Myrtle
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Posts posted by Myrtle
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I was thinking of just doing 4B and 5B to get in as much physical science as I can. Would that work well do you think? And is the activity guide like an teachers manual for the activity book? Thats my guess from the sample pages online. Thank you for all your help so far!
The activity guide tells you what supplies you need to get together for each activity. It was the most unused item that I had since I could figure out from the activity book what items I'd need. One supplement that I did use in the 6th grade but didn't for the earlier grades is "More Notes: Teacher's Handbook." It fleshes out the information in the textbook for the teacher by giving more details and sometimes historical context of the scientific principles. I'm pretty sure someone with a degree in science would not need this. Eventually my son just started reading the the handbook for himself. :tongue_smilie:
I think you will be pleased with the lessons on physical science in this series.
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A month or two ago I ordered a copy of Serge Lang's "Basic Mathematics."
Serge Lang was a member of the Bourbaki (Wiki entry on Lang) and went on to write this book on "everything you should have learned in high school about math." He says in so many words in the preface, but much more diplomatically than I'm paraphrasing, that students are showing up to college incompetent and that this book should be used to brush up on whatever it is that you might have missed out on.
I finally got around to looking at it again, because at the time I ordered it I was wondering how good of a high school text it would make, (not very good since there aren't enough problems in it for the average student.) However, I started thinking that since a lot of folks might be rusty in some topics that this might be a good book for mom to brush up on quadratics or polar coordinates or whatever. The problem I had when relearning forgotten math, the first time I did this a couple of years ago, was that I didn't want or even need to really, rework a billion problems in a book, and so abbreviated problem sets might actually be useful in cases such as mine.
But the really neat thing about this book is that it has a ton of proofs in it. Serge Lang proves everything. And so, at any rate, if you aren't inclined to track down out of print Dolciani's, this book is still in print and has all those proofs in it. Because I'm sure that deep inside the burning question of "Why is the multiplicative inverse unique?" has been keeping someone up late at night and this it, baby, the lofty weight of this existential angst will be lifted from your mind as you explore its contents.
It is expensive though, at $50 a pop you might want to try interlibrary loan. The used ones I could find at alibris and bookfinder.com started at $24 and rapidly went up from there.
And even better, it looks like a bunch of pages are previewable in Google books so you can decide for yourself if this along the lines of something you can use.
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Next year we will be doing 4B and 5B since it fits best for Physics. Do I need the Activity book and Activity Guide and Higher Order Thinking Skills in addition to textbook and workbook? I was thinking I would not buy the Teacher's guide. Thanks.
KLA
The Higher Order Thinking books are available only for 4th and 5th grade. I really thought it worth while to buy them since they offer some very well-thought out and challenging questions. (If I recall correctly they are done in test format, so it's like a more challenging version of the test) I felt my son really benefited from these stumpers and was disappointed that this isn't available at other levels.
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Just musing here really...
So I remember reading all about moms switching phonics curriculum because this one wasn't working and then that one didn't work either and so on and so forth. When in actuality if they had simply waited until the child was ready to read, the first curriculum would have been fine.
Does anyone think the same could be said for algebra? There is a lot of talk here and on k-8 about algebra and which curriculum is the best. "This one didn't work for us so I tried this other one." Could it be that the child just wasn't ready for algebra? And if parent had waited another year or so child would have been fine with the first choice? Maybe it's not the curriculum at all, it's that the child's brain isn't ready?
I'm just wondering! I haven't had a child go through algebra yet. For that matter, I've only had to teach one of three how to read and he was ready so the first curriculum worked.
I don't think it is the same for algebra.
There are 25 year old college drop outs who dropped out because they couldn't ever make it out of remedial arithmetic classes, their brains are plenty mature...well, chemically speaking.;)
One problem with the maturity issue has do with the amount of generalization that the author of the text expects the student to be capable of. This is a matter of pedagogy rather than the subject matter of algebra per se. For example, I can explain a concept in great detail and include every step, or I can leave out a step and expect the student to fill in the blank. When I hear someone say that there kid did poorly in algebra it's not clear why. Was it the kid himself? Was it the kids preparation? Was the algebra text expecting the kid to make to great of leaps on his own? If you leave out to many steps there will be kids that can't figure out what happened in between, if you put in too many steps there will be kids who get lost in all the details.
Another thing to take into consideration, and I am speculating here, is that success in algebra requires the ability to handle and think up long chains of inferences, "IF x squared is equal to 9 THEN x squared minus 9 is equal to zero, AND IF x squared minus nine is equal to zero AND x squared minus nine can be factored THEN either the first factor OR the second factor must equal zero...blah blah blah"
Now some people catch on to this naturally. Textbook authors don't usually come out and discuss how logic is needed in algebra, they just expect the student to magically be capable of doing it. If the kid was in an arithemetic program which encouraged this kind of thinking (Singapore does through the mental gymnastics that kids have to do in those hairy word problems) and in the 60s a chapter on mathematical logic was specifically taught before launching into algebra proper and it also it may be that a bit of geometry before algebra may promote this since kids who have had to deal with the "IF these sides are parallel THEN this angle.."blah blah" in synthetic geometry will have had some experience also. However, a kid that's come out of K8 and has never had to reason his way through a problem because he was specifically trained to deal with them mechanically, then he may not do well in algebra. In a case like this, it's not because his brain is immature, it's that he was never taught logic nor ever required to use it in a sophisticated way as algebra problems frequently require.
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My 5yo dd has been asking pointed questions about God, death, and aging since she was a little older than 2yo. At first the questions were along the lines of "Who is God? How does he watch over us?" and her concerns about me dying became very overwhelming to her for awhile (and were freaking me out a bit). I always answer her questions as honestly as I can because she remembers everything and I never want her to think I am lying. She also always asked for clarification through other questions so seemed to understand the answers I gave her.
Lately, though, her questions have been more difficult for me to answer because many of them are questions I still find myself asking... "Why does God let little children get sick and die?" or "Why doesn't God just talk to me? What if he sends me a sign and I miss it or misinterpret it and get it wrong? Why doesn't he just tell me what he wants me to do so I know?"
I have honestly tried to answer these types of questions but often, on further questioning from her, have to just admit that I really don't know the answer and only God really knows.
So, to my question and yes there really is one after all that, has anyone come across a good book explaining these things to children? She reads and comprehends on about a 4th-5th grade level. She is not easily pacified with simple childish answers either which is what has made her questions difficult to answer. I find myself having problems with knowing exactly what she is looking for in an answer and worry about giving her too much information at such a young age.
There is a philosophy curriculum for kids that encourages just these sorts of inquiries. Each grade level has a story and in the story the children discuss the issues that are important to them. So, things such as fairness, death, etc., come up and the author has had to have each major point of view represented. It doesn't so much answer questions, but it does a good job getting the child to think about more questions in a gentle sort of way.
Here is an article in the Standford Encyclopedia for Children on the fifth/sixth grade level
Their publications catalogue is not terribly helpful with the kind of details that you are probably looking for, but here is the link anyway.
I called on the phone and got much more information in person and others have said that they were able to get sample pages emailed to them by requesting this.
Here is the home page and honestly, the way describe it sounds like hoakie "values clarification" but it doesn't come across like that at all, to me anyway, when I read the stories in the books.
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OK... our computer sound card isn't working and maybe I have the wrong link.
Are you saying all the antagonistic-towards-TT posts Charon made were posted as an April Fool's Joke? I think this whole thread needs to be pulled. This could be very damaging to the TT authors.
Until kids who've used TT for some time are tested with the ACT/SAT, we won't know if it "works" or not. We've had this whole argument about MUS not being rigourous enough. Yet some who've used it for years score very high when tested. Programs don't have to be head-bangingly rigourous and tedious to "work."
I imagine people can cut down most any math program if they have a mind to. Tomorrow (when it's not April Fool's Day) I'll ask about Math Relief. LOL
No. The TT discussion is serious. (do a search on this topic on these boards to see that these kinds of discussions go back for several years) The Rickrolling is comic relief.
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Gail,
Charon fell for it! I didn't get a chance to videotape his response, but I couldn't have posted it anyway, it went something like this "(#*$Y(@#$, that's the fourth time you rickrolled me today! LOLOL"
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Just to review....
What programs did you use? At what grades? What did you use to supplement? What happens with Latin from here?
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I'm soliciting fellow pranksters to help me rickroll someone. One. More. Time. I've gotten Charon three times today and I don't think he'll fall for it from me again. PM me.
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... that your child fit into the "accelerated learning" category? At what point did you realize that your child was different from the norm? Did you, at some point, choose to have an evaluation done and at what age?
Thank you. :)
My older son is accelerated because when I gave him a placement test for algebra in the fifth grade the test said he was ready for algebra. Indeed he has been working in a very rigorous algebra program. I think that means he is accelerated in this one area only because sixth graders in public school aren't doing this sort of thing and I've noticed that a lot of people say that their kid isn't ready for algebra in the sixth grade from these boards. I don't know if this means he is necessarily gifted. He's not accelerated in any other area.
I have a seven year old who I do think is gifted in math even though he is not as accelerated as his older brother. For example, once in the car he asked me to teach him the multiplication table. I explained that it was repeated addition and gave him some examples but left it at that. A few weeks later I said "now let's learn the six times table" as we sat down to do math and he rattled the whole thing off non stop and then said, "I know this already mom, because you explained it to me." He figured out the mutiplication algorithm on his own and he learned long division with only two examples. This morning he figured out how to determine the area of a right triangle without any explicit instruction at all.
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I only bought one "keys to" book and that was on percentage. Frankly, I thought it was some of the worst teaching I have ever seen. It had the student memorize how to do cross multiplication without ever explaining why it works. It told the student that if there was a decimal point in the divisor to move it over (without bothering to give problems where numbers such as 25.0 were the divisor), the word problems weren't nearly as challenging as Singapore word problems on the same topic. In fact, it seems that the whole point of the book was to make sure the student did not have to put out any effort in thinking at all by spoonfeeding every last step along the way. Nonetheless, I won't buy another one of their booklets again. If you have a 1965 Doliciani you have pure gold in your hands. Math from the 60's was all about justification and explaining why.
Now to contrast and compare: Foerster's has the student memorize multiplication with negative numbers, "the product of two negatives is a postive" and that sort of thing. The Dolciani Algebra II book that I have explains why it works that way. That is not to say that Foerster is a bad book, it's actually probaby the best algebra book still in print, it just doesn't spend as much time on justification as Dolciani does. If you don't personally place value in the why, why, why of math and just want to "get er done" then the sort of in depth treatment you will get out of the Dolciani series (early 60's) may be a ball and chain rather than liberation. Dolciani probably does not come with a teacher's guide and if you need that sort of thing you will want to avoid Dolciani.
You may have noticed that Dolciani has a perverse fascination with sets and expressing the solution to problems using set notation. That is because all of modern mathematics is more or less expressed in the language of set theory. It is handled trivially and mindlessly and seemingly without purpose in algebra I and perhaps algebra II, but if you continue with the 1960's math you'll end up seeing this set theory stuff at the verge of turning into abstract algebra by the end of high school in what they called "Analysis" and we today call "Pre-Calc." For an overview of what is involved in math as a field and to get a better idea of this bifurcation of the field you might enjoy reading David Berlinski's Infinite Ascent It is written for the lay person. He only lost me in the chapter on Goedel. We are using a math book similar to Dolciani, by the way.
On the other hand, for whatever reason, if you don't have an abstract algebra and pure math fetish like we do and are have engineering calculus in your sites then I understand that Foerster is a very good choice. It's still in print and has support materials. While Foerster perhaps doesn't go into as much depth as I personally want to see, it does at least give formal definitions and list the properties of the real number field. In other words, it doesn't teach lies or have the student memorize slop.
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I absolutely noticed this. I ended up doing a blog entry on it here after I figured out a way to solve the problem. In short, here is the solution:
Teach child to always write the "number sentence." In the primary grades rather than have the child "show his work" vertically, have the child always, always, always show his work horizontally. Now, if he needs to stack up numbers vertically to find the answer, that is done on a separate sheet of paper and we call that scratch work.
The hard part, I have found, with younger kids is teaching them to reinterpret the number sentence so that the thing which they are solving for is isolated on one side of the equal sign. For example, in a word problem such as "Jane had 20 stamps and Xiuli gave her some more, now she has 50. How many did Xiuli give her?" All of my kids would begin by writing that as an addition sentence. It took a lot of work to get them to express that as an subtraction sentence. Clearly, they were subtracting in their heads without realizing it and coming up with the correct answer and not knowing how they got to it. To teach them how to convert an addition sentence to subtraction I stopped and added more practice with "number families" which, in effect, is working with the formal definition of subtraction (If a + b = c, then c - a = b) Then you have to repeat this sort of thing when you hit multiplication and division.
The other thing you will have to do is explicitly teach the use of parenthesis in equations so that they can express a two step word problem as a single sentence. The way that I got my second grader to do this (and I wish I had a gif uploaded to show you how this works) is to have him write two horizontal sentences which he knew how to do as a result of how I worked with him as I explained in the above paragraph. So he writes the first step and then sees that the answer is used in the second step. I had to explain to him, on a seven year old level, the principle of substitution. I'd circle the expression which yielded the answer in the first step and draw an arrow to where he used the answer in the second step. Then, I had him do that with the arrow as well with his work.
When he could do that I said, "I can express those two sentences as a single idea like this.... And I'd write the second step leaving a big gap with empty parenthesis which would be filled with the expression from the first step.
For example: Mr. Lin had 112 tomatoes. 8 of them were rotten. He packed the good tomatoes into packets of 8 each. How many packets of tomatoes did he get?
In stage one Child writes:
A) 112 -8 = 104
B) 104 ÷ 8 = 13
Stage two: child draws arrow from the 104 in first sentence to 104 in second sentence. Seems mindless, but a seven year old needs to have the fact that you use this number twice pointed out to them.
Stage three:" I am going to express these two sentences as a single idea."
(112 - 8 ) ÷ 8 = 13
"Do you see that I replaced the 104 with the expression 112-8?" Child should say yes. "I can replace 104 with that expression because they are equal." In effect, you have to explicitly teach the child this principle of substitution. Because they will be using exactly the same set up each time with two step word problems, even if they don't generalize the principle, they will be able, with enough practice, to catch on to the formula. In other words, rote will do where understanding will not when it comes to a pinch.
At any rate, my second grader is now at the stage where he will sometime skip over writing out the A & B steps and immediately write out his equation. Not always. Sometimes he needs the two prior steps to help him think it through, that is fine. No hurry. Later on, when he learns that the fraction bar can also represent division I'll have him start expressing division using the fraction bar. By the end of P6 he'll learn that x can represent the unknown and he won't have to have make sure the answer is to the right of the equal sign. It will just be an x inside an equation or expression. He won't know how to manipulate the equation to get x, that actually manipulation of x is something we save for algebra when he can understand the technical justifications for such manipulation (in our algebra program you aren't allowed to do a thing to x until you can write out a full blown proof of why it's justified)
To make myself clear, even though in the sixth grade the child may show his work with an x in the expression, I am not requiring him to solve for x or manipulate these multi-step problems, I'm having him explain the thought process that went behind his thinking. He can solve the problem mentally or by scratch on a seperate sheet of paper if he wishes.
The sample you see in the gif to which I posted a link is the last step in this process: Using x for the unknown and formally declaring the variable. You must declare the variable. You must declare the variable.
When my sixth grader went into algebra he had no problem with it because he'd already been habituated to showing his work in a way in which it would be show in algebra. Having him declare the variable also has made word problems in algebra much easier for him as well as proving theorems. I could go on to explain how the above steps removed a learning burden when it comes to proving theorems (something that I was excited to see "work") but that is getting further off topic.
It is much easier to teach a kid who already thinks mathematically to show his work properly than it is to get a kid who can show his work properly to think mathematically, and that is why we stuck with Singapore despite this apparent deficit.
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Does it matter? Yes and No.
Conceptually speaking algebra is not required for geometry. Euclid didn't know algebra. Historically it seems that geometry was taught one or two days out of the week during math class before the student even got to algebra. I think Kiselev's geometry and Birkhoff might be set up for this kind of scheduling (not sure).
More realistically, modern publishers assume that you've already taken algebra and will put problems in their text which require skill in algebra to solve. There may be a few elementary school geometries that don't do this, but since you are talking about geometry in the context of algebra I'm assuming you mean a higher level of geometry than elementary school.
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"Joey Goes To Sea" is a fictionalized story about a real cat and real events aboard the author's tall ship in the 1930's. The cat is portrayed a bit like Winnie the Pooh and the animals talk to each other. The ink illustrations are in the style of Alice in Wonderland. There are five short chapters in the book and I read it aloud to my kids in two evenings. It is perfect for K,1,2 grades.
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\Wasn't Saxon designed originally as a kind of remedial program for kids who struggled with maths, and it was presumed they struggled because they couldn't remember stuff they had learned before? i can see why its designed that way. Isn't their motto something like "turns maths haters into maths high flyers ". I always thought it was funny they didnt say it turned them into maths lovers!The other thing I have often thought about Saxon is, sheerly doing that much Maths each day is going to have to create a large section of the brain dedicated to Saxon maths. Its a LOT of maths.
We did Saxon for 6 months, my daughter who had previously liked maths, absolutely hated it, so I changed. She doenst love Maths but she self teaches- spends about 45 minutes a day on it in grade 9. Gets most of it right. Understands it. How much torture does math have to be ?
:001_smile:
The "Saxon is a remedial program" is a topic that I've seen come up a few times on various places on the internet. Here's my interpretation of how this belief might have gotten started. Saxon markets (or used to at least) itself based on the successful rise in test scores it had in public schools whose students were otherwise just doing awful in other programs. When mathematicians like Wayne Bishop discuss Saxon on forums for math teachers Saxon is discussed in this context of studies showing remediation of kids behind in math such as this one. I think because they were trying to sell themselves on the fact that they successfully "remediated" problems that folks might be concluding that it is a "remedial" program. In this sense the term "remedial" is being conflated. But I don't think that it's remedial in the sense that it's intended for children with learning handicaps.
It's also not so much that kids "couldn't" rememeber what they had learned before in the sense that the kids were brain damaged, but in the sense that they only had two days of practice with basic facts because they were in rotten programs...that is my impression from following the math wars in other forums. There are some things that seem quirky about Saxon but it really makes more sense when you bear in mind that this program was intended for use with public schools by teachers who didn't necessarily have the math background to teach a program that left it up to the teacher to fill in the gaps (like Singapore does! And we hear of parents who can't teach out of Singapore more often than we hear of parents who can't teach out of Saxon. They aren't criticizing the content of either so much as accessibility/pedagogy )
As a digression, it is interesting that Saxon/Wang have told the truth and nothing but the truth content-wise, but that they haven't told the whole truth, so to speak, because accessibility is something they keep in mind. Before we are too criticial of such a strategy bear in mind that a similar thing happened in the Soviet Union when Kolomogorov took over the reform of K12 math ed during the Sputnik era. He recieved high criticism for not teaching set theory and pure math and his response was that he could only include those topics in the curriculum that the teachers had the educational background to teach. The Russians then selected the better students for what amounted to an after school program and personally taught them this other side of math. Meanwhile, in the United States, American mathematicians idealistically clung to the belief that pure math and set theory could be taught in the regular school curriculum and it was a catastrophe! There is no question that the actual content was superb but it was misinterpreted, misapplied, and mistaught by both publishers and teachers and turned into a giant mess (immortalized by Tom Lehrer). True, the teachers that had degrees in math started churning out future mathematicians at a rate the US has not seen since (maybe ten times more than we see today) but almost no one teaching had a math degree and what about them and their students? They hated it. They were exposed to content of the highest quality and they couldn't stand it. So while math ed came tumbling down in the US, the Russians who had opted for something less idealistic and more mechanical and boring kept on successfully chugging along.
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The lady down the street from me had her son tested for GT when he read Harry Potter in kindergarten. He tested one point below genius level. The school then made sure he had "their best" teacher for the next few years. The only accomodation that I heard about was that the teacher spent more time nitpicking his spelling and grammatical errors on essays than she did for the other kids. The mom was very pleased with this outcome. So I guess that's what counts. Other than that, he makes straight As doing grade level work with kids his own age (hes not accelerated in any subject) and everyone seems very pleased with the situation.
It's not an outcome that I would have wanted for my kid, but as they say, "it works for their family."
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We are working on multiplication tables. I am using ProfB, btw. Anyway, right now we are on the 6s. He knows them but when given the problems as suggested in the ProfB workbook, he gets half the problems wrong.
He has to do problems like 765,374,342 X 4. He keeps forgetting to add the carry over. Granted, it is a tedious problem and if you mess up once, the whole answer is wrong. He does do better with WAY smaller problems but this type of long problem is in the book. So I assume that the child is supposed to be able to do these successfully.
Maybe in your particular program it's required, but the ability to do tedious long-winded calculations without error is not conceptually prerequisite for success in math later on in high school or college. Hopefully this eases your anxiety a bit!
I think it is instructive to have a few problems like this to drive the point home that the multiplication algorithm works with 2,3,4, and n-digits in the multiplier. There are also a few long-winded multiplication problems which yield intersting patterns in the product. I would try giving him one these and say, "If you are careful and multiply this correctly, you'll see something really cool."
Multiple 142857 by 1, 2, 3, 4, 5, 6, 7 and look at the results.
Here is another:
Find the exact value of each expressions (He'll have to multiply then add something to it, a slight twist, but it gives him something interesting to look at when he's finished)
a) 9 x 9 + 7
b) 98 x 9 + 6
c) 987 x 9 + 5
d) 9,876 x 9 + 4
e) 98, 765 x 9 + 3
f) 987, 654 x 9 + 2
g) 9,876, 543, x 9 + 1
h) 98, 765, 432 x 9 + 0
i) 987,654,321 x 9 - 1
j) 9,876,543,210 x 9 -2
To get a little closer and more intimate with the multiplication algorithm inside and out try taking one of his long hairy problems, giving him the answer BUT removing a digit or two from the multiplier and seeing if he can't work his way backward to figuring out what the missing digits are. These are called "missing digit" problems and can quickly lead into more interesting multiplication problems such as, "1ABCDE x 3 = ABCDE1" if each letter stands for a different digit, what is this number?
At any rate, this skill of keeping track of the details is related to the interest that the child has in the problem at hand. Kids don't tend to get sloppy with problems they find interesting (They figure out ways of remembering the phone number of a new friend, but need weeks to memorize digits in the expansion of the square root of two, they can pull miracles in logical thinking when it comes to problem solving in video games, but not on a word problem that should take about 10 seconds of thought)
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The details of if we do a drill sheet, if I explain it or let the book explain it, etc, varies with each child. However, one thing that we do with all three kids is try to teach them "the bigger picture" and we do that in an informal and conversational way.
With the older child who is in algebra we ask questions that we know in advance will be answered by a proof later on. For example, "Why is it that some numbers repeat as decimals and other numbers just end when you divide them?" "How can someone know that there isn't going to be a whole number between 7 and 8?
With the younger ones we give them interesting problems to think about that they haven't been given the skills yet to solve but we think they might have a chance at solving if they just think about it hard enough, or they surely will understand the solution if explained. We've asked the second grader, "What's 3 x 3 x 3 x 3? "How many odd numbers are there between zero and ten? How many odd numbers are there between zero and a hundred? What fraction is in between 1/2 and 1? What fraction is in between that new fraction and 1? And that fraction and one? Can this go on forever or will it stop? How do you know that there aren't any numbers that evenly divide 31? And his younger sister in the first grade gets, "What's 7 + 7 + 7 + 7? Can you skip count by 11? If you skip count by 5 will you ever make it to 93? What if you tried skip counting by fives in a different way? Maybe you just haven't thought of just the right way yet." They are sent on goose chases like this from time to time. Dad can ask better questions than I can. We don't tell them the answer if they don't know. Like a magician's trick, if you can't figure it out you'll just have to be tormented by wondering.
While the "let's do this lesson in your book" approach takes care of technical skills for us, the math guys in the family seem to think that it's much more important in the long run to use foreshadowing of upcoming topics, instill wonderment, accustom the student to be comfortable spending a long time thinking about a single problem, and in general to approach math top down.
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It's as clear as mud to me now.
"It is not the purpose of formal logic to discover truth. That is the business of everyday observation and, in certain more formal circumstances, empirical science. Logic serves only to lead us from one truth to another. "
So is what is "true" only those things that correspond to physical entities? That's the "correspondence" theory...I think...goes back to Plato, and then there's a bunch of other theories. But there are philosophers who argue that something can be absolutely true without having a physical existence. And many philosophers would say that there is no certainty in truth from everyday observations and that empiricism is not trustworthy. So does Cothran not believe in a priori "truth"? If he doesn't, and he only believes in a posteriori truth or empiricism, that would support the view that he's hostile against mathematical logic as a method of acquiring truth, since mathematics is not an empirical science, but a priori.
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Either way, though, I can see how the exposure to any formal logic (and Cothran would argue that his is a formal logic in the classical sense... as opposed to informal logic) would make algebra easier. You make a very interesting point/case. You always do. :) You're like SWB to me. Everytime you write something, I have to read it 20 times before it all sinks in.
I would be interested in knowing about what courses teach the symbolic logic as it teaches the algebra. Is it Gelfand?
THanks so much for your reply. I'll let you know what I do, but you've about convinced me to go ahead and start the logic and let the algebra come later.
Robin
I will have to go back and look at how Cothran characterizes his logic.
There seems to be two meanings to the word "formal." We average chickens tend to mean "officially and directly teach a subject" when we say formal..as in "to formally study ballet" or some such thing. However, I think that formal and informal when used to describe logic mean something else. I'm hoping someone can jump in and help out...A "formal" system is a bunch of symbols along with some very strict definitions and rules about how those symbols can be manipulated. Mathematical logic would be formal logic. Informal logic is the study of argumentation using natural language. A high falutin' distinction is the following, my emphasis on the last sentence...
Wherever there is reasoning, there is a logic that seeks to articulate the norms for that type of reasoning. Informal logic differs from formal logic not only in its methodology but also by its focal point. That is, the social, communicative practice of argumentation can and should be distinguished from implication (or entailment)—a relationship between propositions—which is the proper subject of formal deductive logic; and from inference—a mental activity typically thought of as the drawing of a conclusion from premises. Informal logic may thus be said to be a logic of argument/ation, as distinguished from implication/inference.{/QUOTE]As an aside, I'm going to have to go think about all of this some more. I've always thought of formal logic as "stuff you do with symbols" and informal logic as "stuff you do with words." I'm wondering if what Forty Two said might not be a good idea given our educational objectives, but I'm also wondering how I'm going to fit yet another year of logic into an already crowded curriculum.
Gelfand does not teach logic, just algebra. He does proofs which require the student to use implications and inferences but he doesn't come out and directly give what those rules are. The algebra program which we use does this but it is old, out of print, and hard to find.
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I don't think symbolic logic and Aristotelian logic are interchangeable. I studied symbolic logic in college, and now that I am working through Socratic Logic, I don't really think there is all that much overlap. While I suppose they both help train the brain to think logically, they really aren't all that similar. Honestly, I will probably have my kids study both, so they will be able to utilize logic well in the language arts and in math. I think both are valuable.
Forty Two, By any chance do you remember what book you used in college?
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If given the opportunity to do what he wants, how would he spend his time?
I just eliminated all tv, video games, and internet games from our home and my first grader and second grader play chess with each other during their free time, they did a bunch of kiddie sudoku, and spend more time outdoors. My older one, about the age of your child, is finding more books to read.
Have you tried project kits such as Snap Circuits, robot kits, etc? He just doesn't like any of it? What have you tried? How does he choose to spend his free time?
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Why does this seem to always mess up my formatting?!
I'll post an image, and then the text is all scrunched up, even if I've spaced in between paragraphs.
Or, it's impossible to get the text down below the picture.
Is there a HTML explanation for this, that a very simple person could understand? :-)
Insert a line height command such <span style="LINE-HEIGHT: 1.4"> at the beginning to unscrunch the lines. Don't forget to close it at the end with a back slash thing.
To prevent problems with deleted photos get an account through a photo hosting website and upload your pics there and then use the URL option in blogger to enter the URL of that particular pic.
I've never been able to have the picture pop up where it's supposed to be, I cut and paste the code to where I want it to show up.
Math problem
in K-8 Curriculum Board
Posted
I interpreted the question as asking, "How many 10/24ths are in 243?"
So I set it up as 243 ÷ 10/24
This is a fun problem, what book did you get it from?