Myrtle
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Here is the URL directly to the blog entry:
http://www.geneveith.com/saving-mathematics/_346/'>http://www.geneveith.com/saving-mathematics/_346/
And here is the blog home page:
http://www.geneveith.com/
Scroll down to see "Saving Mathematics"
Both links are working for me.
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Here's an interesting blog entry on a topic that I don't come across very often. A literature professor questions the role of math in the quadrivium a la classical education and respondents to the blog entry include two mathematicians as well as somebody else you might recognize:
The discussion boils down to if the study of math should center around its applications to solving the problems of the physical world or if it should be studied for its own sake--The age old rigor vs relevance argument.
Although that is confusing for me because in the algebra program we are using the applications are studied, they are just treated rigorously rather than heuristically.
As an aside, the proofy algebra has been going okay. I busted out Euclid and started having my son model his proofs in algebra based on how Euclid did it rather than how purely how Frank Allen does it. This amounts to beginning the proof with "the enunciation" or stating in prose what concept he wishes to prove. The second part is declaring the variables to be used, the third is restating the concept symbolically, the fourth is the actually proof written as a series of implications (if, then statements) and finally the conclusion.
The kid is not doing these entirely from scratch but certainly can do anything that amounts to a derivation from scratch. He'll see something like, "Show that -(a - b) = b - a and will recognize, according to him, that "this is just a special case of the general case that we just proved" however, actually proving that the additive inverse of a number or expression is equivalent to the product of that number or expression and negative one takes a bit of Socratic prompting.
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What would you use for calculus if you had never taken it yourself?
I'd make use of my local community college to teach it to my child.
I really would.
I would just be too worried that whatever program I chose is a "box check" that we did calculus on transcript rather than really doing a good job teaching it according to objective standards.
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We were going along tickety-boo (Singapore 3A) and then BAM.
He can divide in his head--but get him to do something like 46 divided by 3. I can put the 1 on top of the line, but he cries out "I'm confused" right when I start writing a 3 under the 4.
What are we missing?
I hope that made sense?
TIA
You are missing the zeros!:D
You will have noticed that in your Singpore text there are many demonstrations of composing numbers by use of cards. For example, there will be a long card with 40 on it and a shorter card with 6 on it. When you line up the right edges you compose the number 46 and the child can lift up the 6 in the ones place to see the zero under it. This is used to demonstrate place value and these cards are very useful when demonstrating the long division algorithm.
Demonstrate your division problems by using these cards. You will need another set for recording the quotient. They are easy enough to make via magic marker and poster board.
So here we go,
You draw the long division symbol and place the 40 card and the 6 card where they belong. Now you ask the kid "how many times to 3 go into 40?" And his only options are 1,2,3,4,5,6,7,8,9, and 10, 20, 30, 40 since these are the cards available to him.
Since 20 x 3 is too big, try 10 x 3.
Place the 10 card in the quotient.
Now for the sake of efficiency we grown ups normally do NOT record zeros in the long division alogorithm but we want an intermediate step for a kid. Multiply the quotient "10" by the divisor "3" and subtract that. Under the 46 you will subtract 30 (this you can write with your pencil on whatever paper you have your cards on) and you will note that normally we simply subtract 3 from the 5, what we are going to do here is simply include those invisible zeros). If you need to demonstrate each problem with hundreds and tens cubes!
Okay, so the kid sees that 46-30 = 16. Now he has to decide how many times does 3 go into 13 ones and he decides "5" and then he places the 5 card on top of the 10 card in the quotient. The remainder of 1 can not be evenly divided by 3 so we record that as "R 1" meaning "and one was left over."
The benefits of this are that it demonstrates the role of place value in the long division algorithm and that since the invisible zeros are explicitly written it eliminates the step of "bring down the next number" which automatically appears in all its glory as the result of subtracting.
I have taught it this way once before with my older son (My son learned long division when he was six) and I'm within a week or two of teaching long division to my seven year old. I have half a mind to let him write it all out with pencil after we work with the cards and simply erase the zeros in the quotient replacing them with significant digits as he needs to. I predict after he does some 5-7 problems like this he'll appreciate me telling him that he need not write the zero to begin with and by that time he'll certainly have a little better understanding of what's going on in the long division algorithm.
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They'd have even more fun plugged into a Playstation II or permanently living at Disney World. :D
My kids have complained about particular assignments being boring and I ask them to propose an alternative. Sometimes it works. They'll say something like, "Can I just do phonics first?" Which is fine. Or, "I'd rather read this other book than what you gave me." And that's usually fine also. I've even let the younger ones spend the morning finishing up some play project they had going in exchange for a promise to do the work in the afternoon.
What's not okay is reject all school work as "boring" when it's really a passive aggressive form of defiance.
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I would hooked my oldest son by reading aloud to him. I used to also get unabridged books on tape and we'd listen to a chapter while eating lunch.
There was one book that I was reading to him that he especially looked forward to listening. When I got to the last chapter I put the book down with the page marked and said, "You know, I don't have time to read this today." And the next day I said the same thing, and the third day he picked up on the book and finished it off himself because he didn't want to wait any longer. That was exactly what I was hoping would happen. He was nine or ten at the time. Later I'd read the first chapter or two of a book and he'd slowly finish it on his own. Recently, he just finished the Golden Compass entirely on his own.
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This doesn't sound like a church issue to me. It sounds like a cultural issue.
We live in a culture which is increasingly viewing children as the ultimate middle class accessory rather than valuing families per se. Mix that in with the common criticism that those with more than their "fair share" of kids are sucking down resources, destroying the earth, or parasites on society and you've got a recipe for prejudice and discrimination.
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I used Daily Grams for second grade this year with my 1st and 2nd grader and it was over 20 lessons before they started to catch on to any of the rules. If a child gets frustrated by not understanding the rules right away then Daily Grams might not be the best thing.
And while I personally love Easy Grammar and use it, the rules that are given are not parsimonious and can be overwhelming unless the child figures out the underlying principle for himself. Now, I usually try to explicitly explain this to the kids and have my own way of explaining parts of speech and rules and so my success with this program might not translate to other parents who aren't doing this.
At any rate, my second grade who has LD language issues is having success with this program. And the program that I have heard many say really works for LD is Shurley Grammar. It is scripted direct instruction and very repetitive and predictable in a way that Easy Grammar isn't. Had my son not caught on to Daily Grams I would have used that instead.
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I don't know anything about that series and I really can't tell anything by looking at the TOC.
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Mathematical Induction is a kind of proof used with a particular kind of problem. Sometimes you see a series expressed as 2, 4, 6, ..., 2n with the last term expressing the what any given number in the series will look like. Sometimes you have to make a general statement that thus n such is true for all of the numbers in this series. Well, it's easy enough to prove about an actual number such as 2 or 4 or 6, but how do you prove something to be true about a nonspecific number? Mathematical induction helps you to do this. It's a syllogism that uses the counting numbers and if you accept the premise and allow a member of the audience to randomly choose any number in the series, you will prove that it's true for that number and then wave your magic wand and it's true for any other number in the series.
It's very much logic based. Too much. I wish it were more math-based.
Here is my blog entry struggling with it. There were a people trying to respond to me to explain it. Once I really had a problem that I liked and needed induction to prove the general case then how exactly it worked made more sense.
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Karin,
Adrian likes Solomonovich geometry because it has translations and he says that Solomonivich "does it correctly" rather than via handwaving. However, it's way of the head of our oldest son.
If you guys have finished Gelfand's algebra I and enjoyed it you might also enjoy Beckenbach's Inequalities. I'm finally getting around to finishing up the axiomatic part of that and I've really enjoyed it. Like Gelfand, he gives you a few tough problems to work on. So far it's involved algebraic manipulations which you already know from algebra I, the manipulations are easy enough but the solutions aren't straight forward. One new topic that is introduced is mathematical induction which will be used in a few times in later chapters I think. Adrian has just spent the past few weeks lecturing on the parts that I didn't understand so he's up on what's going on in that book if anyone ends up with any specific questions or getting stuck
It has solutions guide in the back although it's not always specific enough to be helpful. So far I've not needed it for the problems themselves but I did need to get help with induction and the very first part of the book but it's been much easier since then.
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I found a Teacher's Manual available for Singapore secondary maths but I will have to order it directly from Singapore. I haven't seen it at all but here is the part of the description that appealed to me was,
"Useful resource for teachers, tutors and parents...this Singapore Math teachers' handbook covers: Common errors made by students and important concepts taught in the new Singapore Elementary Mathematics curriculum..." -
Singapore Science has the potential to mesh with WTM a little more than you might think. You don't have to give it all up.
For example, 3rd grade science spends the the first half of the year on biology, the last quarter on human biology and the last quarter on magnetism.
So, instead of a full year of biology, you spend 3/4 of a year on biology. In the fourth grade there are four main topics that are covered and each segueys into the next. There aren't enough activities, lessons, worksheets, and tests to have science every day of the year, and you have plenty of time, perhaps half the year, for outside reading and summarizing for a science notebook.
In general, (and I'm not totally confident when I say this) but it seems that their science program is on a two year rotation of life science, physical science, and chemistry excluding earth science. There is one cycle for 3/4, another for 5/6 and one last one in 7/8.
People who think that an entire academic year is too much to spend on an entire topic but still want to spend a lot of time on a single topic might find that this provides the amount and depth of coverage they are looking for.
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Myrtle, I have been looking at "Introductory course to Geometry" by Ruszcyk for my ds. The website says it is an honors course. I also have the Jurgensen's Geometry text. Would you recommend the Ruszyk Geom. course? I like the fact that it is an online course.
Thanks,
Nissi
Our starting point for evaluating synthetic geometry programs were these two questions:
1. Did a mathematician write the text? Not a high school math teacher, not math ed, not a contest winner, not ghost writers, nor even a curriculum specialist, but a real mathematician.
2. What set of axioms or postulates are used? Foundations of Geometry
I think what Adrian has on tap for analytic geometry is Gelfand's Functions and Graphs, and Method of Coordinates.
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Am I missing something?
On the yahoo group they discuss like mad how hard these things are to understand but they seem fairly self-explanitory. Am I missing something?
They show the rods and the numbers that the rods are supposed to represent and you need to find the missing number--right?
We just started these and I feel like I am either missing something or it is so simple that it is almost silly. So fill me in.:confused:
It really depends on what level and what kinds of word problems you are working with. The ones in the third grade do seem obvious to me and I think that's the whole point. You start when it's easy and the increments in difficulty are so slight over the next few years that you only realize that it is difficult when people jumping into the middle of the program have problems with it.
In later grades when there are multiple steps involved, especially when dealing with fractions and ratio, you will find yourself at least temporarily stumped every now and then.
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The diagnostic test for Rusczyk's Algebra is here: http://www.artofproblemsolving.com/Books/IntroAlgebra/pretest.pdf
and seems to require that the student already know how to solve linear equations and work with radicals before beginning this book. This isn't covered in Singapore primary school math.
The post-test which the author has a link to is indicative of the kinds of problems that the student will solve after working through the book and seems to cover topics normally taught in Algebra II.
I would want to go through this book topic by topic and see if it isn't really more of an algebra II book before starting my child in it.
The Singapore primary math series does not cover all the topics normally taught in arithmetic but does finish up these topics in the first few chapters of NEM I. I would recommend either finishing up those chapters before switching programs or taking the placement test for whatever you plan on switching to.
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As Andre Toom recommended to someone, you don't want your G&T 10 year old in a program designed for dull 14 year olds, you want him in a program designed for bright 10 year olds. By simply accelerating your child through the same ole same old, you arrive at the same destination as anyone else, engineering calculus. Your child will not have benefitted from this education in any way that is different from simply going through it at the normal pace. By the time that your bright child is 20 and my average child is 20 they both will have ended up with exactly the same math education and classes.
What I mean by "dull" 14 year olds is that any math program designed for students who need black and white dots to "see" negative integers is not catering to the same intellect or math background as one that develops the concept of the negatives based on their formal definition (that of the additive inverse) that you would see in a rigorous program.
Arguably acclerating a child might even in fact result in him not getting as much out of the program as if he had waited another couple of years and were able to handle a more rigorous algebra program such as Foerster's or Doliciani. There are ten and twelve year olds that really can handle that level of abstraction and don't need watered down, visual analogies to "explain" algebra (and these illustrations are not explanations in any mathematical sense of the word).
One option for a child that has finished a normal arithmetic program on the early side is to work in arithmetic programs designed for bright 10 year old students by supplementing with something like Art of Problem Solving (which teaches that level of abstraction that is needed for rigorous math), Singapore Challenging Word Problems, Math Olympiad problems, or
Russian arithmetic, or Mathematical Circles designed for bright middle school and junior high students.
I am very glad that we waited what amounted to about six months or a year after my son finished his arithmetic program to work on these other things. He is in a program that is teaching him how to prove theorems in algebra. Some of the theorems that he has proved are that the additive and multiplicative inverses are unique as well as other simple proofs such as the null set is subset of every set, that negative one is not a positive number (and although that sounds lame he did it with Beckenbach's ordering axioms) he can use field axioms to prove why multiplying two negatives is a positive, etc. As a result of using these axioms in proofs he can quickly recite the field axioms and as of a few weeks ago the defintion of a group, and with the ordering axioms he knows the definition of an ordered field. He is also able to handle Gelfand's problems as well. Had I stayed in Jacob's, which I seriously considered, I would now be in a position of having to chose yet another watered down geometry program since he'd be no better equipped to handle either abstraction or rigor. I have also begun to notice that he is able to understand mathematical prose in a way that he couldn't before and can read expository text with less assistance. In other words, he doesn't need it explained in hueristic terms by a third party since he's being explicitly taught formal mathematical justification and the correct vocabulary in order to understand it on his own.
Not being able to solve all of Gelfand's problems is not necessarily a sign of failure or immaturity on the part of the student. If you follow how the Russian mathematicians teach algebra to kids they give the kids some extremely hard problems that they don't expect anyone with less than a genius IQ to solve. We were told by Andre Toom that it wasn't reasonable to expect anyone under the age of 12 to do these problems, that a bright 12 year old could work on them, but that it was certainly reasonable to expect the average 14 year old to do them. Even so, unlike an American math program, these problems are not all easy and the author doesn't even expect that the average student will get them all. In similar programs, the author of Mathematical Circles, says that in his experience working with G&T middle school students the entire class as a whole can only solve less than 20% of those kinds of problems.
It is through the attempt to solve the problem that the growth occurs, but this presumes that the child is really dedicating himself to trying to figure it out, or in other words, is motivated on his own and not by a parent.
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The new HEB off of 249 and Louetta carries it and possibly the other HEBs do as well. It's not in the isle with the baking supplies but is sold in the isle with bulk organics. Ask an asst. manager to point it out.
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I succesfully taught all three of my children to read without teaching them any letter names.
I taught the names of the letters about a year later when we began formal spelling.
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I frequently do science or history informally by recounting an interesting episode of fact while we are in traffic in the car. You could also do this conversationally during dinner like a story teller would.
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Dad wants the kids to do delta-epsilon Calculus.
Mom wants the kids to read Latin fluently.
We both want them to have read Plato, Kant, and Hume.
If we find a high school that does this we'd consider enrolling them.
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When my kids have had problems remembering the steps its usually because they can't remember the "whys" so I might ask "What's the next step?" But after they tell me I ask, "Why?"
Part of the goal of arithmetic is for the student to develop reasoning skills that will later be used in algebra. There are two goals in algebra, one is to teach generalized arithmetic, e.g.the kid knows how to add fractions with unlike denominators but in algebra they learn how to do this using letters instead of numbers. And the other goal is to formalize the "whys" of arithmetic. So, a solid heuristic understanding of why common denominators are needed will be very useful when the kid later has to give formal mathematical justification for the steps.
Of course, not all kids even remember the "whys" must less the steps. I have one that forgets, forgets, forgets as well. If it gets too too bad then I'd consider putting her in Saxon which reminds, reminds, reminds. :D
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I'm going to buy Runkle's Geography online, but before I do I'm going to call and ask if it's okay to return it if I don't like it.
Many businesses have return policies that will allow you to return merchandise that you are not satisfied with for any reason at all, not just if it's defective, it will just cost you the return shipping which might net you more than resale. Normally I would just keep merchandise that I'm not happy with that I've bought online, but it looks like Runkle's with the student workbook is going to cost around $100!
If Runkle's says that they won't accept a dissatisfied customer return then I'll try to get it through interlibrary loan. In fact, our library has Jacob's Geometry and Art of Problem Solving books in their system already, but many other things can be viewed simply by putting in a request...and I think that almost all of the books that I got through interlibrary loan I did end up buying.
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How do you schedule the text, workbook, CWP, IP, & cd's (Vroot Vroom)? Do you work in certain books on certain days, or a little of each every day? I have the HIG, but I don't see where CWP and IP are scheduled, am I missing something? Please help me by posting your schedule.
Teach lesson from text
Child does at least one entire assignment in workbook.
I've used IP for revision if necessary. At about midway through the program or at the end of the year I do schedule a mess of word problems from CWP. Then I have the child take the "test" which is really a "revision" in the workbook. At the end of a grade level we do Federal Test Papers, which really are practice tests.
I do the CDs on days I need a break, or if I can remember, to reinforce a topic taught in the text...it would probably be useful to go through the text and pencil in a giant warning sign to vist the same topic in the CD so that I'll have a reminder when I get to that point. The kids manage to do all the activities on the CD simply out of boredom or curiousity without me making a point to make sure to schedule it, but it would probably be beneficial to do it along with textbook.
What can I do with the boneless, skinless chicken breasts in my freezer?
in General Education Discussion Board
Posted
I made chicken curry and rice last night.