Larry: Every college student has to pass English composition, because it is necessary for every student to be able to communicate in that language. Every student whether law, theater, art, music, engineering or science must be able to understand basic relationships whether quantitative or qualitative to function as an informed citizen, that is grasp at an elementary level such things as what global warming means, that the mortgage rate determines not just what monthly payments are but also that much more will be paid over the purchase price, etc, etc. Thus all at minimum require the "About" courses. Clearly those in STEM need to use math and science and will have to pass "Do" courses. Did i answer your question? herb On 7/30/2012 6:25 PM, Larry Romsted wrote: > Herb: > > I think I get your points, > although you did not really > address the one called do students > have to pass "About Algebra" or > "Doing Algebra." to get to college > in theater, or arts, or law > school, etc., that is some area > (major) for which traditional > algebra is of no value. > > When I wrote about teaching > algebra as a visual subject on a > computer, I had both types of > courses in mind actually. I do > organic chemistry because I am a > visual person (more than an > equation person) and because I > think equation generated graphics > are cool (especially my own). I > was found turtle graphics great > for generating images with self > generated equations, until I > realized I could not figure out > how to use them for my work. And > so it goes. > > Larry > > > > > > > From: herb fox > <[log in to unmask] > <mailto:[log in to unmask]>> > Reply-To: Science for the People > Discussion List > <[log in to unmask] > <mailto:[log in to unmask]>> > Date: Monday, July 30, 2012 5:00 PM > To: > <[log in to unmask] > <mailto:[log in to unmask]>> > Subject: Re: Is Algebra Necessary? > Rightwing Accelerates dumbing down > of US Citizens > > The article is provocative, yes, > and likely to stimulate support > from those who experienced poor > teaching of the subject. However > it is not to be dismissed. What > Hacker writes might well be > written of other subjects. > > Here is a personal experience that > i believe will better get at the > point i wish to make than an > abstracted discussion. > My 5th born, a son, was accepted > at Vassar college as a physics > major. He had taken 2 semesters of > physics in HS and an enrichment > course at Harvard. He got a kick > out of physics, by which i mean > doing cool things like competing > in building bridges. At the end of > the 1st year at Vassar he was > doing poorly in physics. Under > advisement he opted out of physics > and into the sociology of race. > The next semester, noting that he > had enrolled in a course on > relativity, i asked him why. His > answer: "I love physics; but I > don't like doing physics." Today > at 35 he plays and teaches bass, > is a recognized sound recording > engineer and does much of this > through a non-profit that serves > kids and young adults in a poor > community. At the end of his > emails is the following: "For the > rest of my life I want to reflect > on what light is." -Albert > Einstein 1916. He still can't DO > physics; but he still loves it. He > can produce a CD for a band and i, > a physicist, can't. > > There are many concepts in > mathematics and other subjects > that are usually expressed > abstractly that can be understood > by non-technical persons. These > are very important for everyone to > understand in order to be well > informed citizens. For example if > something increases at a constant > rate, no matter how small, the > amount it increases every year > will also increase and over time > it will become arbitrarily large. > That can be taught concretely by > manipulatives such as starting > with one toothpick and doubling > the number of toothpicks each day. > These are the kinds of things that > students find cool. They are like > games. They don't have to be > abstract thinkers. > > Students have differing > capabilities. We cannot teach as > if one size fits all. For some the > algebra course has to be About > Algebra. For others the course has > to be Doing Algebra. Teachers for > each of these branches must teach > quite differently. But, the answer > is not to eliminate algebra, or > physics, or etc. How will we ever > have a population that grasps that > a system that requires a constant > growth rate is unsustainable if > they do not receive an education > that enables them to grasp that > simple fact? > > herb > > > > > > On 7/30/2012 12:04 AM, Michael H > Goldhaber wrote: >> >> Andrew Hacker may be >> idiosyncratic, but calling him >> right-wing is a considerable >> stretch. >> >> I tend to agree with Larry. It is >> not necessarily more sensible to >> require algebra than to require >> physics for high school >> graduation. These courses should >> certainly be available, and >> should be well-taught, but often >> they are poorly taught in >> reality, and many otherwise >> bright people founder on these >> subjects. I know several very >> intelligent people who could not >> pass algebra, but somehow managed >> anyway to graduate from high >> school and go on and get >> doctorates. They were both lucky >> and not poor or they couldn't >> have succeeded. >> >> Also, I just encountered the sort >> of doctor who probably got into >> medical school by passing courses >> such as calculus but had nearly >> zero empathy and as a result >> nearly bungled terribly in a >> life-or-death situation. >> >> Why should possibly quite >> talented people lose out because >> of a requirement that with the >> teaching available they can't get >> their heads around are turned off >> from school? >> >> And why should math whizzes get >> high pay on Wall St. to, in >> essence, steal money from the >> pension funds of the less canny? >> >> >> Best, >> >> Michael >> >> >> On Jul 29, 2012, at 7:11 PM, >> "Romsted, Laurence" >> <[log in to unmask] >> <mailto:[log in to unmask]>> >> wrote: >> >>> >>> All: >>> >>> I want to play devil's advocate. >>> From what I could tell in the >>> comments section in response to >>> the NYTimes article: no one >>> dealt with a major issue of the >>> article, students dropping out >>> of high school or college >>> because of algebra or some math >>> requirement. (see example >>> paragraphs below) If I were to >>> guess, those students are not >>> primarily the sons and daughters >>> of middle income people or the >>> children of professionals. They >>> are from lower income families. >>> >>> So, lets ignore the beauty and >>> logic of math as being good for >>> everyone for the moment and ask >>> instead, is there a negative >>> consequence of math requirements >>> for the offspring of low income >>> people? Does the algebra >>> requirement even have a racial >>> component to it? Are many of the >>> poor math teachers in schools in >>> low income neighborhoods? >>> >>> I understand the obvious demand >>> for high quality education for >>> all, and I certainly agree, but >>> it is not hard to create an opt >>> out of algebra option for some >>> students so they can go to >>> college and get a degree in >>> something for which algebra is >>> truly unnecessary. >>> >>> I don't know how algebra is >>> currently being taught, but the >>> beauty of math relations can be >>> easily expressed by computers >>> drawing images and structures >>> that reflect the equations. Can >>> be in color too. Might encourage >>> some to want to understand the >>> relationships that lead to such >>> images. >>> >>> Nevertheless, does passing >>> algebra in high school or >>> college need to be a requirement >>> for many majors? >>> >>> Larry >>> >>> >>> *From the article* >>> >>> >>> The toll mathematics takes >>> begins early. To our nation's >>> shame, one in four ninth graders >>> fail to finish high school. In >>> South Carolina, 34 percent fell >>> away in 2008-9, according to >>> national data released last >>> year; for Nevada, it was 45 >>> percent. Most of the educators >>> I've talked with cite algebra as >>> the major academic reason. >>> >>> Shirley Bagwell, a longtime >>> Tennessee teacher, warns that >>> "to expect all students to >>> master algebra will cause more >>> students to drop out." For those >>> who stay in school, there are >>> often "exit exams," almost all >>> of which contain an algebra >>> component. In Oklahoma, 33 >>> percent failed to pass last >>> year, as did 35 percent in West >>> Virginia. >>> >>> Algebra is an onerous stumbling >>> block for all kinds of students: >>> disadvantaged and affluent, >>> black and white. In New Mexico, >>> 43 percent of white students >>> fell below "proficient," along >>> with 39 percent in Tennessee. >>> Even well-endowed schools have >>> otherwise talented students who >>> are impeded by algebra, to say >>> nothing of calculus and >>> trigonometry. >>> >>> California's two university >>> systems, for instance, consider >>> applications only from students >>> who have taken three years of >>> mathematics and in that way >>> exclude many applicants who >>> might excel in fields like art >>> or history. Community college >>> students face an equally >>> prohibitive mathematics wall. A >>> study of two-year schools found >>> that fewer than a quarter of >>> their entrants passed the >>> algebra classes they were >>> required to take. >>> >>> "There are students taking these >>> courses three, four, five >>> times," says Barbara Bonham of >>> Appalachian State University. >>> While some ultimately pass, she >>> adds, "many drop out." >>> >>> Another dropout statistic should >>> cause equal chagrin. Of all who >>> embark on higher education, only >>> 58 percent end up with >>> bachelor's degrees. The main >>> impediment to graduation: >>> freshman math. The City >>> University of New York, where I >>> have taught since 1971, found >>> that 57 percent of its students >>> didn't pass its mandated algebra >>> course. The depressing >>> conclusion of a faculty report: >>> "failing math at all levels >>> affects retention more than any >>> other academic factor." A >>> national sample of transcripts >>> found mathematics had twice as >>> many F's and D's compared as >>> other subjects. >>> >>> From: Sam Anderson >>> <[log in to unmask] >>> <mailto:[log in to unmask]>> >>> Reply-To: Science for the People >>> Discussion List >>> <[log in to unmask] >>> <mailto:[log in to unmask]>> >>> Date: Sunday, July 29, 2012 4:29 PM >>> To: >>> <[log in to unmask] >>> <mailto:[log in to unmask]>> >>> Subject: Is Algebra Necessary? >>> Rightwing Accelerates dumbing >>> down of US Citizens >>> >>> Is Algebra Necessary? >>> By ANDREW HACKER >>> July 28, 2012 - nytimes.com >>> <http://nytimes.com/> >>> >>> /*NOTE: Read the comments that >>> follow this article at the NY >>> Times >>> site:*/*http://tinyurl.com/bmsyqz7*. >>> /*They speak volumes to the >>> absurdity of this position. The >>> NY Times will give voice to this >>> rightwing nonsense, but will not >>> give voice to those eductors who >>> are providing successful >>> critical math skills to US >>> students thru new alternative >>> forms of pedgagoy and >>> curriculum. It is my hope that >>> this hack job of an essay will >>> stimulate progressive math >>> educators to quickly come up >>> with a coordinated response like >>> an open letter to Hacker and the >>> NY Times signed by hundreds of >>> math educators from K thru >>> graduate school.-- SEA*/ >>> >>> A TYPICAL American school day >>> finds some six million high >>> school students and two million >>> college freshmen struggling with >>> algebra. In both high school and >>> college, all too many students >>> are expected to fail. Why do we >>> subject American students to >>> this ordeal? I've found myself >>> moving toward the strong view >>> that we shouldn't. >>> >>> My question extends beyond >>> algebra and applies more broadly >>> to the usual mathematics >>> sequence, from geometry through >>> calculus. State regents and >>> legislators --- and much of the >>> public --- take it as >>> self-evident that every young >>> person should be made to master >>> polynomial functions and >>> parametric equations. >>> >>> There are many defenses of >>> algebra and the virtue of >>> learning it. Most of them sound >>> reasonable on first hearing; >>> many of them I once accepted. >>> But the more I examine them, the >>> clearer it seems that they are >>> largely or wholly wrong --- >>> unsupported by research or >>> evidence, or based on wishful >>> logic. (I'm not talking about >>> quantitative skills, critical >>> for informed citizenship and >>> personal finance, but a very >>> different ballgame.) >>> >>> This debate matters. Making >>> mathematics mandatory prevents >>> us from discovering and >>> developing young talent. In the >>> interest of maintaining rigor, >>> we're actually depleting our >>> pool of brainpower. I say this >>> as a writer and social scientist >>> whose work relies heavily on the >>> use of numbers. My aim is not to >>> spare students from a difficult >>> subject, but to call attention >>> to the real problems we are >>> causing by misdirecting precious >>> resources. >>> >>> The toll mathematics takes >>> begins early. To our nation's >>> shame, one in four ninth graders >>> fail to finish high school. In >>> South Carolina, 34 percent fell >>> away in 2008-9, according to >>> national data released last >>> year; for Nevada, it was 45 >>> percent. Most of the educators >>> I've talked with cite algebra as >>> the major academic reason. >>> >>> Shirley Bagwell, a longtime >>> Tennessee teacher, warns that >>> "to expect all students to >>> master algebra will cause more >>> students to drop out." For those >>> who stay in school, there are >>> often "exit exams," almost all >>> of which contain an algebra >>> component. In Oklahoma, 33 >>> percent failed to pass last >>> year, as did 35 percent in West >>> Virginia. >>> >>> Algebra is an onerous stumbling >>> block for all kinds of students: >>> disadvantaged and affluent, >>> black and white. In New Mexico, >>> 43 percent of white students >>> fell below "proficient," along >>> with 39 percent in Tennessee. >>> Even well-endowed schools have >>> otherwise talented students who >>> are impeded by algebra, to say >>> nothing of calculus and >>> trigonometry. >>> >>> California's two university >>> systems, for instance, consider >>> applications only from students >>> who have taken three years of >>> mathematics and in that way >>> exclude many applicants who >>> might excel in fields like art >>> or history. Community college >>> students face an equally >>> prohibitive mathematics wall. A >>> study of two-year schools found >>> that fewer than a quarter of >>> their entrants passed the >>> algebra classes they were >>> required to take. >>> >>> "There are students taking these >>> courses three, four, five >>> times," says Barbara Bonham of >>> Appalachian State University. >>> While some ultimately pass, she >>> adds, "many drop out." >>> >>> Another dropout statistic should >>> cause equal chagrin. Of all who >>> embark on higher education, only >>> 58 percent end up with >>> bachelor's degrees. The main >>> impediment to graduation: >>> freshman math. The City >>> University of New York, where I >>> have taught since 1971, found >>> that 57 percent of its students >>> didn't pass its mandated algebra >>> course. The depressing >>> conclusion of a faculty report: >>> "failing math at all levels >>> affects retention more than any >>> other academic factor." A >>> national sample of transcripts >>> found mathematics had twice as >>> many F's and D's compared as >>> other subjects. >>> >>> Nor will just passing grades >>> suffice. Many colleges seek to >>> raise their status by setting a >>> high mathematics bar. Hence, >>> they look for 700 on the math >>> section of the SAT, a height >>> attained in 2009 by only 9 >>> percent of men and 4 percent of >>> women. And it's not just Ivy >>> League colleges that do this: at >>> schools like Vanderbilt, Rice >>> and Washington University in St. >>> Louis, applicants had best be >>> legacies or athletes if they >>> have scored less than 700 on >>> their math SATs. >>> >>> It's true that students in >>> Finland, South Korea and Canada >>> score better on mathematics >>> tests. But it's their >>> perseverance, not their >>> classroom algebra, that fits >>> them for demanding jobs. >>> >>> Nor is it clear that the math we >>> learn in the classroom has any >>> relation to the quantitative >>> reasoning we need on the job. >>> John P. Smith III, an >>> educational psychologist at >>> Michigan State University who >>> has studied math education, has >>> found that "mathematical >>> reasoning in workplaces differs >>> markedly from the algorithms >>> taught in school." Even in jobs >>> that rely on so-called STEM >>> credentials --- science, >>> technology, engineering, math >>> --- considerable training occurs >>> after hiring, including the >>> kinds of computations that will >>> be required. Toyota, for >>> example, recently chose to >>> locate a plant in a remote >>> Mississippi county, even though >>> its schools are far from >>> stellar. It works with a nearby >>> community college, which has >>> tailored classes in "machine >>> tool mathematics." >>> >>> That sort of collaboration has >>> long undergirded German >>> apprenticeship programs. I fully >>> concur that high-tech knowledge >>> is needed to sustain an advanced >>> industrial economy. But we're >>> deluding ourselves if we believe >>> the solution is largely academic. >>> >>> A skeptic might argue that, even >>> if our current mathematics >>> education discourages large >>> numbers of students, math itself >>> isn't to blame. Isn't this >>> discipline a critical part of >>> education, providing >>> quantitative tools and honing >>> conceptual abilities that are >>> indispensable --- especially in >>> our high tech age? In fact, we >>> hear it argued that we have a >>> shortage of graduates with STEM >>> credentials. >>> >>> Of course, people should learn >>> basic numerical skills: >>> decimals, ratios and estimating, >>> sharpened by a good grounding in >>> arithmetic. But a definitive >>> analysis by the Georgetown >>> Center on Education and the >>> Workforce forecasts that in the >>> decade ahead a mere 5 percent of >>> entry-level workers will need to >>> be proficient in algebra or >>> above. And if there is a >>> shortage of STEM graduates, an >>> equally crucial issue is how >>> many available positions there >>> are for men and women with these >>> skills. A January 2012 analysis >>> from the Georgetown center found >>> 7.5 percent unemployment for >>> engineering graduates and 8.2 >>> percent among computer scientists. >>> >>> Peter Braunfeld of the >>> University of Illinois tells his >>> students, "Our civilization >>> would collapse without >>> mathematics." He's absolutely right. >>> >>> Algebraic algorithms underpin >>> animated movies, investment >>> strategies and airline ticket >>> prices. And we need people to >>> understand how those things work >>> and to advance our frontiers. >>> >>> Quantitative literacy clearly is >>> useful in weighing all manner of >>> public policies, from the >>> Affordable Care Act, to the >>> costs and benefits of >>> environmental regulation, to the >>> impact of climate change. Being >>> able to detect and identify >>> ideology at work behind the >>> numbers is of obvious use. Ours >>> is fast becoming a statistical >>> age, which raises the bar for >>> informed citizenship. What is >>> needed is not textbook formulas >>> but greater understanding of >>> where various numbers come from, >>> and what they actually convey. >>> >>> What of the claim that >>> mathematics sharpens our minds >>> and makes us more intellectually >>> adept as individuals and a >>> citizen body? It's true that >>> mathematics requires mental >>> exertion. But there's no >>> evidence that being able to >>> prove (x^(2) + y^(2))^(2) = >>> (x^(2) - y^(2))^(2) + (2xy)^(2) >>> leads to more credible political >>> opinions or social analysis. >>> >>> Many of those who struggled >>> through a traditional math >>> regimen feel that doing so >>> annealed their character. This >>> may or may not speak to the fact >>> that institutions and >>> occupations often install >>> prerequisites just to look >>> rigorous --- hardly a rational >>> justification for maintaining so >>> many mathematics mandates. >>> Certification programs for >>> veterinary technicians require >>> algebra, although none of the >>> graduates I've met have ever >>> used it in diagnosing or >>> treating their patients. Medical >>> schools like Harvard and Johns >>> Hopkins demand calculus of all >>> their applicants, even if it >>> doesn't figure in the clinical >>> curriculum, let alone in >>> subsequent practice. Mathematics >>> is used as a hoop, a badge, a >>> totem to impress outsiders and >>> elevate a profession's status. >>> >>> It's not hard to understand why >>> Caltech and M.I.T. want everyone >>> to be proficient in mathematics. >>> But it's not easy to see why >>> potential poets and philosophers >>> face a lofty mathematics bar. >>> Demanding algebra across the >>> board actually skews a student >>> body, not necessarily for the >>> better. >>> >>> I WANT to end on a positive >>> note. Mathematics, both pure and >>> applied, is integral to our >>> civilization, whether the realm >>> is aesthetic or electronic. But >>> for most adults, it is more >>> feared or revered than >>> understood. It's clear that >>> requiring algebra for everyone >>> has not increased our >>> appreciation of a calling >>> someone once called "the poetry >>> of the universe." (How many >>> college graduates remember what >>> Fermat's dilemma was all about?) >>> >>> Instead of investing so much of >>> our academic energy in a subject >>> that blocks further attainment >>> for much of our population, I >>> propose that we start thinking >>> about alternatives. Thus >>> mathematics teachers at every >>> level could create exciting >>> courses in what I call "citizen >>> statistics." This would not be a >>> backdoor version of algebra, as >>> in the Advanced Placement >>> syllabus. Nor would it focus on >>> equations used by scholars when >>> they write for one another. >>> Instead, it would familiarize >>> students with the kinds of >>> numbers that describe and >>> delineate our personal and >>> public lives. >>> >>> It could, for example, teach >>> students how the Consumer Price >>> Index is computed, what is >>> included and how each item in >>> the index is weighted --- and >>> include discussion about which >>> items should be included and >>> what weights they should be given. >>> >>> This need not involve dumbing >>> down. Researching the >>> reliability of numbers can be as >>> demanding as geometry. More and >>> more colleges are requiring >>> courses in "quantitative >>> reasoning." In fact, we should >>> be starting that in kindergarten. >>> >>> I hope that mathematics >>> departments can also create >>> courses in the history and >>> philosophy of their discipline, >>> as well as its applications in >>> early cultures. Why not >>> mathematics in art and music --- >>> even poetry --- along with its >>> role in assorted sciences? The >>> aim would be to treat >>> mathematics as a liberal art, >>> making it as accessible and >>> welcoming as sculpture or >>> ballet. If we rethink how the >>> discipline is conceived, word >>> will get around and math >>> enrollments are bound to rise. >>> It can only help. Of the 1.7 >>> million bachelor's degrees >>> awarded in 2010, only 15,396 --- >>> less than 1 percent --- were in >>> mathematics. >>> >>> I've observed a host of high >>> school and college classes, from >>> Michigan to Mississippi, and >>> have been impressed by >>> conscientious teaching and >>> dutiful students. I'll grant >>> that with an outpouring of >>> resources, we could reclaim many >>> dropouts and help them get >>> through quadratic equations. But >>> that would misuse teaching >>> talent and student effort. It >>> would be far better to reduce, >>> not expand, the mathematics we >>> ask young people to imbibe. >>> (That said, I do not advocate >>> vocational tracks for students >>> considered, almost always >>> unfairly, as less studious.) >>> >>> Yes, young people should learn >>> to read and write and do long >>> division, whether they want to >>> or not. But there is no reason >>> to force them to grasp vectorial >>> angles and discontinuous >>> functions. Think of math as a >>> huge boulder we make everyone >>> pull, without assessing what all >>> this pain achieves. So why >>> require it, without alternatives >>> or exceptions? Thus far I >>> haven't found a compelling answer. >>> >>> /*Andrew Hacker is an emeritus >>> professor of political science >>> at Queens College, City >>> University of New York, and a >>> co-author of "Higher Education? >>> How Colleges Are Wasting Our >>> Money and Failing Our Kids --- >>> and What We Can Do About It."*/ >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> ---------------------------------- >>> s. e. anderson >>> author of The Black Holocaust >>> for Beginners >>> www.blackeducator.org >>> <http://www.blackeducator.org/> >>> www.blackeducator.blogspot.com >>> <http://www.blackeducator.blogspot.com/> >>> If WORK was good for you, the >>> rich would leave none for the >>> poor. (Haiti) >>> -------------------------------------------- >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> Sent from Sam + Rosemari's iPad >> >