I said
PPS, my former student aced his tests but skipped his homework, and is now repeating Algebra I. As soon as I can photocopy a few pages, I'll share some of the stupendous howlers I found on a quick perusal of his new text. Amazingly, it's *not* Prentice-Hall ...
Key Curriculum Press, Discovering Algebra, An Ivestigative Approach, by Murdock, Kamischke, & Kamischke. Along with a committee filling two columns on page ii, including five Multicultural and Equity Reviewers, two Social Sciences and Humanities reviewers, and, get this, three Scientific Content Reviewers, and one Accuracy Checkers (sic!). Seven hundred pages of irrelevant color pictures (e.g., Elvis impersonators) with inane captions (e.g., "Dead skin cells are one of the components of dust."). The people I know who are good at algebra had books with *zero* pictures, and few, if any, black and white graphs. Those books weighed maybe five times less, and contained way more than twice the algebra. (I learned it from my grandmother's.) If I were an aspiring algebra student, I would be deeply offended by this book for diluting the subject beyond recognition, as if algebra were so difficult and distasteful as to require huge doses of eye and brain candy, and for forcing me to lug to school hundreds of stupid pictures far less interesting than an equally heavy stack of magazines of my own choosing. And I came here to learn algebra, not to be cured of racism and sexism. And as a teacher faced with this book, I would invite any "student" who wished he was elsewhere to place his favorite magazine inside his open book. The pictures would be at least as relevant. I'll bet that even those who get an A in the course will be completely unable to apply algebra to any problem that appears to differ significantly from those "investigated" in the book. Howlers: In a section devoted to wind chill, p227, photo: snow blowing across highway across a barren plain. Caption: High wind speeds in Saskatchewan, Canada, drop temperatures below freezing. Just to make sure you understand, p228, photo: orange tents and heavily clad people on an expanse of snow. Caption: The wind chill factor drops temperatures well below zero in Antarctica. Wow, I had no idea how many of those poor Katrina victims must have frozen to death. According to this table, a temperature of 5F with a 20mph wind gives a chill of -31. So the temperature of an object at 0F should decrease rapidly. Think of the starvation we could avert by giving each victim a cheap refrigerator--a fan in a box! And those stupid citrus growers actually think they can avert frost damage with giant blowers! And imagine the wind chill at 40 below and 1000mph. It must be dang near minus infinity. And yet those idiot Europeans built the Concorde out of titanium because they thought aluminum would melt! Geez I'm glad I stayed in school. Oops, here in the main text it says wind chill is only how cold it *feels*. How do you measure how cold it feels? Does snow in Saskatchewan stay frozen because the wind makes it feel cold? In a section on radioactive decay, photo: human skull. Caption: Archaeologists can approximate the age of artifacts with carbon dating. This process uses the rate of radioactive decay of cabon-14. Carbon is found in all living things, so the amount left in a bone, for example, is an indicator of the bone's age. This is a plastic casting of a skull found in 1997 in Richland Washington. Carbon dating has dated this skull as 9200 years old. It's less frightening now that I know it's plastic. I wonder if the Scientific Content Reviewers and the Accuracy Checker used their real names. This skull, by the way, is of the infamous Kennewick Man, http://www.harbornet.com/folks/theedrich/hive/Kennewic.htm . Apparently, someone slipped it past the Multicultural and Equity Reviewers. In the fractals section, p19(!): As the Koch curve develops [For some reason, the book studiously avoids the name Snowflake], segment length decreases as the number of segments increases. As you draw higher stages, the length of individual segments approaches, or gets closer and closer to, what number? What number does the number of line segments approach? ZAP! Without even knowing it, the student has been infected with the poisonous notion that infinity is a number. And the poisonous notion that this line segment recursion actually defines which points are on the fractal. There is, of course, no mention of dimension. As a student, I would wonder how Mandelbrot and Sierpinski got so much credit for "discovering" designs that people have doubtless doodled since the invention of writing. The authors could have promised a discussion of dimension in a later chapter, although it might have required a few thousand more intervening pages of photographs. E.g., antique photo of seated woman. Caption: Maria Mitchell (1818-1889) was the first professional woman astronomer in the United States. Relevance: nil. But the Multicultural and Equity Reviewers must have detected a patch of inequity. I would think that even female students would begin to doubt the competence of women, if they require such heavy-handed propaganda. Side by side on p15, Caption 1: Because a coastline, like a fractal curve, is winding and irregular, it is not possible to measure its length accurately. The Koch curve can be used as a model of a coastline. [...] Photo: Aerial shot of a pair of beautifully smooth, crescent beaches! Then, to perfect the confusion, Caption 2: At later stages, the Koch curve looks smoother and smoother.[!] But if you magnify a section at a later stage, it is just as jagged as at Stage 1. So much for self-similarity. Photo: a minority adolescent holding a magnifying glass over a Snowflake approximation to reveal a part of the initial hexagram (Heaven forbid that I say Star of David), but with HUGE, FAT line segments! Line segments are the bane to understanding fractals. A properly drawn line segment is invisible! (Except as a color boundary.) p72, problem 9: The graph at right is a hexagon [True] whose vertices are seven[!] ordered pairs. Two of the points are (3,0) and (1.5,2.6). The hexagon is centered at the origin. a. What are the coordinates of the other points? HUH?? Assuming regular, even though it isn't? There are three kinds of mathematicians: ... To sum up, p295, Caption: Wall Drug is a landmark in South Dakota. The store's fame began during the 1930s--the Great Depression--when it offered free ice water to travelers. --rwg (Confidential to you-know-who-you-are: There is only one b in Fibonacci.) --------------------------------- Take the Internet to Go: Yahoo!Go puts the Internet in your pocket: mail, news, photos & more.
Yes, I'm about to completely ignore the point of rwg's delightful book report on Algebra I texts. But let me pull out the following quote where Bill pines for the texts of old:
[...] Those books weighed maybe five times less, and contained way more than twice the algebra.
How do people feel about this construction, in which you use the phrase "five times less" to colloquially mean what a formal description would have to call "one fifth as much" or the like? This came up on a blog I read, in which commenters seemed about equally divided between "This is just fine, it's completely obvious what the construction means" and "that's literally meaningless, no reasonable person should produce such a statement." At the time I wondered what the breakdown would be among a mathematician audience, and this seems like a chance to find out. --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.
[...] Those books weighed maybe five times less, and contained way more than twice the algebra.
How do people feel about this construction, in which you use the phrase "five times less" to colloquially mean what a formal description would have to call "one fifth as much" or the like?
This came up on a blog I read, in which commenters seemed about equally divided between "This is just fine, it's completely obvious what the construction means" and "that's literally meaningless, no reasonable person should produce such a statement." At the time I wondered what the breakdown would be among a mathematician audience, and this seems like a chance to find out.
My vote is against "x times less", where x>1. I do not use it (but it is used by German speaking people as well). Christoph
I agree that it's a bad usage, rather like "500% discount!" which I never see here in the U.S. That could be taken to mean that they give you money, and it's not that different from "five times less." Steve Gray Christoph Pacher wrote:
[...] Those books weighed maybe five times less, and contained way more than twice the algebra.
How do people feel about this construction, in which you use the phrase "five times less" to colloquially mean what a formal description would have to call "one fifth as much" or the like?
This came up on a blog I read, in which commenters seemed about equally divided between "This is just fine, it's completely obvious what the construction means" and "that's literally meaningless, no reasonable person should produce such a statement." At the time I wondered what the breakdown would be among a mathematician audience, and this seems like a chance to find out.
My vote is against "x times less", where x>1. I do not use it (but it is used by German speaking people as well).
Christoph
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Monty Python: Yes, mothers, new improved Whizzo butter containing 10% more less is absolutely indistinguishable from a dead crab. Steve Gray <stevebg@adelphia.net> wrote: I agree that it's a bad usage, rather like "500% discount!" which I never see here in the U.S. That could be taken to mean that they give you money, and it's not that different from "five times less."
My patented Blammo butter has the most less cholesterol, more than 280% less than actual butter, much more less than Whizzo. Buy some today! Steve Gray Ed Pegg Jr wrote:
Monty Python: Yes, mothers, new improved Whizzo butter containing 10% more less is absolutely indistinguishable from a dead crab.
Steve Gray <stevebg@adelphia.net> wrote: I agree that it's a bad usage, rather like "500% discount!" which I never see here in the U.S. That could be taken to mean that they give you money, and it's not that different from "five times less."
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A 500% discount is bad, but it is 100% less bad than the "You can save up to 15%, or more..." that certain car insurance companies have been known to advertise. Mark -----Original Message----- From: math-fun-bounces+mdtorge=sandia.gov@mailman.xmission.com [mailto:math-fun-bounces+mdtorge=sandia.gov@mailman.xmission.com] On Behalf Of Ed Pegg Jr Sent: Thursday, August 23, 2007 10:47 AM To: math-fun Subject: Re: [math-fun] Algebra I (RiP) Monty Python: Yes, mothers, new improved Whizzo butter containing 10% more less is absolutely indistinguishable from a dead crab. Steve Gray <stevebg@adelphia.net> wrote: I agree that it's a bad usage, rather like "500% discount!" which I never see here in the U.S. That could be taken to mean that they give you money, and it's not that different from "five times less." _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Thu, 23 Aug 2007 09:28:01 -0700 Steve Gray <stevebg@adelphia.net> I agree that it's a bad usage, rather like "500% discount!" which I never see here in the U.S. That could be taken to mean that they give you money, and it's not that different from "five times less." I agree that it is bad usage because it may be confusing, but I don't think it is quite *AS* bad as misusing percent discounts. 500% discount is always meaningless (unless, as you say, they pay you 4 times the original price to take it), because we have a convention that already defines the meaning of N% discount. In contrast, there is no accepted convention that defines "a is X times less than b". Part of the reason I think "times less than" is bad (although I have to confess that I've caught myself using the phrase) is that I don't think there *is* a good way to conventionally define "a is X times less than b", because the common usage (i.e. that "a is X times less than b" is equivalent to "b is X times as much as a") is not consistent with the English language connotations of the phrase "less than". "Less than" could/should imply subtraction --- just as "2 times more than" could be the same as "3 times as much". On the other hand, defining it to be strict about "less than" implying subtraction would violate the colloquial usage, so would introduce more confusion than it would clear up. As far as RWG's original topic, I am sickened by what I see in my kids' official math textbooks [luckily my 12 and 14 year olds read other ("real") math texts recreationally]. Even when the texts aren't wrong, they rigidly mandate rules that must be followed or else the student is "wrong". We just moved coasts and the kids are entering a school which is switching to "Singapore Math" --- a curriculum that seems at odds with mathematics (it seems to really be against abstraction of any sort) and promises to be even more mind-numbingly prescriptive than the crap we've gone through until now. I am too depressed about the general topic to want to start this thread, though, unless people have useful suggestions (and home schooling is not practical for us). Science textbooks are bad in a different way: they are not as clearly *wrong* as the math books I've seen, but usually so unclear and vague that they convey *no* information whatsoever, except for some fuzzy feeling that _something_ is being explained. The specifics are never clear, it isn't quantitative (unless it is an extreme oversimplification), no causal relationships are ever described, and the notion that an experiment demonstrates or disproves something cannot be found. The entire notion that science is a way of answering real questions about the real world (one of the things that I found so exciting as a kid) is gone. In any case, this is not math "fun" --- it is math "pain" --- so doesn't belong on this list. Christoph Pacher wrote:
[...] Those books weighed maybe five times less, and contained way more than twice the algebra.
How do people feel about this construction, in which you use the phrase "five times less" to colloquially mean what a formal description would have to call "one fifth as much" or the like?
This came up on a blog I read, in which commenters seemed about equally divided between "This is just fine, it's completely obvious what the construction means" and "that's literally meaningless, no reasonable person should produce such a statement." At the time I wondered what the breakdown would be among a mathematician audience, and this seems like a chance to find out.
My vote is against "x times less", where x>1. I do not use it (but it is used by German speaking people as well).
Christoph
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A related amusing one is WRT temperatures: referring to something being twice as hot as something else [or more perplexing, half as warm or twice as cold]. /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
This makes perfect sense if you are measuring in Kelvin. I think the "five times less" is plainly a case of the general theory that one should be liberal in what one accepts, and stringent in what one produces. If you can understand it, fine. But try not to propagate the problem. On Aug 23, 2007, at 1:57 PM, Bernie Cosell wrote:
A related amusing one is WRT temperatures: referring to something being twice as hot as something else [or more perplexing, half as warm or twice as cold].
/Bernie\
-- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
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On 23 Aug 2007 at 14:07, Tom Knight wrote:
This makes perfect sense if you are measuring in Kelvin.
On Aug 23, 2007, at 1:57 PM, Bernie Cosell wrote:
A related amusing one is WRT temperatures: referring to something being twice as hot as something else [or more perplexing, half as warm or twice as cold].
Have you ever seen anybody actually intend that when they say it is "twice as warm in Phoenix as in Nome" that they mean that it is something like 500°K in Arizona that day? :o) /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
At 04:45 AM 8/23/2007, Bill Gosper wrote:
I said
PPS, my former student aced his tests but skipped his homework, and is now repeating Algebra I. As soon as I can photocopy a few pages, I'll share some of the stupendous howlers I found on a quick perusal of his new text. Amazingly, it's *not* Prentice-Hall ...
Perhaps this story will make you feel better (this jolly good Fellow was home-schooled): ---- Local teen works to advance encryption technology  By Johnny Jackson jjackson@henryherald.com Billy Dorminy runs about two miles each day on his familyÂs 23-acre property in McDonough. It is his opportunity, he says, to clear his mind and get rid of his frustrations. Occasionally, he sings a country tune or two as well. ÂI sing really badly, he said. ÂBut I have fun. A driven 16 year old, Dorminy is one year and $40,000 into collecting scholarships for college, which is still two years away. He recently received a $10,000 scholarship through the Davidson Fellows Scholarship Program, a nonprofit based in Reno, Nev. Dorminy earned the scholarship for his research and presentation on ÂImproper Fractional Base Encryption, a science project which incorporates concepts of improper fractional bases into a new encryption software. Dorminy created a new, more secure method of encryption using reduced redundancy representations of improper fractional bases, which effectively takes up less computer memory and uses both confusion and diffusion to hide messages. ÂI was thinking about these (fractional) bases, he said. ÂI thought theyÂd probably be interesting, and thereÂs probably something that hasnÂt been discovered yet. As such, his is the first secure method of encryption using improper fractional bases that allows a second encrypted message to be undetectable within the body of a main message, which itself opens a new era for encryption exploration. ÂI think BillyÂs project certainly has the possibilities of helping (a lot of people), said Tacie Moessner, Davidson Fellows program manager. ÂAnd he and all the fellows, their projects will really benefit society and move us forward in their various fields ... These students are going to be the ones who are going to change the world. Dorminy says he would like to see change toward a freer world, with less government intrusion. ÂIÂd like way less government. I believe a lot in freedom and having government stay out of our daily lives, said Dorminy, who has come to value his own autonomy over the years. As a homeschooled student, he says he is allowed to break away from the mold and pursue more intensely those things that interest him. ÂIt means I can rush through things IÂm not interested in and get to my programming, said Dorminy, who also studies advanced mathematics through the Art of Problem Solving online school. He says he hopes to continue with his mathematics and computer science studies in the Ivy League. ÂBasically, I want to get a degree from college in computer science, he said. ÂIÂd like to be a computer scientist. Though a math whiz, he says his love is computers  building them and operating them. ÂI put one together, before I took one apart, said Dorminy. He owns three himself and built one for his parents. ÂItÂs very nice; I have in-house I.T., said his mother, Ann Dorminy. ÂHeÂs never taken an IQ test. WeÂve always known he was smart, and we donÂt need anything to quantify that. Dorminy has received numerous scholarships, honors, and awards this year alone, including the Scientific Depth and Rigor scholarship from Alcatel-Lucent, the first place prize from the Association for Computing Machinery, and a perfect score on the 2007 American Mathematics Competition 10. He has also been a finalist in the ReaderÂs Digest Word Power Challenge.  On the net: Davidson Fellows: www.davidsonfellows.org Copyright © 1999-2006 cnhi, inc.
participants (10)
-
Bernie Cosell -
Bill Gosper -
Christoph Pacher -
Ed Pegg Jr -
greenwald@cis.upenn.edu -
Henry Baker -
Michael Kleber -
Steve Gray -
Tom Knight -
Torgerson, Mark D