Hi Nee,

I'm going through your links, and the quote below stood out to me.  It is one of those brilliant insights that you get from immigrants that are not poisoned by the culture they now live in.  I definitely see the same thing in the states, where immigrant families understand that they have to take control of their kids' education (especially early education), because they know no one else will do that.

"‘Most people think that you should let your kids go out and discover the world on their own, and decide for themselves what they want to do, but my answer to that is No,’ says Usman (Ahmed) emphatically...‘If parents don’t influence them, they don’t become independent, they simply become susceptible to other influences instead - their friends, or what they watch on TV, or what they read in magazines."

Hi Nee,

Lots of questions.  I'll need to review my records in more detail, which I can do when I get back home in a bit.  For now, based on my notes, I actually show David as completing 5 books (i.e., through Algebra 1/2) in 12 months.  He started right at Age 7.  He did skip the first 40 sections of at least the first 4 books, but then skipped only 20 sections in Algebra 1/2.  Starting at Algebra 1, he didn't skip anything.  I based that on what the material was, and the first 4 books clearly were review for the first 40 sections - maybe with a few new concepts sprinkled in, but not enough to warrant doing the entire sections.  The later books had a lot less review, so he had to do more (or all) of the books.

As far as which problems he did, we would work the practice problems together, and then I would cut him loose on the 30 or so problems in the for that section.  He always, and I mean always, did every problem of each section (other than the sections we skipped at the beginning).  He would give me his work, and I would mark off the ones he got wrong, and he would have to try them again, until he got them right.  I made sure that he was able to do every problem in a section before we started on the section.  Also, because he didn't like doing the work very much, I suspect, I made him check every problem he did, as he had tons of careless errors.  If it was bad enough, I tore up the paper and made him do the section all over again (but that was rare).  Saxon is also very clear on this - the kid must do all of the problems in each section.  In fact, I think the biggest stumbling block to success with Saxon was teachers (mainly) that thought they knew better and would try to cherry-pick problems.  Do not try that.

As to hours, I estimate that we averaged about 3 hours per day, maybe 2 or 2.5 during the week days and 4 to 5 hours on weekends.  I didn't set a goal as to the number of sections per day, but my recollection is that we were doing about 3 sections per day for the early books, 2 sections for the middle books, and 1 section per day for the later books, as those problems got complicated.

As to slowing down, that was more me than him.  My notes say that in addition to the first 5 books in 12 months, he finished the next one, Algebra 1, in 2 months (he can thank having done Math 87 and especially Algebra 1/2 for being able to speed through Algebra 1).  At that point, he slowed a bit, with my notes showing him completing Algebra 2 in 4 months, and I really need to check that, as I was trying to slow him down at that point.  Assuming that timeline holds, it means that David had finished Algebra 2 at 8.5 years old.

Finally, we went through the Advanced Math (pre-Calculus) book.  It is a thick book with a lot of tough problems, but once you finish that you're ready for college-level Calculus.  We really slowed down then, and he took around 1.5 to 2.5 years to finish.  At that point, he was ready to take Calculus in college, and did so, starting a bit after he turned 11.  There were several reasons we slowed down so much - first, we were building a house and running the project, so that took a serious amount of my time and second, he was just too far ahead for his own good.  There comes a point of negative returns, and finishing Algebra 2 (i.e., 10th grade math, if on honors track for Calc in high school) at the age of a second grader is just too young to be useful in the real world, so we actually regressed a bit, purposely, to give him a chance to grow a bit.

Korrale4kq,

Don't forget to include the extra time spent reviewing material, due to the slower pace.  I also think the hours you have listed are pushing the definition of "teaching hours" a bit, as 6 hours per day is about the total non-lunch hours in a school day - so study halls and PE are included in those 6 hours.

So the amount of time needed drops significantly even from your numbers.

Thanks people.  PokerDad - yea, I wanted someone else to do the math regarding summer breaks, because it was even too much for me to handle.  You're looking at possibly being able to double the rate of math learning without even increasing the intensity used today (i.e., something under an hour a day), just by eliminating extended breaks.  Then double the hour to two hours per day (maybe up to 2.5 hours), and you get the 4X rate that David was able to move at in the early Saxon books.  And just to reiterate, when you're going at that clip, and using Saxon the way we did, there is no need to be testing the kid, as Saxon does that by default.

Also, I've noted that our pace went down after the first 4 books, to 2 books in the next year.  From there, it didn't make much sense to keep rushing on, and I also promised him a laptop once he finished Algebra 2...so I stalled him as long as possible to wait on prices to go down (LOL).  Anyway, I think the pace does slow down after the 4 books, as the problems get more complex and time consuming and the sections are designed, I suspect, to be used to also assign homework to the kids.  No big deal in the end.  Just racing through the first 4 books means the kid will be at least 3 grade levels ahead and likely more if he starts prior to 4th grade.

Bottom line - this isn't rocket science, it's just the combination of a extra time each day (an hour or two beyond the one hour the kid should be doing anyway), not having extended breaks, and using Saxon properly.

Thanks all,

As usual you guys have given this more thought than myself.  What I was really getting at were just the early years in education, when the kids really need to learn to read, in order to be good at it, and likewise with math.  I should have included, for sure, learning to speak a foreign language in those years (thanks Mandabplus3).  What was bothering me is that math and reading are put on the same level as the other time-fillers, which then ends up meaning that relatively little math and reading get done in those years, and thus it gets dragged out over many more years.

After those early years, if you keep going that way, you wind up with 10 to 12 year old kids that are ready for college, which is probably too much for society (and them) to handle.  So, like you say, Mandabplus3, you slow down the pace of the academics somewhat and let them see and try out the rest of the world.  I like it.  My kick on PE is mainly restricted to having PE displace time in the classroom, as it does now, right through high school.  On after-school sports, I'm kind of mixed, but I would agree that anything that gets kids active, rather than spending their late afternoons playing video games is a good thing.

Good point here, Korrale4kq :  "I think the wasted time is when the students are sitting around making penguin crafts for a week in an attempt to learn about arctic animals."  Good point also on pointing out that reading can (and should) be used to learn other subjects, like science.  Maybe where it gets carried away is when kids have to make "penguin crafts" (LOL) rather than simply read about penguins.

I think part of my narrow focus is due to my own experience with David, where I concentrated on reading, and then math, and at that point basically let his schooling (being it the Christian school, or college) take over from there.  We did do other things (tee-ball, violin, piano, karate), but I didn't see David get much out of any of them...so I would tend to not treat them at the same level of what worked for him - although for other kids, they may get much more out of those types of activities.

Finally, thanks Nee, on the summer break info.   For kids, and most adults, math simply isn't necessary or useful day-to-day, but reading is used practically non-stop (for good readers), so it makes sense that math would be pushed back in the brain over an extended period of time (i.e., summer break).  As most people know the concept of a summer break originated from having the kids "help out at the farm", but has since worked its way into union contracts.  I doubt that there was ever any academic justification for the breaks, just the slow inertia of changing things keeps them intact.   Saxon, at least in the earlier books, lines up perfectly with your data, where they spend the first 40 sections reviewing the prior material at the beginning - which works out to 9 to 10 weeks, at their standard pace.  So, to really get a feel of how summer break affects math development, you have to pretty much double the time of the break - and at that point, you see more and more months disappearing and it becomes easier to see why math drags out so long, when we all know it doesn't have to.  Reading is kind of interesting too.  I think the slower-paced children probably just turn off attempting to read during the summer, as it is such a struggle - so they regress there also.  But good good readers will gobble up everything in sight.

For you out there looking to change things (and I know who you are), getting rid of summer break is probably the fastest way to get results.

Not much posted here lately, so I'll add a bit.  In meeting with several Brill moms recently one thing we struggled with was figuring out was how kids could spend 6 to 7 hours per day in school, and learn next to nothing.  We wondered what they were doing with their time, when we parents can double or triple the speed of their development with around 3 hours per day of concentrated work (and no training), which is even possible with the kid still enrolled in school.  For example, as I've mentioned before, David was in 2nd grade when we started on Saxon (Saxon 54), and we got through 4 grade levels (through Saxon 87) in one year.  He did this while enrolled in school full time, traveling to visit relatives around the country, going skiing for a week, and doing some things that other kids do at that age (karate and piano).

So I'll list a few things, some I've likely mentioned before:
1) Summer Vacations (2 to 3 months to forget things)
2) Field Trips (lots of fun, but no educational value for young kids)
3) Substitute Teachers (understandably) unable to pick up the work
4) Non-Academic Subjects* - like art, music
5) Premature Academic Subjects* - like science and history
6) Watching Movies
7) Diversionary Curriculum*
8 ) Physical Education*

*see below for more info


Non-Academic subjects:  I think are just to tweak the kids to see if they have any talent in those areas.  At least that's the best that I can come up with.  Touching on these areas might be ok, but dedicating a large chunk of time means other subjects are missed.

Premature Academic Subjects:  These are academic topics that are not doing the kid any good at his age, and will be fully repeated later, as in high school.  There is nothing gained by these subjects in grade school and little gained in junior high.  In David's case, he didn't have Biology or Chemistry until he was in college (most people have them in high school), and did well enough in both - so if he had them earlier, even in high school, the additional benefit would have been marginal.

Diversionary Curriculum:  This is my term for teaching core subjects in a way that will not work effectively for most (maybe all) kids.  I call it "diversionary" because reading is still called reading and math is still called math, but they are taught in ways designed to fail (I would use weaker language - but the people at the top levels have had enough time to figure out that they simply don't work).  So, for reading, it is the use of Sight Words, instead of phonics, from Kindergarten through Third Grade.  For Math, it is "Discovery Math", sometimes called "Fuzzy Math", often with calculators, and never with memorizing of addition and times tables or long division.  So, in both cases, the parents are told that their kids are learning math and reading, so they typically walk away happy.  For the parents that did their own research and are on to this scam, they are told that the these new ways are "tested" and "proven" and the results won't be seen immediately, just "trust us".  That probably takes care of nearly all of those parents.  Of course your kids are only kids once, so it's too late when these parents realize what's really going on.

Physical Education:  It seems that we are constantly being told that kids need PE and without it they turn into fat, useless, blobs.  Well I don't think that's the case because exercising actually burns very few extra calories, compared to just sitting around doing nothing (for example, to burn off an extra McDouble, an average person has to walk 12 miles or run about 4 miles - that's a lot for a small sandwich), since but I'm not a nutritionist, so I won't go any further.  As to the kid really needing the exercise during school hours, I don't see it, providing that he's not simply going to his room and playing video games constantly after school or on weekends.  If he's doing that, then he'll need Army boot camp and other help - school PE just won't do anything for him.  So, for a kid that gets around a bit after school, and is otherwise normally-active (as it was understood prior to video games and facebook), he's probably getting all the exercise he needs.  This leads back to David and his physical development.  He was enrolled in his Christian school through what would have been 6th grade, based on his age.  During that time, he did have PE, and that was fine.  But once in college full time, starting at what would have been 7th grade (again based on age) he no longer had any PE or other organized exercise (Karate was long gone by then).  Did he get fat? - nope.  In fact, just before he turned 18, we went to Yosemite National Park and I pretty much challenged him to climb the Upper Yosemite Falls Trail.  It was considered an 8 of 10 as far as strenuous day hikes are rated, about 3,000 feet vertical and 7.5 miles round-trip.  We both made it.  My knees were feeling it at the end (having also descended that elevation).  But even though he violated every rule in the book for a kid, he still made it, and probably could have done quite a bit more.  So I think this PE push is bull.

To GeniusExperiment,

I don't know anything about the Jakow Trachtenberg system of speed math, so I could only find what you found.  Regarding the faith method, it's interesting that you mentioned it as stopping your progress, as it very nearly stopped mine too.  In my case, it was getting into complex analysis (for engineering, beyond Calculus).  You have to simply forget about understanding anything when you go into that world.  An example is Laplace Transforms.  You start with a differential equation from the real world that's understandable, then you do a Laplace Transform, do some algebra, and what you get makes absolutely no sense at all.  But then you do an Inverse Laplace Transform and enter the real world again and your answer makes sense.  So why do the Laplace Transform in the first place?  Because the problem is either very difficult to solve in the real world, or impossible to solve - but you go into a system that makes no sense, then come out of it, and you easily get the right answer.

"We told her that we wanted our son to learn how to spell, and we wanted him corrected in class. She stated she would not do that because it would damage his self-esteem."

First, sorry all for being such a slacker, I needed some time off...

Anyway, the above quote from Nee's posting (May 9) is very enlightening.  The word brainwashed is used a lot by critics of our education system and I try to stay clear of it.  But I'll use it here, but not in the usual way.  What this quote tells me is that the teacher is brainwashed into thinking that she is an absolute expert, above reproach, and that parents are a bunch of dimwits.  And that is true in the vast majority of cases, as this hapless parent found out.  It is futile to get into a discussion of methods or curriculum selection with them, they will simply tune you out and do whatever it takes to get you out the door.  As far as they're concerned, they have the degrees, the training, and the experience to teach properly.  Having read Thomas Sowell, I knew this was not the case from the beginning, which is why I only attended one parent-teacher conference during the 7 years or so that David was in his Christian schools, and only then because the teacher (a real basket case) demanded both parents show up.

The bottom line is that your kids' primary education (math and reading) has to be done under your control.  Public schools are not under parental control because their money comes from government, so that's who they answer to (and sometimes, as we learned in Texas with CSCOPE, that is may not even be the case).  Private schools are somewhat better because they know you can walk away, but the major issues with public schools rubs off on them to - and often due to other parents.  I may have mentioned it before, but my wife was a substitute at one of David's Christian schools.  Now I still remember from 40+ years ago how happy I was when I saw a "sub" because I knew it was a day off.  But not with Susan - she had the kids work in class, do homework, and was about to test them (she had the class for a week).  Then she got fired, because too many parents complained...

You really have to do it yourself, or do it through a learning center which doesn't claim to be a school in any way.

One more comment on the Russian woman that I know through work, who is using Saxon for her 2 kids.  I verified that it was 11 Russian families in her group that are now using Saxon.  She had told me earlier that when they saw the books, they knew it was exactly what they were looking for.  So yesterday I asked her if the books reminded her of Russian math books (she still has young relatives back in the old country that she helps tutor).  She said no, the Saxon books are much better.  She noted that the Russian books are still better than US textbooks (which isn't saying much), but she emphasized that Saxon was still better.  She also told me that the Saxon virus is now spreading to the Indian community, at least in one case that she's familiar with.  I'm surprised it took them so long to figure it out, as they were the closest people to being able to compete with David in spelling and math (and, I'm sure, still stunned that he cleaned their clocks).

I'm still waiting for the first American-born person to ask me about using Saxon (outside of this forum, of course)...

No, you're not a "mean mummy", at least if your experience winds up anything like mine.  While I talk about David screaming at me, the fact is, today, with what he knows now, he would kill to have me force him into those lessons, if he were starting over.  Your effort (and others here) will ALWAYS  be appreciated by your kids (at least when they're a bit older).  And by the way, David probably had dozens of lessons that I made him completely redo, due to laziness.

To Tamsyn,

I think there is now an optional Saxon Geometry Book, but no Trig book that I know of.

As it was, the original series didn't have either Geometry or Trig, but rather integrated them through their series of math books.  Saxon didn't like the idea of a kid completing Algebra 1 and then taking 15 months off before continuing on with Algebra (i.e., Algebra 2), so he built in the Geometry to the Algebra books.  Trig, I think, he just squeezed into the Algebra 2 and Advanced Math books.

Hi PokerDad,

David was so far ahead by the time he was at Math 87, I said what the heck, just do it.  As far as his anger towards the math world back then, it didn't matter which book he was using it was PURE TORTURE (to him) - that's how we both remember it.  As you note, Math 87 is basically optional in their series - if the kid is good in math, it's not really needed (per Saxon's advice).  I liked the idea of him having a chance to sharpen up his skills before advancing to Algebra, so I recommend it in all cases (unless there's a real time crunch in some way).

As far as Algebra 1/2, I said on Amazon that it is simply the best math book ever written, and I stand by it.  That book, more than any other, blew my mind away as to how it got kids ready for Algebra.  Saxon doesn't consider it option and neither do I, by a long shot.  When you get there, you'll see what I mean.

I only had the Homeschool Editions, so I'm not familiar with the Teacher's Editions.  Even the Homeschool books had at least some of the answers in the back, and being David is like me (in the bad ways), I too ripped out those pages, so he would have to do the real work.  But I only used the text book and the solutions manual, so I think you're good, based on the answers being removable.

As to Saxon Physics and Calculus, I did buy both, but didn't use either.  It was pointed out by someone that Saxon Physics is not calculus-based, which means it's not college-level Physics.  I checked my book and he's correct...no integral signs.  So the book is still probably good to learn on, but you'll need a more advanced book to cover college level (such as below).

Regarding other books.  One piece of advice I can think of is to use the ratings at Amazon starting at Calculus and College-level Physics.  Unlike the earlier grades, I don't think you'll have to deal with the bile of the public school establishment when it comes to judging those books, as they usually don't care about college-level kids on a science/engineering track (they have other ways to reach them).

For Calculus, he used:  Larson, Hostetler, Edwards, 5th Edition (50%)
For Physics, it was Serway and Jewett, 4th Edition (50%)*
For Linear Algebra, it was David C. Lay, 3rd Edition (50%)
For Partial Differential Equations, it was Richard Haberman, 4th Edition (15 to 20%)

The percentages after the books represent the approximate percentage of answers at the end of the book.  In the first 3 cases, they have answers to the odd-numbered problems.  In the last one (which is quite a way up there in the math world), it's only scattered answers...hopefully junior will be taking at least that class in college.  The Physics books also has a partial solutions manual that will help you work through around 20% of the problems (in addition to the odd-numbered answers) - I actually worked through the first half of that text book (for the fun of it) a year ago... challenging!!

Those are the books he used, and he liked them all - but we don't have any real basis for comparison, and we don't know how they'll be for a home school environment.  Also, you can try, but don't expect to have much luck getting your hands on solution books for college-level text books, as the publishers are pretty tight about distribution.  Finally, in case it's not obvious, there's no need to get later editions of any book - as you'll see the earlier editions can be picked up for next to nothing.

Sonya and Linzy,

Thanks for the help in answering the question and I agree with what you wrote.  You guys are much closer to Saxon than I am now.  And I agree, their word problems do build up in difficulty, but in a controlled manner so as not to leave the kid lost.

Manda,

We had our own "Saxon Wars" in our house, but of the opposite type, where it was one kid doing all he could to get away from doing math problems (LOL).  Unfortunately for him, his parents weren't particularly interested in him being happy while learning nothing (as opposed to being unhappy and learning math), so he lost those battles.  Yes, the number line approach worked very good, as he was otherwise lost.  It seems easy for us parents to think that kids should just be able to memorize 100 combinations of numbers (i.e., the addition table), but at that age and with no experience with numbers it's a total blur to them, or at least David, where he would simply guess at the answer, even if he saw the flash card 10 seconds ago...that's why many kids start out counting on their fingers.  The number line was similar, but, being on a marker board, I could wean him off it, which is what I did.  I have no clue how things would have went without it.

I kept David's work, but can't find it right now.  The only things that I remember giving him trouble were the time problems and the cube problems (where there's an arrangement of cubes next to each other, and then the outside of the arrangement gets painted, and you have to figure out how many cubes get painted on 1 side, 2 sides, or 3 sides - it's an ingenious problem, by the way - requires higher order thinking skills - LOL).  The clock problems were more my fault, because it took a bit to develop a method for them - and then he was fine.

I'm not sure what you mean by faith, but if you mean teaching math without any attempt at physical representation, then yes, it worked great for David.  I was surprised myself, or I wouldn't have wasted my time trying to teach him the concepts first.  But he did have something to fall back on, which was that he could count.  Once he could count, then he could do the arithmetic (addition and subtraction problems) on a number line, which he did at the beginning.  Then the number line (which was on a marker board) slowly got less detailed, as numbers were erased, so he had to interpolate between what was left, then there were no numbers, just tick lines, and then no number line at all.  So, he had to use the number line in his head, which worked (He struggled a bit, so I asked him what was wrong.  He told me the number line in his head didn't have any numbers, so I gave him permission to repopulate the numbers...then he was fine).  For whatever reason, times tables went much faster, and he picked them up right away.

I realize that it defies logic, but it did work for us.

I don't know if this is a good analogy, but this discussion somewhat reminds me of Laplace Transforms.  For those who aren't engineers or equivalent, Laplace Transforms is about the highest level of math reached when working towards an engineering degree, a couple of years beyond Calculus.  They are used to transform what would be a very complex problem (differential equation) into a problem one can manipulate with Algebra 1, by going into some weird world of math (then once you do the manipulation, you back out and go back into the real world again).  I kept struggling with them because I tried to understand the physical meaning of what they represented (after transforming).  Finally, I gave up and just decided to do the math in the blind and see if I could solve the problems...and that actually did work, so I was finally able to do those problems.  In other words, it wasn't until I jettisoned my attempt at applying "higher order thinking skills" that I was able to do the problems.