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Joined: Nov 2007
Posts: 864
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Wow, Dave, this is so helpful. I haven't been reading the posts in the last few days, except for here and there. I have to go back and reread this entire thread.
It's funny, but I've been thinking that what I won't know how to do is the silly fun stuff. For example, this weekend, DS's assignment is to make a leprachaun trap and to bring it into school on Monday. It's all he can think about and talk about. If we go forward with the HS, I have to remember things like that. Or maybe that's what I have a babysitter do?
I'm also curious to check out the Life of Fred books. We just got the Penrose the math cat book and DS is begging to start it. He also likes the math trek, Sir Cumference and G is for Googol books. I said to the psychologist last year that he learns best when he doesn't know he's learning at all.
I also was interested in your comment about textbooks. I pulled a chemistry off the shelf in the library yesterday out of curiosity and thought to myself, this looks boring, DS is not ready for this. It certainly would be nice to avoid them for as long as possible if they're truly not necessary.
Thanks again for your input. Later this weekend, I'll read through all these posts. I have to say that when I first stumbled on this site, I thought HS was out there. No more. And frankly, I think it sounds like fun.




Joined: Sep 2007
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Thanks for your thoughts and advice Dave! Lovely post. I also have a level of discomfort using the word "gifted", but unfortunately that's the only way to get any kind of services at all is to be tagged with this label. In our 1st grade classroom this year, I am seeing all kinds of kids at all ends of the spectrum not being served well, and it is sad. I also think all children have great potential if nurtured properly. "IQ" is only one piece of the puzzle.
Your children sound incredibly lucky to have you as a homeschooling parent! Hope you continue to jump in and offer your thoughts when you can.




PhysicistDave
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Lorel,
You wrote of the �Life of Fred� math books: >the stories are so enticing that my kids tend to read ahead and do not always do the math along with them.
Yeah, that certainly happens! I don�t really think it is a problem unless the kids simply refuse to ever do the problems when they reach the level at which they really can handle them.
Of course, it is not possible to really learn math without doing a lot of problems (or, at higher levels, proving a lot of theorems). But math is not fundamentally about doing problems � it is ultimately about understanding concepts. Simply reading through the silly stories in the �Fred� books will help the kids get the concepts, so that, when they are ready to do the problems, they will be better prepared.
Again, I am not offering any excuses for simply avoiding problems � you have to do problems, and, ultimately, you�ve got to learn how to get the right answer and be secure knowing that you can get the right answer and why it is the right answer. But reading serious books about math (and the �Fred� books are serious despite the silliness) can be as important as actually doing problems: the two things are not mutually exclusive.
There is a wonderful book long out of print but still available through abebooks.com etc.(and nowadays through publiclibrary interlibrary loan services � though I recommend buying a copy) that illustrates my point, Irving Adler�s �Giant Golden Book of Mathematics.� It has no problems at all, but does a fantastic job of getting kids to think about math up through calculus, infinite series, etc. It�s at a middleschool reading level and only requires knowledge of gradeschool arithmetic (i.e., no knowledge of algebra required at all). A friend of our family gave me a copy when I was nine or so and I devored it � it was quite easy for me to read. And yet, I only fully understood all the implications of the book after I got my Ph.D. � for example, Adler remarks on an interesting formula for pi, which you can easily check by hand or with a calculator, but I finally learned where that formula comes from only as an adult.
So, the Adler book has an �openendedness� to it that allows a kid to get the basic ideas but keep coming back and thinking more about things, wondering if he has really seen the whole picture. That�s what real math (and real science and, for that matter, real history, literautre, music, etc.) is all about, but it is something that most textbooks simply ignore.
Let me emphasize again that I am not excusing the sort of �fuzzy math� that makes excuses for kids� never learning to get the right answer. The mantra should be �right answers through conceptual understanding�: neither right answers without understanding nor understanding without right answers is acceptable.
(Liping Ma has a wonderful book making just this point, �Knowing and Teaching Elementary Mathematics,� that every parent interested in their child�s education ought to read.)
Lorel also asked: >the books have relatively few problems and I wonder if that is "enough" to cover a subject.
Probably not, though I think it depends on the child. I myself needed a lot of drill on the arithmetic tables and arithmetic algorithms (this is at a lower level than the Fred books of course), but, starting with uppergrade school math, I grasped the algorithms with a very small amount of pracitce.
Stan has a system with the regular problems versus his �bridges� (test problems) that I would generally advise following. We�re now in his �Fractions� book, and, since the kids have already done that level in �Singapore Math,� I�m letting them skimp a bit on the �Fred� problems. Once we get to the �Fred� algebra books, I expect to follow Stan�s recommended system.
The nice thing about homeschooling is that, since I interact closely with the kids, I�lll know if they are really getting the stuff. I expect that I may have to pick up some other algebra books for some extra problems, but we�ll see. Of course, they will be doing arithmetic and algebra anyway in physics, chemistry, etc. and that too will provide some additional practice.
Sorry for writing a treatise in response to your brief questions, but I�m rather passionate about kids� learning math the right way! Math is quite fascinating once you understand that solving problems is only the tip of the iceberg (a very important tip, to be sure), but most children (and adults) never have the opprotunity to learn what math is really about at all.
All the best,
Dave




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questions wrote of her son:
>I said to the psychologist last year that he learns best when he doesn't know he's learning at all.
Yeah, don�t we all?
Most adults I know have some hobby � cooking, gardening, etc � that they know a huge amount about but not as a result of taking formal classes for a grade. Humans are designed to learn � we can�t run fast like a cheetah, fly like an eagle, etc. � but, boy, can we learn.
Let me make clear that I am not making excuses for not ultimately achieving adequate mastery in important subjects. But no one can achieve complete mastery of a significant subject in just a year. The idea that someone �knows� calculus or physics or US history because he �had� the subject in school is simply foolish: what he �had� was a very brief overview of a very deep subject. Specifically, I have never met a human being who really �got� calculus on the first exposure � and I have known some people who were among the most gifted in my generation in math (for example, I went to college with a kid who started graduate school in math in his midteens).
So, people who think that diligently working through one textbook gives mastery of a subject (especially given how horrible most American publicschool textbooks are) are just fooling themselves. Better, for example, to casually read a halfdozen good, serious books about biology and slowly start to pick up and master the concepts than to diligently try to memorize one single mediocre biology textbook.
After all, no great cook simply memorized one cooking textbook! She perused and borrowed from a variety of cookbooks, and then, of course, started doing her own thing.
You also wrote: >It's funny, but I've been thinking that what I won't know how to do is the silly fun stuff. For example, this weekend, DS's assignment is to make a leprachaun trap and to bring it into school on Monday. It's all he can think about and talk about. If we go forward with the HS, I have to remember things like that. Or maybe that's what I have a babysitter do?
Well, I suppose �arts and crafts� is my own weakest spot. By and large, I didn�t much like them as a kid (except for perspective drawing � but then that�s really math). I was sort of nervous about that when we started homeschooling. But my experience has been that it more or less takes care of itself. Let kids have access to crayons, pencils, paper, scissors, and tape and they make stuff (we seem to end up buying a lot of tape for some reason!). One of my daughters seems to have some real talent for drawing, which I certainly did not teach her (although we have made books available that explain how to draw).
Also, this is the sort of thing that your local public library has weekly sessions for and that most homeschooling moms are very good at, so it�s not too hard to seek out group activities for arts and crafts. We did that initially, but now I pretty much just let the kids do it on their own. Of course, I can�t teach the kids, for example, how to do wall frescoes, but unless someone is serious about pursuing art as a career, I doubt that is really central to one�s education.
Remember, too, that almost all homeschoolers do rely on outside sources for some subjects. I�m a marginally competent swimmer, so we paid for the kids to take swimming lessons. Obviously, I cannot teach ballet, and, though my wife plays piano, she did not feel competent to teach it. So, our girls take dance and piano lessons outside the home. That sort of thing also provides some of the allimportant �socialization.� We were worried about �socialization,� too, but we�ve found out what we should have known all along: humans are naturally social beings, and kids will make friends with other kids easily and rapidly. They do not need to be with other kids thirtyforty hours a week to make friends.
I hope I�m not sounding as if I�m poohpoohing anyone�s concerns and nervousness about homeschooling. I�m still nervous about it after four years of doing it, to tell the truth � I�m always trying to think about what we�re missing. However, it does seem in the end to take care of itself, if the parent is diligent about supervising the kids� learning and, most importantly, about making learning resources available to the kids � above all, books, which thanks to public libraries and modern Internet interlibrary loans, simply requires a parent to seek out good books via the Net and through information from other parents and kids.
My own education is in physics, not teaching, after all. But we underrate ourselves if we think we do not know how to help our own kids learn. Human parents have been teaching their own children for tens of thousands of years. Our ability to do this is tied in to the basic and extraordinary human ability to learn. It ends up being easier, and more fun, than it might seem.
One caveat: it does require a parent who is willing to continue learning on his or her own. I�m currently teaching my kids Chinese; however, I don�t know Chinese � my wife is fluent in speaking Mandarin (she�s the daughter of Chinese immigrants), but I only knew a few dozen words before starting to teach the kids. So, I�m �teaching� by learning along with them (actually, they�re a bit ahead of me and I�m frantically trying to move fast enough that I can continue to supervise their work). I�m having fun with this, but I suppose there are people who would hate this situation and could not tolerate their kids� being ahead of them.
I don�t think this is a problem for anyone on this forum, but I suppose that people who really hate the idea of learning themselves probably should not be homeschooling parents. I�m pretty sure you yourself would have fun homeschooling (but, yeah, there will be some nervousness and anxiety, now and then!).
All the best,
Dave




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kimck,
Yeah, I can see how one has to use the label �gifted� in dealing with the publicschool bureaucracy. We ourselves are homeschooling through a public charter school which sends a teacher out once a month to check on us, so I do see a tiny bit of that bureaucracy myself. Thankfully, our charter school is known for being very unbureaucratic, and our teacher was actually homeschooled herself, so we do not have to deal with very much bureaucratic nonsense.
Incidentally, I�m not trying to make any sort of �politically correct� objection to the term �gifted�: obviously, some human beings do have greater innate talents in some areas than others. For example, I took a couple of years of trumpet as a kid, and I have absolutely no doubt that Wynton Marsalis in innately more gifted at the trumpet than I am!
And, I certainly do not see any reason why anyone whose kids are way above average intellectually should hide that fact anymore than parents whose kids are �gifted� athletically or musically should hide the fact.
I do think, though, that the unfortunate antiintellectual bias in our country is a problem not only for parents of intellectually �gifted� children but for all parents who care about their kids developing to their potential. Even �normal� sixyearolds, as far as I can see, would rather learn about knights and castles or Egyptian mummies than learn the firemanismyfriend pabulum that passes for �social studies� in so many public schools. No doubt �gifted� kids are indeed much smarter than most people realize. But I think that even intellectually mediocre kids are much smarter than most people realize. As the clich�, says, a mind is indeed a terrible think to waste, and I fear we are wasting many millions of young minds, and not just the �gifted� ones.
All the best,
Dave




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questions,
Thanks for the link � I had not seen the article.
I generally agree with the points mentioned in the Times� article. In fact, many of the quotes from the panel�s report sound as if they could almost have been lifted from the book I mentioned above, Liping Ma's �Knowing and Teaching Elementary Mathematics." Specifically, Dr. Ma mentioned the point about fractions, and she has some very concrete and very useful suggestions for how to teach division of fractions, which is the sticking point for so many children (and teachers).
My one reservation is that I fear that the panel�s recommendations, as quoted in the Times, solid as they are, will be twisted and misused by the time they work their way into the nation�s elementary classrooms.
For example, the Times says: > The report tries to put to rest the long, heated debate over math teaching methods. Parents and teachers have fought passionately in school districts around the country over the relative merits of traditional, or teacherdirected, instruction, in which students are told how to do problems and then drilled on them, versus reform or childcentered instruction, emphasizing student exploration and conceptual understanding. It said both methods had a role.
Indeed. The problem, though, is that some of the �childcentered� (AKA �constructivist�) programs out there have avoided making sure that students master the traditional algorithms in favor of letting the kids develop their own algorithms.
That is not a good idea.
The traditional algorithms have been worked out over centuries by some very bright people. Those algorithms always work, and they are fairly easy to understand and very efficient for paperandpencil calculation.
I�m good enough at math that, when I am doing math in my head, I often invent a new algorithm on the fly. But I already know the traditional algorithms. To encourage kids who do not already know the traditional algorithms to do this is unwise. Also, the traditional algorithms transfer nicely into more advanced math: for example, �synthetic division� of polynomials is basically a generalization of the traditional longdivision algorithm learned in gradeschool arithmetic. If you do not understand the traditional longdivision algorithm, you are going to have trouble understanding synthetic division.
I�m also concerned about the point that: > The report, adopted unanimously by the panel on Thursday and presented to Education Secretary Margaret Spellings, said that prekindergartentoeighthgrade math curriculums should be streamlined and put focused attention on skills like the handling of whole numbers and fractions and certain aspects of geometry and measurement.
There has indeed been a lot of silly topics in the �fuzzy math� curricula that should just be abandoned, and, yes, the first priority in gradeschool math has to be mastery of whole numbers and fractions (the latter including decimals and percents).
But, especially for bright kids, there can also be exposure to real ideas in math that give a sense of what real math is about beyond gradeschool arithmetic � everything from prime numbers to a peek at what has been done with infinity. Infinity, incidentally, was central to twentiethcentury mathematics: as a physicist, I routinely work in infinitedimensional spaces (socalled �Hilbert space�), but I doubt that very many adults, aside from mathematicians or physicists, even know that infinity is not a vague philosophical idea but an integral part of modern mathematics.
So, I�m a bit afraid that, if the panel�s recommendations are followed, the best we can hope for is a return to the way our parents were taught math. That would be a real improvement on what now prevails in many grade schools. But it�s not optimal, especially for the brighter children.
On the other hand, the report�s points about committing elementary facts to longterm memory so that you can focus on higherlevel activities, about intellectual achievement being based on extensive knowledge of facts, and about mastering math being a result not simply of talent but primarily of hard work are, in my experience, quite true, and, as the Times suggests, are now backed up by a good deal of research in cognitive science (and, of course, common sense).
All the best,
Dave




Joined: Dec 2007
Posts: 902
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Welcome to the board, Dave.
Thank you so much for all the insight. I will have to go back and check some of the books you have mentioned.
I too like Fred's books. They are funny, easy to read and very engaging. It's a new and different way of teaching math. My son really liked it, but we haven't touched in a while. I am not sure the books provide enough exercises though. DS5 picks up new concepts very quickly, but I don't think I would use it as the only source. Dh and I are both math geeks and we are getting to the point when we really want the right person to teach DS math. Definitely a big reason to hs.
LMom




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LMom,
You say you and your spouse are math geeks. Can you define �math geeks�?
Okay, putting it that way probably proves that I am a math geek! But, seriously, are you both folks who really like math, are you both in technical fields, were you both math majors or what?
I�m curious because I�m always trying to figure out how to teach math better to our kids, who are middlegrade school by age, uppergrade school by math grade level (tests show them as five years beyond grade level, though from my own experience I think they are not quite that far ahead � I�d peg them as three years beyond grade level).
I learned a lot of math, not thoroughly but at a beginning level, years before I was �supposed� to, largely by random sampling. For example, I learned the basic ideas of Galois field theory (not all the theorems, but enough to do some calculations) from some book (I�ve forgotten which) in high school just for fun. This turned out to be a good thing, because, after I finished my Ph.D. and was out in the real world, I serendipitously was talking with a coworker and found that he was working on a project using Galois field theory for satellite communication systems. I ended up being copatentholder on several patents using GFT for satellite and computer harddisk applications.
So, I�m trying to replicate my experience with our kids. As I�ve said above, while mastering the standard algorithms is of course an absolute must, I�m really keen on trying to convey the idea that math is more than that � it�s basically a set of beautiful concepts and a way of thinking about the world.
That�s hard to convey.
The nice thing about the Fred books, of course, is that they have a �young� feel to them but that they do real math, so that a child whose math ability is well beyond his chronological age but who is not quite ready for the formality of higherlevel books can learn a lot from them.
I assume your son is very accelerated in reading if he can read the Fred books. As you know, the beginning one starts with fractions. Is your son accelerated enough in math that he can handle that mathematically? My kids are several years older than yours and are finding some of the problems somewhat challenging.
On the issue of supplementing �Fred� with additional problems, I�m philosophically opposed in general to relying on one book to teach a subject and then just relaxing. I think the parent always needs to ask himself or herself if the kid really �gets� it or if using other books would help for different perspectives, additional problems, etc. Usually, I think, the answer is �Yes � other books would help.� We�re doing that even for Chinese � instead of just going through one introductory curriculum until we have it memorized, we�re jumping from one to another (this turns out to be a good thing, among other reasons, because all of the introductory series have some real lacunae in their vocabulary).
Anyway, I�m curious to know where you and your spouse are coming from mathwise and if you have any thoughts on how to replicate my own personal experience with learning some �advanced� math before one is �supposed to.� I�m hoping to do it in a little less random way than happened to me personally, but without simply trying to push kids to plow through collegelevel math books. Math can be so beautiful, but it is usually taught in such an ugly way!
All the best,
Dave




Joined: Sep 2007
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I totally agree LMom. DH and I are both mathy too. We are a bit disturbed at the basic Everyday Math curriculum and the fact that at least our 1st grade teacher seems to hate and avoid math. I'm sure that is a common theme among elementary education teachers. But I do think it's important, especially for mathy kids (and better yet, all kids) to get exposed to math from someone who actually "gets" math and enjoys it. My son and I are having a lot of fun playing with Singapore math just 15 minutes or so a day. I can imagine how we'll fly once we're actually homeschooling and have an hour or more to commit to it.
We will have to check those books out! Thanks for the recommendation.




