Math Quotes


"In my opinion, two-thirds of the students are doing
just fine in math class. The other 15% just needs a
little more help."
Found in the Soundoff section of Seattle PI article


(Opposed) The objections to the revised standards, while motivated by genuine concerns, are not well thought out. Someone ran for a local school board based solely on the platform that calculators not be used through 8th grade. This would effectively remove from instruction the Pythagorean theorem and the theory of compound interest. Doing these calculations by hand would be a waste of valuable instruction time. People who object to the standards typically want to go back to a way of instruction from the 1950s and 60s, which is to explain a math concept and do problems until the theory is well grounded. Today's instructors are trying to think about math problems in a real world context. The revised standards are not perfect. But people who have looked at them see improvements in emphasis on computational fluency. There is no reason for further delay. Bill Marsh---testimony before the Washington State K-12 education committees

Wow, my 5th grader was able to compute Pythagorean theorem w/out a calculator last Friday and get the correct answer...it didn't take him long, he thoroughly understands the formula and how it is used. Bill Marsh better make sure he doesn't play the game "Are you smarter than a 5th grader"! Parent comment.



"Strange as it sounds, the power of mathematics rests on its evasion
of all unnecessary thought and on its wonderful saving of mental
operations."
-- Ernst Mach, physicist

"A mastered algorithm in the hands of a student is an incomparable
tool laying bare the conceptual structure of the mathematical
problems that the algorithm solves. With such tools, and with the
guidance of good teachers in their use, a student can grasp and
integrate in twelve years a body of mathematics that it has taken
hundreds of geniuses thousands of years to devise."
 David Ross, Ph.D., a mathematician at Kodak Research Labs


Mathematics is the language in which God has written the universe...
-Galileo Galilei


“You can buy mathematical software, for less than $50, that will compute for you the derivatives of any functions you are ever likely to run across. So why should you learn how to compute derivatives for yourself? A reasonable answer is that you should know enough of what is going on to have an idea of what kinds of answers to expect, so that you can at least monitor that you are using the software and entering formulas correctly. If you have no idea of what to expect in the way of an answer, you will have nothing to clue you in to the fact that, for example, you might have made a typo entering the formula of the function to be differentiated. The reason for learning not only the formulas for computing derivatives, but also how to compute some derivatives from the definition, is to see that the rules and formulas for derivatives are not magical – they come from somewhere, and can be figured out and understood by real human beings. Education should not be a matter of memorizing mysterious formulas – it should be a matter of understanding.

Quote from the book Calculus by Elliot C. Gootman, Ph.D.


It would be easy to make a sweeping generalization that everyone must study calculus or risk being left behind in today’s technologically advanced industrial society. However, we will always live in a society in which there is plenty of demand for people who will pick up animal carcasses off the highway and staff the guardhouses at the local retirement villages. But it is also true that most of the higher-paying jobs, particularly those in emerging high-technology industries, require some mathematical aptitude. More and more, the ability to converse knowledgeably about quantitative ideas and to understand mathematical concepts is becoming the prerequisite for a successful career.

Weaver, Jefferson Hane. Conquering Calculus: The Easy Road to Understanding Mathematics. Plenum Press, NY. 1998.

If yuo cna raed tihs, yuo hvae an itnerseting mnid! Cna yuo raed this?
Olny 55 plepoe out of 100 can. i cdnuolt blveiee taht I
cluod aulaclty uesdnatnrd what I was rdanieg. The
phaonmneal pweor of the hmuan mnid, aoccdrnig to a Rsheearch at
Cmabrigde Uinervtisy, it dseno't mtaetr in waht oerdr the ltteres in a
word are, the olny iproamtnt tihng is taht the frsit and last ltteer be in
the rghit pclae. The rset can be a taotl mses and you can still raed it
whotuit a pboerlm. Tihs is bcuseae the huamn mnid deos not raed ervey
lteter by istlef, but the wrod as a wlohe. Azanmig huh? yaeh and I awlyas
tghuhot slpeling was ipmorantt! if you can raed tihs forwrad it.


“While we applaud those districts and teachers who say they are getting results from other programs, effectiveness was not one of our criteria.”
Susan Stickel, asst. supt. in Elk Grove and member of the state curriculum commission advising the California board on textbooks, 2001.


Math Standards fun:
Order numerals from 1 to 10.
I'll have a 6 with ketchup and onions and a 9 on the side. To go please. Thank you very much.

Math Quotes - Mathematically Sound Foundations

This following quote very much applies to math standards.

Progressives do not want clear standards. They understand that without such standards it is nearly impossible to engage in so-called “high-stakes” testing to enforce accountability, that is, to retain poor-performing students and to terminate poor-performing teachers and schools. Progressives prefer no-stakes, no “pain” testing. Kohn has said, “learning is threatened by specific, measureable, uniform standards.” Better we should have loose, unmeasureable standards, because then we can avoid any consequences for failure. ... The pacific Research Institute, relying on the testimony of Susan Phillips of Michigan State University, concludes: “Some people think that multiple-choice items can only measure factual knowledge and basic skills. That’s not true. Well-written multiple-choice items can measure higher-order thinking skills. Likewise, performance assessments don’t necessarily measure higher-order skills… The bottom –line is that multiple-choice questions offer the best value in terms of cost, breadth, reliability, validity, and ability to generalize.”

p. 212 Class Warfare: Besieged Schools, Bewildered Parents, Betrayed Kids and the Attack on Excellence by J. Martin Rochester

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