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Entries from RussianMathematics
RussianMath 07 Jul 2005 - 22:44 CatherineJohnson
I've just ordered a copy of Mathematics: An Award Winning Textbook from Russia from Perpendicular Press. The translator's press release is here, and Barnes and Noble has posted this 2004 review from Book News:
The textbook won the national competition for best textbook when it was first published in 1987, and is still in use today by sixth graders throughout the former Soviet Union. Harte (mathematics, George Washington High School, Cedar Rapids, Iowa) ran across a copy and decided it was much better than anything he used: there are (almost) no distracting graphics, misguided explorations, or colorful sidebars about courageous people; only half a dozen carefully sequenced lessons with examples and exercises.
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RussianMathPart2 07 Jul 2005 - 22:43 CatherineJohnson
My copy of Mathematics 6 came yesterday, and it is incredible. A beautiful, beautiful book. The design is exquisite (in my next life I'm going to be a graphic designer) and I've learned things just reading the first 5 pages. I'm pretty attached to the Saxon books, but I actually feel love for this one. [Now I'm thinking . . . do I sound completely nuts? Well, if I do, the beauty of a Bliki is that I can DELETE THIS POST later on today, after I've come to my senses.] I'm going outside right now to do the problems in Chapter 1.1 Factors and Multiples.
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WhyILoveCarolyn 07 Jul 2005 - 22:01 CatherineJohnson
Carolyn just told me she's known a few Russian mathematicians, and 'they have chops.'
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ItTakesChops 07 Jul 2005 - 22:09 CatherineJohnson
It takes chops to solve this when you're eleven:
Two cars leave simultaneously at 9 a.m. heading toward one another from different cities that are 210 km apart. The average speed of one car is 50 km/h while the other car averages 70 km/h. Come up with an appropriate question and answer it.
This problem appears on page 5, 'Review,' of Mathematics 6: an award-winning textbook from Russia, by Enn Nurk and Aksel Telgmaa. The 6 in the title stands for 6th grade.
+ + +
update: OK, I solved it.
But I couldn't think of a bar model.
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RussianMathPart3 07 Jul 2005 - 21:54 CatherineJohnson
The chainring (attached to the pedals) on a one-speed bicycle has 44 teeth while the freewheel (on the back wheel) has 20 teeth. Determine the least number of turns the chainring must make in order for both the chainring and feewheel to return to their original positions. How many turns does the freewheel make during this time?This is a problem from Mathematics 6: an award winning textbook from Russia by Enn Nurk and Aksel Telgmaa, a 6th grade book. I've prime factored each number, since that seems to be what's called for. But now I'm stuck.
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AnotherWikiPossibility 19 Sep 2005 - 23:07 CatherineJohnson
Another possibility for communal Wiki pages is to do something like the thread for RussianMathPart3: pose a problem or a lesson everyone can comment on. I'm interested in comments on the fraction lesson J. D . Fisher has posted at Math and Text. My immediate reaction to J.D.'s post is that it would be terrific for developing teachers' conceptual understanding of mathematics, and possibly for developing teachers' pedagogical content knowledge (pdf file). But I wouldn't be able to teach it to Christopher, even though he does know that a fraction is (also) a division problem. (I'll pull my thoughts together on this later--time for a bike ride now.) I'd love to get other people's reactions.
WickelgrenOnIntroducingAlgebra 08 Jul 2005 - 17:19 CarolynJohnston
I've been looking again at one of Catherine's favorite books, Math Coach (by Wayne and Ingrid Wickelgren). Wayne and Ingrid have a lot to say about what they consider the most difficult aspects of elementary math -- long division and fraction manipulation. But it's what comes after that that interests me now: their discussion of the importance of teaching algebra early. Wayne suggests that the most important thing you can show your kid, what should motivate them most to want to continue in math, is the power of algebra to solve hard problems. Most problems in prealgebra and early algebra start out something like this:
John is 27 years old. If his age is 3 times Pete's age, how old is Pete?If you have a kid like Christopher or Ben, you know he's going to spit out the answer on the spot and tell you not to waste his time with this stupid letter stuff. That's why Wayne Wickelgren suggests that, when you're ready to introduce your kid to the notion of algebra, the first thing you should do is sit down with him and let him watch you do a problem like this one:
In two years, Jean will be twice as old as Chris will be. In six years, Jean will be four times as old as Chris was last year. How old is Chris now?In short, start with a demonstration of how algebra-at-your-fingertips gives you mindblowing powers. I was reading this last night and thinking: if I tell him that this problem is what algebra is all about, Ben will be blown away. Why scare him off? Maybe start with something simpler... But the hard thing about this sort of problem isn't going to be doing the algebra: it's going to be setting up the equations, given the word problem. And that's going to be hard no matter how I try to teach it. Doing the mindless rote stuff required to crank out the answer, once you have the equations, is the easiest part of the problem. And I know Ben: he'll think that's the cool part. Given that, I can't see a reason to hold off introducing algebra. Once a kid is at the sixth or seventh grade level in math, the heck with guess-and-check and pan-balance problems; the heck even with bar models. The most general tool that we currently have for solving word problems, and the only one that we have that isn't stymied by some word problem or other, is algebra. He may as well be motivated to go full speed ahead with the letters and symbols. Wickelgren says that algebra is the key to the castle; it's the most effective means for solving tricky math problems that's ever been devised. As such, you want it to be the tool that kids reach for instinctively when they have a tricky math problem to solve. Here's a quote from a great article by Ethan Akin, "In Defense of Mindless Rote":
On the other hand, mathematics is cumulative and there are a great many skills that you have be unthinkingly familiar with. Every grumpy calculus teacher will tell you that most of the problems his students have come from weaknesses in algebra. For the students who say "I really understand it but...." the but is that for them algebra is not easy background knowledge. They are trying to build on a foundation of dust. A lot of college majors need a bit of calculus or statistics which are simply walled off to students who don't have sufficient skills in algebra. These are basically not hard subjects but they appear unnecessarily terrifying to such students. Conversely, a practiced facility with algebra can provide its own positive reinforcement. Not only is the mathematics built on the algebra, but facility in algebra gives the student confidence in the face of new mathematical challenges. As the above discussion makes clear, such confidence is entirely justified.I am motivated now to try to introduce real algebra by the end of the summer. No more pussyfooting around!
Wickelgren on introducing algebra
Wayne Wickelgren on algebra in 7th & 8th grade
Wickelgren on math talent & when to supplement
late bloomers in math & Wickelgren on children's desire to learn math
Wayne Wickelgren on mastery of math & on creativity & domain knowledge
Wickelgren on why math is confusing
MeasurementAdviceFromCarlL 08 Jul 2005 - 21:46 CatherineJohnson
Re: Measurement My first year teaching high school freshman (I just finished my 3rd year at a urban neighborhood school) I was completely shocked that none, and I mean none, of the kids could measure using an inches ruler. How can they get out of middle school, or even grade school, not knowing how to measure? I still have no clue. I doubt its the constructivists fault due to their fondess for hands-on, manipulatives, and project, which all lend themselves to measurement. What I have observed:I intend to take this advice.
SummerProgramUpdate (measurement skills)
HappyJulyFourth 22 Jul 2005 - 18:04 CatherineJohnson
notes from Lone Ranger on homeschooling her daughters using Singapore Math:
Just a quick note that I didn't know where to put on this forum. I started homeschooling my daughter in August 2004. She had been in public school since kindergarten and was a rising 4th grader when we started homeschooling. She had suffered through 3 years of "Math Their Way" and then 1 year of "Everyday Math" before I woke up to the fact that she was not learning math well. Her third grade test scores showed her to be working at the 50% in math. Well, after one year of homeschooling using only Singapore Math Levels 2B- half of 4A and supplementing with Singapore Math's Intensive Practice her total math score on the Iowa Test of Basic skills is now at the 99%!! More importantly her confidence, fluency, and ability to work through difficult problems have gone through the ceiling as well. Happy 4th of July
We are taking home educating one year at a time. This coming year we will home educate again using Singapore Math. I am quite impressed with the program. At first glance it looks rather simplistic and lacking in review. However, I have found it to be very systematic in its presentation and its ability to build understanding is amazing. This is not your inch deep mile wide program at all. The review is there but usually disguised in word problems. Our school system is in terrible distress and using constuctivist math and science, whole language, and very little basics. The private schools are full and all but one have selected curricula I cannot tolerate. So for now it's home schooling. I'd love to hear what other people are using for high school level math. I keep hearing about the following titles: Jacobs Algebra and Video Text. What are good programs? Lone Ranger I used Singapore math books 2B, 3A, 3B and half of 4A before having my daughter take the ITBS test. She completed the 2B placement exam but took 3 times as much time to complete it as was recommended. I thought better to start her slightly below her level to build confidence, learn the rod diagrams, and build speed and fluency with her facts and basic procedures. We also used Intensive Practice books 2B, 3A, 3B, and part of 4A (not every problem though) I made the decison to use Singapore because through my research 2 titles kept appearing over and over: Saxon and Singapore. Saxon is expensive and did not seem to be a good fit for my youngest daughter. Singapore seemed to be the best one to try first, since I wouldn't be out a lot of money if it flopped! Not very scientific or glamorous but the truth. Once I worked with the program and saw the children's response to it I was sold. I am average in my math ability and studied through Trig in college. I think at first Singapore can be intimidating, but after working with it, it is fairly straightforward. I used the Instructor Guide for 2B and have not really used it since. I try to work out all the rod diagrams, and boy am I getting good at them. Jenny, at the Singapore Forum board, is a great help if I am hopelessly stuck. All problems at this level can be solved without using algebra and Jenny is very helpful for teaching people how to set up the rod diagrams. (singaporemath.com) I also am learning much along with my daughters. I think Saxon is also a great program and a few of my homeschooling friends' kids are doing very well with it. I am going to look into the Russian Math program too.
Rod diagrams are another term for bar models! Honestly, the only thing I did with the Singapore program was to follow it. This is what a day at our kitchen table looked like: First a warm up. At first this consisted of basic facts practice. Usually a worksheet of facts isolated by family (ie: just 9's in multiplication) until enough families were learned to combine them. The text presented them this way as well. Eventually we did our multiplication and division randomly mixed and often multiplication facts presented as missing factors 9 X ___=72. Sometimes the children practiced on a hand held device called "Math Shark" or used flash cards. After the children mastered their multiplication and division facts the warm up was several problems from the series that were difficult for them. These problems came from prior days' instruction and I often changed the story slightly and always changed the numbers. We would repeat "types" of problems each day until these problems became routine and easy to solve. Also, once they learned to compute equivalent fractions and reduce fractions to lowest terms I would have them do a warm up of these types of problems until I saw mastery of the procedure. This part of our lesson took about 5-10 minutes. The second phase of our Kitchen Table Math consisted of 1 or 2 pages of Intensive Practice from a book one level below the text. For example we are working in book 4A but are working in Intensive Practice book 3B. I found this was a great way to provide extra review and also not overdosing on the topic currently being studied in the text. Also parts of IP are quite challenging and having extra skills did not hurt. This part took about 15 minutes. The third part was the actual lesson in the text. The children worked orally and on white boards. They completed most of the practice exercises. Sometimes if I saw they had mastery, they only completed a few. We also completed every word problem using bar modeling if appropriate. This took 10-20 minutes. The final section of our lesson consisted of the children completing the corresponding workbook page(s) independently usually taking 5-20 minutes. I reviewed their work and had the children correct errors immediately. That's it!
IndusAcademy 14 Jul 2005 - 04:40 CatherineJohnson
from Anne Dwyer:
Indus Academy is an independent math academy started by math PhD usually trained in another country to teach their children here. I know there is one in Newton, Mass started by Russian mathematicians and they use Russian texts. In Russian. One of Daniel's friends was going to this school so I asked to sit in on a class. They give a placement test...very challenging and it tests lots of different math concepts. Just to give you an idea, I sat through one class on a Satuday morning. Every child except one was Asian or Indian. That morning, the teacher introduced the students to geometric and arithmetic series. (These kids are 3-5 grade.) A geometric series is when you add 1 + r^2 + r^3+....+ r^n. So the teacher started by picking an r and generating the first couple of term. Then, he started asking students, "OK, now how would you generate the next term? How would you generate the 10th term? How would you generate the 19th term?" And then he led them through the process. In this way, the students start to think about advanced concepts in manipulating numbers. And picture the juxtapostion: these kids are sitting through Everyday Math which is at least a year behind their grade level and learning advanced mathematical concepts on the weekends.
I'd put both Christopher & me in that class in a heartbeat.
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MathAndLanguagePart2 22 Aug 2005 - 18:26 CatherineJohnson
Carolyn M is back! So, while I have her attention, I'm posting my new Russian Math question. This is from a chapter section called:
1. A quotient greater than 1. ... In this case the quotient shows how many times larger the dividend is than the divisor. The number 8 is 1.6 times bigger than the number 5. 2. A quotient equal to 1. ... In this case, the divisor and the dividend are equal numbers. 3. A quotient less than 1. In this case, the quotient shows what part of the divisor the dividend is. And so, the number 6 is 3/4 of the number 8.
This was, believe it or not, the first time I had ever seen a quotient greater than one defined as how many times larger the dividend is than the divisor. Wonderful! However, I was then surprised to find that a quotient less than one was not defined as how many times smaller the dividend is than the divisor. Here's my question. Is it incorrect to say that a quotient less than one tells you how many times smaller the dividend is than the divisor? Or is it that the authors view the definition they give (what part of the divisor the dividend is) as more important or more fundamental or more profound? If it is incorrect to say that a quotient less than one tells you how many times smaller the dividend is than the divisor, why is this incorrect? Thanks!
Another thing: I've never seen a 'quotient larger than one' defined as anything other than 'how many times the divisor goes into the dividend' or 'how many of the divisor are in the dividend.' Last, but not least, I don't think I ever was made conscious of 'decimal' or 'fractional' phrases like '1.6 times larger.' 'Two times larger,' sure. '1 '1/2 times larger,' yes. But '1.6 times larger'--never. This is important, because it looks like we're hardwired to understand 'friendly fractions.' Five year olds know what one-half is.* Five year olds do not know what 6-tenths are, and they certainly do not know what 1 and 6 tenths are! Morever, our brains do not automatically or easily generalize from 'one half' to '1.6.' This is another reason to object to the exclusive focus on friendly fractions in constructivist curricula. Friendly fractions are the fractions children know without having to be taught.
*Hunting, Robert P. (1999). Rational-number learning in the early years: what is possible?. In J. V. Copley. (Ed.), "Mathematics in the early years", (pp 80-87). Reston, VA: NCTM.
What Counts: How Every Brain is Hardwired for Math, by Brian Butterworth
The Number Sense: How the Mind Creates Mathematics by Stanislas Dehaene
Children's Mathematical Development: Research and Practical Applications by David C. Geary
(fyi: It is possible to buy Geary's book for far less than the $124 Amazon wants for it, or the $55 I paid for a used & extensively highlighted copy...)
Carolyn on math and language 7-2-05
Carolyn on math and language again 7-3-05
the language of numbers is not language 7-3-05
WilliamKSmithCalculus 16 Sep 2005 - 12:16 CatherineJohnson
Here's another recommendation from Barry Garelick: Calculus with Analytic Geometry by William K. Smith (also available at Amazon) I've already ordered my copy. Have I mentioned I'm planning to take calculus? Well, I am. I'm planning to take calculus. But first I have to 're-take' algebra & geometry. Then trig, which I've never studied. You folks here at ktm are helping me so much. Even though I'm a writer, I can't locate the words to describe what you've given me. The reason I can't 'locate the words,' of course, is that I don't actually know what I'm learning from ktm. I study & absorb what people say, but then forget the source of my new knowledge once it's been assimilated into my store of old knowledge. I'm left with the hazy feeling that 'I'm learning a huge amount from the Commenters at ktm.' So I'm going to start taking notes. God is in the details. thank you!
Mathematics 6 by Enn R. Nurk and Aksel E. Telgmaa, though. I could probably add & subtract integers in my sleep. (Though I did have to do some review last year when I first re-encountered the topic, which I take as a sign that my knowledge was more procedural than conceptual.) But last night, after working with Christopher for awhile, who was semi-lost (I don't think he could pass a test at this point) the Math Fog rolled in. This is the good thing about working with people who know less math than you do. Concepts and procedures you thought you understood turn out to be not quite so clear. I assume that's what Bernie meant when he said the other day that he'd realized there were aspects of reciprocals he hadn't thought about (if I've got that wrong, Bernie, I'll change it!) Carolyn has said something similar at times. I'll be asking her about some elementary concept that, for her, is as simple as breathing in and out, and suddenly she'll see why Ben--or anyone else--might get confused.
extended response (pdf file)requirement that's taken over IL state rubrics. At least, for the time being I am. [update 5-14-06 sorry, link no longer works])
Mathematics 6 and turned to the section on adding & subtracting integers. The first thing that struck me was the fact that this topic appears at the very end of the book. Prentice Hall Pre -Algebra* opens with integers, and I question that. I question it not based on any profound grasp of pre-algebra as a coherent whole. I question it on grounds that Nurk & Telgmaa are geniuses, and they put adding & subtracting integers last, not first. I'm sure they have their reasons. (I intend to figure out what their reasons were.) Reading through Nurk & Telgmaa's discussion, I realized why I was confused. I think I realized why Christopher was confused, too. I hope so. We were both, I believe, stumbling over this type of problem: Saxon Math 8/7 & Russian Math teach addition & subtraction of integers using the number line. Saxon's lessons were particularly strong, I thought. But when I tried to untangle myself by resorting to the number line, I got stuck. Start at zero, move five to the right, then.......then what? What was my next move? My very next move, without renaming or re-expressing - (- 7) as + 7 ? I was stuck. Reading through Mathematics 6 I realized that the problem is something Wayne Wickelgren & his daughter Ingrid have raised: the same letter or sign has been made to stand for two different things. There are two 'minus signs' in 5 - (-7). One means 'opposite,' and the other means 'subtract.' One means 'perform an operation' and the other doesn't (I don't think. Is 'taking the opposite of a number' considered an operation? I don't know.) In any case, for both Christopher and me, 'subtract' and 'take the opposite of' are two different things. Mathematics 6 has a formal demonstration of the fact that: Mathematics 6 I realized that's what needed to happen with 5 - ( -7):
We'll see how it goes. This morning I had Christopher quickly rewrite 12 subtraction problems as addition problems. (I haven't explained to him why a subtraction problem can be rewritten as an addition problem, and I don't know whether I'll get to that today. I haven't closely studied Mathematics 6's presentation to see whether I can introduce it 18 hours before the test. Fortunately, Ed had already introduced the idea that 'subtraction is addition' last night, when he used the addition-of-debt-to-debt (a concept that is not foreign to our household) to show Christopher that:
*new title: Prentice Hall Mathematics: Explorations & Applications
keywords: subtraction negative minus absolute value subtraction is addition integers extended response
RussianMathQuestion 04 Oct 2005 - 15:54 CatherineJohnson
page 240, #905
The answer is yes, obviously, but I'm wondering whether I've got the rule right. I come up with yes, when b < 0. I'm starting to look forward to getting back into proofs. I think.
RussianMathProblem961 05 Oct 2005 - 17:19 CatherineJohnson
A point with a coordinate of -3 moves along the number line in the following manner: First, it goes 5 units in the positive direction; Then it goes 7 units in the negative direction followed by 10 units in the positive direction and 8 units in the negative direction; Then it goes 3 more units in the negative direction and, lastly, 13 units in the positive direction.
Question: What is the final location of the point on the number line?
Mathematics 6 by Enn R. Nurk and Aksel E. Telgmaa, page 255
RussianMathProblem976 09 Oct 2005 - 22:14 CatherineJohnson
A rectangular park is 400 m longer than it is wide. The ratio of the length of the park to its width is 5:3. How long will it take someone walking at a rate of 2 km/h to go around the park?
(I hate the way this looks. I need Quark.) Anyway, using the bar model you see that you have a bunch of equal units, and that two of these units equal 400. Therefore, each individual unit equals 200. So the width has to equal 3 x 200, or 600 and the length has to equal 5 x 200 or 10,000.
length = l = w + 400 5/3 = l/w
5/3 = w + 400/w
What I can't remember is whether the book has taught kids to use two variables...
FinishedRussianMath 18 Oct 2005 - 18:35 CatherineJohnson
started: June 6, 2005
finished: 10:05 pm, October 14, 2005
number of chapters: 6
number of lessons: 59
number of pages: 300
number of problems: roughly 10,000
number of gratuitous graphics: 0
It just struck me. This is probably the book that got me hooked on math. Not Saxon Math 6/5, not Primary Mathematics, not even Challenging Word Problems 3. Mathematics 6
RussianMathProblem624 30 Dec 2005 - 15:23 CatherineJohnson
One think I love about Russian Math is that problems are numbered sequentially from beginning to end. The authors don't start over again from 1 with each chapter. This means you've left the realm of the friendly numbers by page 22. (First problem on page 23: #102.) 300 pages
1118 problems A lot of those 1118 problems include as many as 9 to 12 separate problems. I figure there are at least 10,000 problems in the book, every one of which I've done. (And I still didn't get the answer to Carla and her 1/3 money expenditure at the amusement park. Is that a diagnostic?) All math books should do this. The sense of progress you feel working your way through the book is tremendous. Plus you get a lot of practice doing percent problems, as in: what percent of the book do I have left if I'm up to problem number 507? Seriously.
what's the answer to this problem? 769. An old brainteaser by Leonty Magnitsky: If a man drinks a barrel of water by himself in 14 days and the same barrel with his wife in 10 days, how many days would it take his wife to drink the barrel by herself?
my next question How do you check your answer? I have an answer, but I've 'checked' it in what seems like a circular way.....that is, I've checked it in such a fashion that I've simply confirmed that I did my calculations correctly.
incorporating 'historic' story problems into contemporary texts Another wonderful aspect of MATHEMATICS 6: scattered throughout the book are 'brainteasers' written long ago by 'Central Asian scholars' and the like. I perked up every time I came across one of these. Mathematics 6 teaches students something about the history of mathematics—and, crucially, about the fact that mathematics has a history—through the problem sets, not through dorky 4-color sidebars that interrupt the text and bring progress to a screeching halt. (Mathematics 6 has no colors. The text and sparse illustrations are black and white. Good.) This is living history. Working a problem somebody thought up in 973 that's still hard today, you feel yourself connected to people living nearly a thousand years ago. It's magic.
624. An old brainteaser by the Central Asian scholar Biruni (973—1048):
If 10 dirhams (a unit of currency) earn 5 dirhams of profit in two months, how much profit will 8 dirhams earn in 3 months?
RussianMathTableOfContents 15 Mar 2006 - 18:56 CatherineJohnson
I've just discovered that the Table of Contents for Mathematics 6 ('Russian Math') is posted online! (pdf file) You can see how beautiful the book is graphically. It's the exact opposite of page splatter. The book is so lovely it made working through 12 trillion fraction problems a pleasure.
speaking of 12 trillion fraction problems So check this out. Here we have Chapter 3, Fractions, Decimals, and Percents.
Look at Lesson 3.3. Multiplying Fractions Lesson 3.3 is 8 pages long. Of those 8 pages, 2 1/2 are lesson. 5 1/2 pages are wall-to-wall multiplication problems. Hard ones. Problems like this one:
I was sweating my way through 5 1/2 pages of this stuff when I looked ahead to see what came next and discovered that my reward for getting through 5 1/2 pages of huge fraction multiplication problems was going to be: Lesson 3.4 More Multilplying Fractions One page of instruction, 6 pages of fractions.
-- CatherineJohnson - 15 Mar 2006
RussianMathLessonFourPointFour 15 Mar 2006 - 18:56 CatherineJohnson
4.7 Circles The circumference of a circle divides any plane into 2 sections. The portion of the plane on the circle's circumference and inside of it forms a disk (fig. 4.9). The center, radius, and diameter of the circle are simultaneously the center, radius, and diameter of the disk. The distance from the center to any point on the disk cannot be greater than the radius.
The problem set begins like this:
I love it that the first 'problem' is: read the text. Since I was slavishly obedient while working through the book, I ended up reading the whole thing twice.
Lesson 4.9 Area of a Circle In Lesson 4.9 we learn that:
Stringent mathematical reasoning has proven that the area of a circle is p times the area of a square whose side is equal to the radius of the circle. If we denote the radius of the circle by the letter r, then the area of a square whose side is equal to the radius is r2. It follows that the formula for the area of a circle is calculated by the formula (fig. 4.14): A=pr2
How often does one come across an expression like "stringent mathematical reasoning has proven" in U.S. math books?
p.s. Remember what Carolyn says about Russian mathematicians. They have chops.
-- CatherineJohnson - 15 Mar 2006
KiselevGeometry 30 Oct 2006 - 19:22 CatherineJohnson
I've just discovered that Singapore Math is carrying Kiselev's Geometry Book I. Planimetry. According to them it's "the most famous Russian textbook":
In Russia, everyone knows it by this nickname: "Kiselev's Geometry." It is by far the most famous Russian textbook. It has been published over 40 times in dozens of millions of copies, and lived through many epochs, wars, reforms and revolutions - and not only in education. For nearly two decades the book had been the standard geometry text for all schools in the Soviet Union, serving the students of the age corresponding to the US grades 7-9. Now it is translated into English and adapted by a professor of mathematics from UC Berkeley to fit common guidelines for a high-school level course in plane geometry. The book is equally suitable for homeschooling, grade school or college classes, teachers' professional development, or independent study. Reviewers, editors, and users of former editions praise the exceptional clarity of exposition, and an excellent collection of problems, counted in hundreds, and with the difficulty level varying from reasonably easy to reasonably hard. Unlike many other textbooks in the same subject, "Kiselev's Geometry" is good not only for being studying geometry, but also for having learned it.
UPDATE 10-14-2006: Linda P has found a terrific review of the book here, as well as the company that sells the book for $29.95. (They have Ron Aharoni's book, too!)
excerpts from Kiselv's Geometry
Aharoni article, part 1
Aharoni article, part 2: America's 'new math' goes to Israel
Aharoni on the fifth operation of arithmetic
Ron Aharoni on teaching fractions & forming units
What I Learned In Elementary School by Ron Aharoni (AMERICAN EDUCATOR)
-- CatherineJohnson - 09 Oct 2006
LindaMoranListserv 11 Dec 2006 - 19:25 CatherineJohnson
I think everyone here knows about Linda Moran's Teens and Tweens blog. I've recently (re)discovered that she has a listserv attached to the blog. I joined last week, and I think some of you might like to join as well. There have been some very interesting posts to the listserv that I don't believe have been posted to the blog itself — and that I don't expect to see posted to the blog itself.
-- CatherineJohnson - 09 Dec 2006