my summary:
(quick background:  3 doors, one has a car, 2 have goats)
1)  Everyone involved knows that Monte will open a door that is not the one selected, but is a goat.  That is part of the rules of the game.
2)  The contestant will pick a door (one of three)
3)  Monte will open a second door, which is a goat
4)  The contestant will be given a chance to change to the remaining door (the one not mentioned above), if he wants to.

Here's our quick answer:
a)  From (2, above), the odds that the contestant picked the right door is one in three
b)  Opening the second door cannot change the odds of the first door, since that step was going to happen regardless of which door was chosen (i.e., no useful information was given to the contestant)
c)  Therefore the odds of the that contestant picked the right door remains one in three
d)  One third door remains not open and one of the two remaining unopened doors still has the car
e)  Therefore the odds for that other door must then be two of three

Hi people,

Here's a British article about how uneducated people are in arithmetic.  Nothing to be surprised about, it's all calculators these days and the results show it.  As I'm sure I mentioned, calculators were out of the question for David, but even with Saxon (the old Saxon) it gets harder as you get to the high school levels.  Towards the end, I was making up trig and log tables, just to keep him from using a calculator.  But then sure enough, he would get problems with lots of digits and no rounding, which could take a couple of hours to do by hand - so I did finally relent a bit, but I still held the calculator and he had to ask to use it on specific problems.

http://www.dailymail.co.uk/news/article-2292043/One-adults-simple-sums-past-100-calculator.html

I throw in my 2 cents here.

I think that a college degree with career potential is definitely as good for a girl as a boy, although a girl (woman) may spend a decade or two raising kids, while the husband works.  In my case, I still can remember when my mom went back to work - I was maybe 5 years old.  She explained that it was only for 2 days a week, but even that was too much.  It then became 3 days, and then 5 days.

It was tough for me, as I was (and still am) very attached to her.  But it wound up being a good move as my dad got sick with brain cancer when I was 9 and died 2 years later.  She needed to work, obviously, for us to have a chance of protecting our lifestyle, so it worked out, even if I was completely out of control.  But the key thing for her was that she has a PhD in Mathematics (I think a total of 2 women got that degree in the United States that year, 1959).

But it was her degree that saved her, and us.  Without that piece of paper, things would have been very tough.

One of the best engineers that I ever worked with was a young woman (so young that she couldn't rent a car on business trips).  The company loved her and was ready to skyrocket her to the upper stratosphere.  Only thing was, she had 3 kids, and decided that homeschooling them was more important.  So she quit.  We all know that, even if we don't have budget, we'll take her back in a heartbeat (i.e., we will "find" budget for her).  But, again, the ticket for her, initially, was her piece of paper, not her brain - for without the paper, we would never have considered hiring her in the first place, even though the work she was doing required, maybe, 10% of her education (if that).

So that is my take on it.

"...the (college) degree is the new high school diploma."

PokerDad, my kid said EXACTLY the same thing after I mentioned it to him, after my posting.  I'm not in a hiring position, but given so many college grads to choose, for any job, why hire someone that you're not even sure can read, much less do arithmetic.

Obviously, what Jenene is calling high-school level, will actually be full college level, by the time she's done educating her kids.  The problem is that so many resumes are now received, that many, many, employers simply jettison the ones that don't have 4-year degrees.  She'll never even get a human review...unless she has an inside contact.

Anyway, those are my (and David's) view - but excellent topic to discuss.

Gutsy.  It's really limiting not having that piece of paper, as Mr. Robinson calls it, when referring to the same subject.  Decades ago, when I was in high school and convinced that I wanted to be an auto mechanic (I was actually running a repair shop at my house in New Jersey at the time - I still have my records from it), my mother said to me:  "Get your engineering degree, and then you can be a mechanic" or whatever you want to be.  Unfortunately it's impossible for me to know how my life would have worked out had I stayed in the auto repair business - I don't think as well, but who knows. 

I certainly won't fault you guys for not holding back your kids.   You all are putting their safety first, so they'll be great.  To be honest, I hadn't considered the option of an academic break (in the sense of the formal flow of academics).  Ironically, here in Texas I would be breaking the law if David wasn't "Enrolled in School" through age 18, and while there are exceptions, none applied to him.  So having 2 four-year degrees just before turning 17 years old wasn't enough here, he still needed one more year of "school", although that could be loosely defined.  I actually used that law a few times to motivate him to study, since he literally would have been sent to the public schools if he didn't keep up in college.

There is also a lot you can do with them academically, outside of actually being enrolled in college.  With David, I had no promises that any college would take him early.  It's up to them, and saying "no" is always the "safe" answer for them (i.e., one college here in the states had a 14 year old girl in the humanities...it was time for a semester abroad, and she wanted to go to South Africa, and her parents wanted the same - the college said no, not safe - the parents sued...I doubt that college will be admitting any more little kids, for a very long time).

So I wondered also...and the best that I could come up with was to keep him moving at the same speed, especially in math, and if he was done with Saxon 5 years before any college would take him, so be it.  I do also have engineering math text books that pick up where Calculus leaves off, and could have keep him busy for another 2 years.   So, in that case, he could hit college and breeze through math there (and likely other subjects), hopefully getting very high grades - so it would bump up his GPA and maybe get him scholarships.  As it was, my wife knew the head of the math department at her community college (my wife had taken a class from her) and asked her to help.  She wasn't sure if a kid David's age could be enrolled, so she checked with some obscure state agency and found out there wasn't any rule against it, providing his standardized test scores were high enough.  As it was, she had to override the computer each time when enrolling him for classes because they asked for the kid's age, and the computer kept kicking it back, asking for a "valid year of birth".  LOL.

I think in the end you guys will find a suitable compromise that allows you to let your kids progress as fast as they are capable, but still allows them to get a good jump on college - so all will work out.

Hi Jenene,

(regarding below) Yes, one major difference between reading and math is that once a kid learns to read, his appetite for reading will be unending and he will always be practicing, as there are always things to read in his environment.  But math is just the opposite.  You stop doing math, then the kid never will think about it all (unless he's one of them super self-motivated types) and what he's learned will bury itself in the back of his brain.  We, obviously, had breaks from Saxon, maybe even up to 3 weeks (typically when we went on vacation).  I don't remember it being a problem but I'd certainly get nervous going much longer.  There's reason the first 20 to 40 sections of each Saxon book is review.  But no, we might have taken a day or two off when David completed a book, but not any longer - he got right to work on the next one.  Also, on vacations, I would sometimes bring the Saxon books, just to have him do a little of it then.


"That was what I assumed of Life of Fred.  Fun and interesting but not a math program in and of itself (for the early years at least - I think the upper level ones are different but I haven't looked into them at all).  That was why I thought maybe we could use it as a fun 'break' between Saxon books but after just having 3 weeks off between books it is taking a bit of work to get back into it so I'm not particularly sure I want to have a break between the books any more."

Hi Kerileanne99,

My comments:
-----------------------------------------------------

"I cannot envision using LofF as a complete program! It is so, so much fun as as a supplement, and it is absolutely awesome for gauging just how much my kiddo has gleaned from her RS, Singapore, and supplemental math....but on its own??? NO WAY for Early Learning!"

From my 5 minutes on their site, I agree.  This is just another in the long string of attempts to make math fun.  Math isn't fun, at least for most kids (certainly most boys).  Attempts to make it fun is futile.  It might be entertainment (as you later say)...but I can't see how they're learning the subject.  I also don't like the swipes they take at traditional methods, they seem a awful lot like our schools.


"Thanks so much for inviting this forum into your living room Robert, as it has highly motivated me!"

Happy to help, where I can.

Kimba,

Thanks for joining in the discussion.  I'll give you my comments:

-------------------------------------

"I am a mother of two little girls who are early learners and so many times I have held them back because of my fear of them being so far ahead and starting Uni at 14 or 15 just scares the heeby jeebies out of me."

I don't blame you...it would be the same for me.  I think what I would do is keep them at least 2 years ahead in math (more is fine), but still at their grade level, or maybe one level ahead.  For math, even if you finish Saxon Calculus when they're in 9th grade, it's not the end of the world...they can take a break for a few years before starting college (they'd still be playing math games in school, so they won't forget much).  Then, maybe at 16, you start them in a community college or commute to a 4-year school.  In that environment, the kids generally leave each other alone, so from a safety aspect they should be good.  When they're 18, then they can go to a 4 year and live there (if it makes sense).  They'll be freshman-aged, so they should be able to handle it, even though they'd be taking upper level classes.  That what comes to mind for me.


"As it is my eldest daughter has been accepted to start school almost a year early and has started reception or what you call kindergarten at age 4 instead of 5. She has taken to it with gusto but I now think into the future when she goes to uni she is going to be almost a year younger than everybody else and not being able to go do the stuff other uni kids can do or getting mixed up in group more to social naivety rather than smarts."

Based on what I wrote above, I would try to keep her away from living at college until at least age 18.  Being a year younger in primary/secondary school may or may not work, it probably depends on the girl.  For college, I think that living in a dorm was my biggest mistake, so if there's some way to have them avoid that, it would be best (i.e., even a 4 year college is good, if the kids can live at home while they're young).  The social end of it should be addressed outside of school (i.e., church, for example), if at all possible.


"Unfortunately that is a real reality for girls even though they do mature quicker than boys do. I feel horrible that as a parent at times I have held her back because of this fear of what 'could' happen to her as an adult and largely felt that the reason I haven't home-schooled her is because the system will slow her down and the internal debate continues."

Your first job as a parent is to protect your kids...that simple.  If you get them through their childhood without the nasty traps (drugs, pregnancy, etc.), and get them a decent education, you win (and they win).  You really won't slow them down permanently anyway - as they get old enough, they'll do great anyway.


"I do send her to an excellent Montessori school which I love but have spent weeks frustrated with even to accept Sophia at the level that she is at."

Welcome to the club.  You must understand that having an advanced kid, you (and the kid) are troublemakers.  You people are distracting the cohesion of the class.  You are the enemy.  Well, that's how the school look at it.  But that rubs off to private schools and even Montessori.  You have to get to the mindset where your kids are getting their education at home, and "school" is really daycare.  We did that with David and it made life much easier.  And we told David the same, which was to feel sorry for the other kids whose parents weren't teaching them and to be patient as they tried to learn at school.


"I think it is a point that at times I have held her back because she is a girl and I am afraid of what will happen even if it is unlikely to happen. I have worried that she would not be accepted by her intellectual peers because the age gap was too big. But this is silly talk. You make a very valid point and I don't think it is sexist at all."

It's not sexist.  The same concerns are for boys too and you have to provide for their social lives in any case (for David it was church).  As far as being accepted by older people, that is possible, but the kid has to behave at that level - in other words if he's a silly, giggly, type, the older people will quickly tire of him.  But if he speaks like an adult and acts that way, then things can be better.


"Once they go to Uni and even if most Uni courses are online if they are going to do Medicine or Law they have to show up to the institution and I can no longer protect them especially when they are under-aged."

Now that is silly, as they should be adults by the time they're in med school or law school (although I wouldn't wish law school on my worst enemy, they way that is now).  Anyway, if the girls are simply going to class and acting mature, they'll be fine.  It's when they're out of your control, like in a dorm, I'd really worry.


"I have started her on ixl for her to do after-school and that is not that tough for her. She is flying through it and I think it is time for something harder. I appreciate you making the above point and I think I need to challenge my own perceptions and allow her to fly than to worry about what will happen if XYZ happen, and think what sex she does not matter I have no right to hold her back because of it."

No, you have the right and the responsibility to hold her back, if you cannot convince yourself that she'll be safe in her pursuits.  So do what you can, but protect is always first (and yes, we were exactly the same with David).

Hi Nee1,

Some comments for you:
---------------------------------------------------------

"Thanks for your contributions, Robert. Highly, highly appreciated.  Robinson cautions against overloading the curriculum in the 'Course of Study' notes on  Robinson Curriculum CDs. I quote an excerpt:"

You're welcome, but thank you for the inspiration.  Like I've said, the people on this forum seem to understand that (nearly) all kids are created equal, except for a small number on both ends of the intellectual spectrum.  The real difference is whether the parents want to take charge of their kid's primary education (i.e., reading and math), as Mr. Robinson did, I did, and most of you guys seem to be ready to do.

As to overloading, needless to say, I agree with Mr. Robinson, and have always believed that much of what is taught in the schools is "busy-time" - which is to give the kids something to do, but not really the critical stuff.  Like he implies, why bother sticking that stuff in their heads, especially if it detracts from the important stuff, and in the end it will have to be re-learned later, when the kid understands the math.   But, if there is free time...then it's probably not harmful either.

Hi Lzp11,

Welcome to the discussion, as you've seen, I don't mind shooting off my mouth a bit.  Hopefully you've seen Dr. Robinson's video.  One of the most important points to get from that is to not let the schools dictate the educational schedule for your kids, simply because they've been dumbing down for decades now, but kids are not getting any dumber (i.e., the dumbing down is political, part of the child-centered trend in society).  I'll post a few comments to your posting now:
------------------------------------------------

"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 love having people from all corners of the world on this thread (or, at least the English-speaking world).  Feel free to ask questions then.  I know from reading UK newspapers that terminology is often different over there.  But since you understand the need for math being a priority, you are where you need to be.


"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 don't agree with the hard number, at least in math, because much of time in math is spent reviewing and testing (and doing problems slow, because of having to go back), maybe half of the time.  With David going so fast through Saxon (he covered 4 grade levels in his first year), he didn't need to review (so I skipped the early sections in each book), and I didn't need to test, because I treated every section as a test.  He would do the section, I would mark it up, and then he'd go back and fix his mistakes, every time (and every, single, problem).  Saxon's method, if used fast and thoroughly, takes care of the need for review and testing.  So with that out of the way, maybe something like a formula would work for the number of hours - something like:  Number of hours necessary = 50,000/(number of hours per week).  So if you spent 20 hours a week, you'll have it mastered in 2,500 hours, and if 10 hours a week, maybe 5,000 hours.  Something like that, but maybe not quite as steep.  I also think with Saxon, that 10,000 hours is way too long, as that would imply something like 7 hours per section for the entire series.  Now working on cars, or especially doing plumbing, or plasma physics, yes, I can see the need for 10,000 hours to be a master.


"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?"

Don't know Rightstart, but l've also heard good things about Singapore Math.  My general rules for a good math book is the following:
1)  Black and white (no need for color)
2)  No calculators (or very, very, little calculator work, as in Saxon)
3)  3 authors at most (typical textbooks have 60 or so now)
4)  No diversity reviewer approval
5)  Likewise no pictures of Nelson Mandela
6)  No fancy new approaches to solving problems (i.e., Lattice Method for division)

I put the Nelson Mandela quip in there because I saw a textbook with his picture.  He actually is a hero of mine, being willing to stay in jail rather for his cause, for decades, while the South African government was willing to release him (I think based on him leaving the country).  But I don't remember him coming up with any great mathematical achievements.


"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 think it's the best, not based on my one case, but based on many, many other examples, starting with its popularity with home schoolers (who have no political agenda).  To answer your question, back when Saxon was independent, they had a page of anecdotes on their website.  One of my favorites was a public school where they gave the old, beat-up, worn-out Saxon books to the students who were in the "average" math level, and gave new cutting-edge math books to the honor's math class.  Needless to say, those "average" students ran circles around the honor's students at the end of the year, when they were all tested.  While one can never promise individual results, I think the best chance for success is with Saxon...now you just have to find a way to get your hands on it, over there.

 
"I like the way that you raise these issues so clearly and eloquently.  My oldest is 3.8 years and not quite rady 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  LOL !!!)."

No, not 20.  And (this won't go over with the feminist crowd too well, but what the heck), I always wonder if I would have gone slower if David was a girl.  The idea of having a little girl that's 11 years old starting in college would have scared me a lot more than David, and I would have worried a lot about her social development.  So you can do less...just don't get to the point where you're doing it in your "spare time", because, if nothing else, your school will take care of filling up that time.


"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."

I think that much of the other stuff you mention is just good parenting and comes over time, not something that you have to do 10 hours a week when the kid is young.  I didn't care about any of that.  I did care that my kid understood that he was NOT anything special...he was just an average kid that had math forced on him early (and yes, he thanks me nearly every day now, especially for being able to skip high school).  I made damn sure that he never denigrated anyone below him academically (except jokingly, as he would call Dr. Robinson's kids slackers for not finishing Calculus until age 15).
 

"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."

It is achievable, as a kid has at least 40 hours of awake time outside of school every week.  It's only a question of priority.  If the kid doesn't make 10 hours of Saxon, it's because other things are more important to the parent, that simple (sorry, but 10 hours is about my minimum).


"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?"

In my case, not much.  We had David initially reading at just about exactly your oldest kid's age (3.8 years).  From there we read tougher books, and then finally, I had him read Hamlet to me, with the proper punctuation and play-acting (really just voicing) the roles, so he would sound like a woman with Ophelia and sound scary when the Ghost showed up.  It was fun, but that was the end of my instruction (about 4.2 years old) - there was nothing more that I could teach him.  I figured the grammar and other stuff would get filled in at school, and that worked out.  The key is simply being able to read, because The System's method is designed to fail the kids (i.e., Sight Words through third grade, and only then phonics).  Other stuff like comprehension isn't can't be taught, it comes over time (but being able to read first certainly helps!), and spelling was a breeze for him, I think because he learned to read properly.  We never did one spelling lesson, other than study for spelling bees, which we won handily.


"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?"

LEARNING to reading is exactly what you said, systemically decoding the English language using phonics.  Everyone eventually does that (if they learn to read), it's only a question of when those connections are made.  If made as a 3 or 4 years old, then the kid is set for life.  If delayed by Sight Words until the kid is 10 years old, he will struggle, no different than trying to learn a second language as an adult.  In between the results are likely on a sliding scale.  The stuff after that will come as the kid picks up vocabulary and context, so I didn't worry about that at all, and I was right.

Mandabplus3,

Thanks for your posting.  I think I pretty much said it too in my prior posting (before I read yours).  I don't want to come across as saying a parent is neglectful if the kid only does 10 hours of Saxon per week, rather than 15 hours.  LOL.  As I mentioned just prior, the key is that the math is learned properly, which means not in school (at least in the US), and 10 hours a week of Saxon will assure that (probably even a bit less).  The idea being that the proper way to do math is drilled into the heads of the kids, so when the "creative" new ways of learning math, like the Lattice Method for division used in this video (and in huge numbers of schools in the country, thanks to Everyday Math) is covered in school, the kid will look at it more as a fun game to play around with numbers, but knowing inside (his head) the real way to do those problems:

<a href="http://www.youtube.com/v/Tr1qee-bTZI&rel=1" target="_blank">http://www.youtube.com/v/Tr1qee-bTZI&rel=1</a>

Achieve that, and you are a hero in my book (and will be in your kids' eyes too...even if they don't appreciate it at the time), regardless of how many activities the kid does outside of school.