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Dave, We only did the Fred Fraction. We read the book together and we did help him with some of the calculations. For example he could figure out how to calculate the number of reasons for a new bike in a year, but he couldn't do the calculation himself. He could tell me what to multiply, but it was me doing the multiplication (he can do it on his own now but not back in fall).

I know that according to the author the long division is a requirement for this book and DS5 couldn't do it then (he just learned it with 1 digit divisor last week), but I cared about the concept. He eventually lost the interest and we didn't finish reading the book. Do I think he is ready for the book? Yes, I do.

He is in Montessori right now and even though they were usually a few steps behind what he could do home, he got a good practice there. I must admit that he got lots of good practice there. We are all for explaining new concepts and bringing new ideas, but not that good when it comes to practicing. I guess new things and new problems is where the fun and excitement is. We will homeschool next year and we will have to change our attitude a little bit

As for math geeks. In my books anybody with PhD in theoretical physics must be one As for us think gifted math & science schools, a prestigious math university (neither one of us did BS or MS in US, DH got PhD in US), advanced degrees in math related fields. You know people who think that evening spent trying to solve a problem from IMO is a well spent evening PM for you with more info.

I don't know how to make them love math. I hope they will and I hope they will find it fascinating. I am not really sure how one gets there. We kind of hope that it will sort of happen. Judging by my DH's family, it is possible. You are years ahead of us and you have much more insight. Have you tried any of the logic puzzle books by Raymond Smullyan? I use to love them back in middle school. I think they show the beauty of math and logic.

We usually talk about math during dinner time and not much beyond that. We do bring up new thinks and even sort of out of the order (probably not a good idea), sometimes he can do it, sometimes it's just too much. It's fun to test what he is ready for. I am all for learning math on their own level. Forget the age, they can and should learn whatever they are ready for.

I hear you on more than one resource. How does one manage that? I fully understand where you are coming from, but I can see myself overdoing it and trying to do way too much, like reading about the same things from more books and perhaps creating double the work just because each book is slightly different.

Kimck, exactly. I would like a teacher which cares about math. A teacher who makes him figure it out instead of giving him the solution. Somebody who understands why the algorithm works not only that it works.

LMom,

It sounds as if you and your spouse may have me at least tied as math geeks � and I do in fact mean that as a compliment.

You wrote:
>You are years ahead of us and you have much more insight.

Well� my kids are a bit older than yours, and we�ve been homeschooling longer, so I�ve had more time to make mistakes! As to how much insight I�ve gained from those mistakes�

You wrote:
>I hear you on more than one resource. How does one manage that? I fully understand where you are coming from, but I can see myself overdoing it and trying to do way too much�

Well, the short answer is that I think the approach you are taking so far with the �Fred� books is basically the right approach. My attitude is that I am entitled to ruthlessly �strip-mine� workbooks and textbooks: i.e., use whatever I think serves my kids� best interests whenever and however we think is appropriate and ignore anything that we find does not serve our purposes.

I think the central principle is to have your kid do as much work as he needs to do in order to master something� and no more. The goal is understanding and mastery, not work for the sake of work.

The workbooks/textbooks exist for us � we are not servants of the books.

Parents, especially when we�re homeschooling, should be able to figure out what the kid knows � if he needs more problems from another book in order to master the stuff, have him do them. If not, don�t.

I�m having our kids do almost all the problems in Singapore Math because SP is not known for busywork problems and the kids seem to find them challenging. Since Fred Fractions repeats much of what we did in SP, I�m more lax there; we�ll probably be more thorough on Fred Algebra.

Reading through Fred Fractions with your kid as you did and working with him on problems makes good sense even if it is not exactly the procedure the author had in mind.

My kids are just getting to the age when I myself was reading good kids� books about math (such as Adler�s �Giant Golden Book of Mathematics� that I mentioned earlier), and I have not quite figured out how to get them to read them as I did � should I assign reading, just make the books available or what?

I do think one of the most important things is to try to talk with the kids about math, including stuff that you know may be over their heads, and see what happens. I talked with them while they were still learning simple arithmetic about the sum of the angles of a triangle being 180 and how this only occurred in flat space and was connected to the existence of a unique parallel. We looked at triangles on a sphere and they could easily see that it does not work on a sphere. I�m doubtful that they really grasped the connection to the existence of a unique parallel (although I certainly understand it better now after trying to explain it to them!).

When we learned the commutative laws for arithmetic in first grade, I pointed out how rotations did not always commute so that commutative laws don�t hold for everything. This is very easy to show with a couple of identical cracker boxes: rotate one 90 degrees around the vertical axis and then 90 degrees around a horizontal axis. Do the same operations in reverse with the second box. The non-commutativity is obvious. The kids still remember this from a couple years ago.

I�ve talked with them about simple ideas having to do with vectors, which they do seem to get. I�ve also had them do simple calculations with a rotation matrix: this is easy to do once you know the basics of fractions. It gave them some practice with fractions and with graph paper, though of course they still do not really understand matrices.

Similarly, we�ve talked about infinity � they understand some of it, but not all of it. Kids do seem interested in the idea of infinity, though.

You know of E. D. Hirsch�s espousal of developmentally *inappropriate* teaching? Hirsch argues that instead of spoon-feeding them each tiny next logical step, kids deserve to hear about the stuff that is actually interesting. Black holes and supernovae are more interesting than pulleys and levers (we�ve read and talked about all of those) and infinity is more interesting than dividing fractions (we�ve worked more seriously on fractions, but we have discussed infinity).

It would of course be unfair to test even profoundly gifted grade-school kids on the mathematical theory of black holes or on Cantor�s theory of transfinite numbers, whereas, it�s fair to expect them to prove some knowledge about levers and about dividing fractions. But that does not mean you can�t talk about stuff that you expect they will be interested in, even though you know they will not fully grasp it.

After all, as adults, we would be really irritated if the news media only told us about things that we were expected to internalize so fully that we could later pass a test on it!

Anyway, it sounds as if you are taking a similar approach to what I am advocating and trying to do myself. I think the important point is to not be afraid of trying out stuff even though it may turn out to be beyond your kid�s understanding (or your ability to explain). Try it out and see what happens. That, after all, is what we adults do with each other. If the child ends up not understanding, well, he will have a shot again when he is a little older.

I hope it�s clear that I�m not advocating in any way skimping on the core material that really must be mastered in grade school � the four arithmetic operations for whole numbers and for the various sorts of fractions and some basic ideas of measurement. But the nice thing about dealing with bright kids is that you can cover that more rapidly than the public schools do, and still have some fun exploring other things.

Sorry for having written a treatise rather than a reply again, but I hope this clarifies what I�ve been trying to do with our kids in math.

All the best,

Dave

I like your attitude. That's a very good advice. I hope I can follow it. I'll at least try. I can see myself making him do more than needed in subjects which are not my favorite. I think I could manage to do it with math, but LA could be a very different story.


I would just make the book available and see if they like it. Or make it an option "Today you can work from Fred's book or this one." or find corresponding chapters for whatever you are doing.

Funny thing, since you mentioned the book for the 2nd time, I decided that I really have to check it out. As a matter of fact we have one of Adler's books at home! It belongs to a friend of us who thought it may be a good reading for our son. I briefly checked and decided that it would be too much for DS. DH looked quite excited when he saw the book. He had exactly the same one when he was a kid and loved it. The book we have is translated, the English original is called Learning with Colour Mathematics. I am not sure how it compares to the one you mentioned. I need to have a better look at it.


This is really interesting. It makes sense they should get the feel for all the exciting things not only those they can really understand. The bigger picture is always more interesting.



It's quite clear and it makes complete sense. It's quite eye opening to have it explained like this.

Thanks

I wholeheartedly agree with this! This is what I try to do in the weekly mathlabs I do in my kids' classes at school. It really gets them fired up about math. I have a bunch of first and third graders following me around the playground, begging me to come do a mathlab

Here's an analogy I like to use when I'm selling my ideas to the teacher: Yes, kids need to learn arithmetic but just teaching them arithmetic without showing them anything else would be like only teaching kids spelling and never reading them a story.

Cathy

LMom,

You wrote:
>I can see myself making him do more than needed in subjects which are not my favorite. I think I could manage to do it with math, but LA could be a very different story.

Language Arts is not my strongest subject either (I was a good student in school in it, but it�s not the area I really am master of). Our kids score well above grade level in language arts, but not as high as they do in reading or math � I�m not sure if that is a sign of their relative innate abilities or a sign that I am doing a better job teaching reading and math.

My own theory is that the core of Language Arts is being successful at communication, both sending and receiving, and, that, the best way to do that is to practice � i.e., to read a lot and write a lot (I guess, to speak a lot too, but humans naturally do that!). We normally go to the public library once every week or two and the kids have been writing little stories from early on. We read our science and history books out loud together, with one of the kids reading and my helping with meaning or pronunciation of difficult words, with complicated concepts, etc.

We avoided LA workbooks completely for several years. (We did have handwriting workbooks, since my handwriting has always been horrible and it seemed best for the kids not to imitate me.) We have recently started on the �Editor-in-Chief� series of workbooks which has the kids finding errors in various written passages � the kids like these a lot and the workbooks seem less mindlessly repetitive than the LA workbooks I had in school. We�ve also just started on the McCall-Crabbs 3-minute reading comprehension exercises, which, I hope, will help advance their reading comprehension (although they do already score very high on that).

The kids have also been doing some work in a series �Hey, Andrew! Teach Me Some Greek!� designed to teach elementary-age kids some real classical Greek. I have not made that a very high priority, but I hope it will help with vocabulary roots. W may try some similar Latin stuff (there�s a Latin series from the same people), since Latin roots seem to be everywhere.

We have not really done any formal spelling at all, but the kids seem to be pretty good spellers. I have taught them the parts of speech, and we will eventually do some sentence diagramming, which I and my friends liked as kids.

Anyway, we�re taking a somewhat laissez-faire attitude to LA, but it seems to be working okay.

You also wrote:
>I would just make the book available and see if they like it. Or make it an option "Today you can work from Fred's book or this one." or find corresponding chapters for whatever you are doing.

Thanks for the suggestion � I think I�ll do that.

My brother, whose kids are older than ours, actually told me some years ago to always give kids choices rather than commands: just frame the choices so it works out fine either way -- kind of sneaky, but it does seem to work. And, in fact, I do usually try to take the tack of �Would you like to practice piano or do math now?� if I can (of course, they often both want to practice piano at the same time, which is not possible), and the kids have some input into the books we choose to study for science and history.

I think you may actually have a translation of the math book I am talking about � I�ll PM you with details so we can find out.

Incidentally, I probably sound a lot more sure of myself on all this than I really am. We just discovered the Fred books last summer and decided to move into them. And, I�ve gotten some writing/composition workbooks through the charter school that I have not yet quite figured out how to use. So, I�m definitely learning by doing! But the kids do seem to be moving forward rapidly and seem to be reasonably happy. The one thing I am pretty sure of is that kids should not be denied learning about interesting stuff just because it�s not �normal� for kids their age or �developmentally appropriate� to learn it.

All the best,

Dave

I love that! I so believe this to be true!
But whenever I say anthing like that I am being fumed over!

I happened to hear Frank Deford this am on NPR, saying much the same thing at the end of his piece: http://www.npr.org/templates/story/story.php?storyId=88519364

Ania,

Yeah, and in fact I really don't want to disrespect the effort and dedication that the top-flight athletes exhibit.

Perseverance and dedication are, after all, virtues, and I think it is appropriate to admire people like Tiger Woods or Michelle Kwan.

The problem is the failure to similarly honor intellectual ability and achievement. I�m not sure why this is. Is it that we all think we could be Michael Jordan, or Tiger, or Michelle since they make it look so easy? Of course, we obviously can�t, but since we can at least (sort of) understand what they are doing, perhaps they are not a threat to that all-American egalitarian belief that we are really all the same.

Since most people cannot even understand what Ed Witten or Andrew Wiles or Stephen Hawking has achieved (I have trouble understanding Witten�s work myself � and he and I are in the same field!), is this kind of top-level intellectual achievement a threat to most people because it reminds us that we really are nothing like equal to those guys?

Are even the achievements of gifted children a threat to most adults because they could not have matched those achievements as kids themselves?

What I think is especially insidious about all this is that, as beautiful as her skating undoubtedly is, Michelle Kwan will not find a cure for cancer or find a long-term sustainable source of energy. Those things, which we really need, will be found by someone who excels intellectually. Furthermore, Michelle will not be weaving her magic or advancing the art of skating when she is in her sixites (although she will no doubt continue to contribute behind the scenes). Yet, Steve Hawking is well into his �60s and still contributing, despite his debilitating disease (I had a chance to meet Hawking when I was a student back in the �70s � at the time, we were assured he�d be dead in a decade from his ALS).

Since few kids will ever be Tiger or Michelle, surely an emphasis on intellectual achievement will tend to serve them better throughout their entire life.

questions,

Interesting article by deFord. He does make me wonder if this �spectator society� (think �reality TV�) has made public adulation (or at least attention) the only thing considered to be of real value. I think that Dick Button, and perhaps even Peggy Fleming, skated primarily out of a love for the intrinsic beauty of the sport. DeFord seems to think this sense has been lost. What a shame. After all, the real point of the sport, both for spectators and participants, was once grace and beauty, not just triple Axels.

All the best,

Dave

Homeschooling my PG kid makes it possible for me to frame things so that his prodigious skills are not the essence of who he is. Don't misunderstand me; his intellectual abilities are very important. But they are an interesting footnote when compared to his person, his character.

The most important thing to me is not that he is ready for calculus by age 10 (although that will probably happen), but that he develops into a person who is curious, kind, and brave.

In school, he would be defined by his unique academic achievements. That would be the label attached to him. As a homeschooler, he is not known among his friends ONLY as an incredibly smart boy. He is known as compassionate, creative, and a very loyal friend. I am so glad that he is growing up with these identifiers bearing just as much weight as the PG label. I greatly appreciate the freedoms that homeschooling offers us in that context.

Best,
Tara

Tara,

That's a very interesting point. I'm curious if you (or anyone else) can elaborate further.

Incidentally my value priorities for my kids are:
1. Ethical and decent human beings
2. Health
3. Able to function adequately in society
4. Academic development
5. Extra-curricular stuff

I really think point 3 largely takes care of itself in the course of normal life (there is stuff like driver�s ed, of course), and all normal parents attend to point 2, so I do tend to focus more on points 1 and 4. It is funny that most people would actually describe me as someone singularly focused on academics, when that is actually not my top priority.

I haven�t listed �happiness� as a goal, because I doubt you can really successfully pursue happiness as such. I suspect that you can try to lead a decent and worthwhile life, and, with a little bit of luck, a nice bonus will be happiness.

I mentioned on one of these threads how one of my kids really annoyed her cousin by telling the cousin that the cousin could not play piano because the cousin was not homeschooled. This of course was not only rude but false -- it was just a matter of which child happened to be taking piano lessons. (Incidentally, I know the cousin very well, and she is in fact extremely bright, quite possibly brighter than my kids. My kid�s not entitled to look down her nose in any way at all towards her cousin.)

However, the kids of most of the people on this board really will end up being greater achievers academically, in an objective sense, than most of their acquaintances, and all of us as parents, as shown by our participation here, put a pretty high value on academic achievement. The kids are inevitably going to pick up on this.

So, since we really do think it is good to be high achievers intellectually, how do we get our kids to understand the distinction between better academically and being better as a human being? Indeed, how do we get them to understand that you can and should rank human beings on particular skills (ice-skating, trumpet-playing, etc.), but, except in terms of basic moral behavior, it is generally wrong to rank human beings as human beings?

I hope my kids learned all of this a bit from the piano-insult incident: we had some long and detailed discussions after that, and my child did choose, without any suggestion from us, to later apologize to her cousin.

I also agree with you about being labeled as �smart and nothing else.� I really did feel that way as a child. I�ve mentioned somewhere that a classmate towards the end of my senior year casually said to me, �You know, Dave, you�re actually okay.� Clearly, she had heard I was a nerd (well, I was!); fortunately, we had gotten to know each other well enough that she came to see me not just as a nerd but as an ordinary guy.

By high school, I was mature enough to grin at this sort of thing, but as a younger child it did bother me.

Can you elaborate on how this works in your local homeschooling group? I know of some kids in ours who are clearly gifted, but the general ethos in the group tends to push them to hide the fact. Again, I�m not sure how to create a situation where everyone can say �Hey, I�m great at basketball, you�re great at calculus, and Emily can really make that trumpet sing!� and everyone can feel that this is wonderful.

Maybe it is an impossible dream.

All the best,

Dave