+OK 17414 octets Received: from smtp03.nwnexus.com (smtp03.nwnexus.com [206.63.63.41]) by mail3.halcyon.com (8.8.8/8.8.8) with ESMTP id JAA14940 for ; Fri, 2 Jul 1999 09:54:50 -0700 (PDT) From: rdyarrow@elnet.com Received: from mail-p.elnet.com (root@mail-p.elnet.com [206.148.64.15]) by smtp03.nwnexus.com (8.8.8/8.8.8) with ESMTP id JAA09142 for ; Fri, 2 Jul 1999 09:54:34 -0700 (PDT) Received: from shell0.elnet.com (root@shell0.elnet.com [206.148.64.13]) by mail-p.elnet.com (8.8.5/8.8.5) with ESMTP id NAA03642; Fri, 2 Jul 1999 13:52:25 -0500 Received: from damer (cpm503.elnet.com [209.224.239.64]) by shell0.elnet.com (8.8.5/8.8.5) with SMTP id MAA02616; Fri, 2 Jul 1999 12:12:45 -0500 Message-Id: <199907021712.MAA02616@shell0.elnet.com> X-Sender: rdyarrow@shell0.elnet.com (Unverified) X-Mailer: QUALCOMM Windows Eudora Pro Version 4.0 Date: Fri, 02 Jul 1999 11:51:58 -0500 To: rdyarrow@elnet.com Subject: Early use of Calculator Debate Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Status: I have always closely followed the calculator debate on the K-12 Math Usenet Group because I am always interested in teacher's attempts to defend the ever-present calculator in the elementary grades. Since they have no research support, I am not surprised that some of them use "boredom" for their defense. Recently the debate has seemed more intense than two or three years ago, and I thought that some of you might be interested in the postings of educators who are opposed to early rampant calculator use. This first article is especially interesting. I didn't include the pro-calculator posts which still make me grimace. Mary 1. Article: 1 of 1 From: Domenico Rosa Subject: FW: calculator article Date: Tue, 15 Jun 1999 22:58:14 GMT A slightly edited version of the following article has been published in the May 1999 issue of Math ed Dialogues with the title "Do we need calculators?" Dom Rosa =========================== We all use calculators in daily life; why should we forbid them in school mathematics classes, hobbling our children as we would never think to hobble ourselves? I believe, nonetheless, that calculators are often detrimental to the teaching of mathematics. As the mathematician Ralph Raimi has written, "Education is not imitation of life; it is an artificial process designed to put ideas into the mind and not answers on paper." At the K-6 level, and given the knowledge base of our average teacher, calculators only produce answers. From the TIMSS results it is clear that mathematical competence at the k-6 level does not require calculators. Two of the highest achieving countries at the 4th and 8th grade levels, Singapore and Japan, use calculators sparingly in elementary schools. At the 7-16 level we might do well to heed the voices of those with the most experience with calculator usage. John Duncan, a mathematics professor at the University of Arkansas and an early advocate for technology in a college setting, wrote these cautionary words in 1995, "Some of us who were very early to use technology to alleviate drudgery, to visualize graphs and surfaces, to conduct helpful experiments, etc. are now alarmed at its use as a substitute for thinking. It even seems to deter problem-solvers from producing general mathematical proofs by holding their focus to computing a few numerical examples."[1] Overseas, Great Britain has been at the forefront of using calculators in both elementary and secondary settings since the 1982 Cockcroft Report. Anthony Gardiner, a mathematician from the University of Birmingham, has graded thousands of competition papers and has developed an excellent sense of the shift in mathematical capabilities of students in his country over the past 15 years. According to Gardiner the worst effects of calculator usage are: (1) The loss of experience in SIMPLIFYING and the consequent loss of student (and teacher/examiner) expectation that expressions should have any MEANING. (2) The DESTRUCTION WITHIN HALF A GENERATION of a hard won, effective algebraic symbolism - developed and proven over centuries, capable of being manipulated as a "calculus" for exact numerical and symbolic calculations, and its replacement by slavish verbatim copies of what appear in calculator displays. (3) The collapse within 10 years of arithmetical fluency within the very best students - with the resulting loss of meaning for symbolic generalizations of numerical expressions. (4) The loss of all attempts to teach pupils to present solutions in forms that others can make sense of - and the decline into mere personal jottings en route to an answer. (5) Which is related - I suspect - to the two most damning outcomes of post-Cockcroftian innovations: (i) The astonishing switch from solving simple problems (i.e. METHODS) to caring only about ANSWERS (i.e. things which appear in the display of a calculator) - exactly the opposite effect of what the innovators claimed they wanted, and so horribly widespread that no one can pretend not to know what has happened; (ii) The inability of students to solve two-step problems, because teachers and examiners have learned to accept mere answers since psychologically it is almost impossible to train students who are expected to use a calculator to write anything else down on paper.[2] One might assume from what I have written and quoted that I am an anti-tech Luddite who forces his students to do thousands of long division problems by guttering candlelight. Not so. I have a dozen computers in my room and 10 ti-92's for student use. But I think too much of my students and the mathematics they need to learn to condemn them to a black box paradise of mindless button pushing merely for the sake of being on the cutting edge of the math reform movement. [1] American Mathematical Monthly, 102(1995), p.194. [2] personal email. Bio: Kim Mackey has taught math and science in Alaska for 12 years. In 1994 he received a Distinguished Teacher award from the White House Commission on Presidential Scholars, and in 1998 he was honored as the National Academic Decathlon Coach of the Year. Kim Mackey Box 1996 Valdez, Alaska 99686 2. Article: 3 of 3 From: Dan Vande Bunte Subject: Re: Influence of Calculators Date: Thu, 27 May 1999 13:15:06 GMT I've made this argument before, and I will make it again. Because students are allowed to use calculators too soon, high school students...HIGH SCHOOL STUDENTS!...do not know that negative numbers squared are positive numbers. Even worse, they do not know that ANY negative number times any OTHER negative number is positive. I've warned them too many times that typing "-3^2" into their calculators often yields incorrect responses due to the implicit order of operations used in the programming of the calculator. Which reminds me, they don't even know the order of operations! THe fundamental issue at stake here is not calculators vs. no calculators. It is philosophical. In order to appropriately answer the calculator question, we must be able to clearly and coherently articulate a sound philosophy of mathematics education. Those who push calculator use tend to feel that mathematics education consists of teaching students a pre-determined list of topics and subjects in the hopes that they learn how to DO math. These are people who are generally considered "applied" mathematicians. Those who urge against the use of calculators tend to see mathematics education as consisting of numerous things: certain topics and subjects, DOING math, LEARNING math, learning mathematical REASONING, developing problem solving abilities, and generally giving students insights into what mathematics is and is about (i.e. what is it that mathematicians do). These people are generally considered "pure" mathematicians. What's the real difference? Applied mathematicians tend not to care about how a theorem or theory was developed, only how it is used. Hence the emphasis on DOING math. Pure mathematicians care little about practical application and more about the beauty that IS mathematics. They care very little about the extra-curricular, and more about thinking mathematically. Hence the emphasis on theory. I myself, if it isn't already obvious, consider myself a "pure" mathematician, often "doing" mathematics just for fun. Hence my displeasure with calculators. Don't get me wrong, they can be useful, but their overuse is something I consider to be a great disjustice to mathematics education. To complicate matters even further, applied mathematicians and pure mathematicians seldom LIKE each other. Applied mathematicians often see mathematical theory with no "real life" application or use as being, well, useless. Obviously, such a philosophy of mathematics would be disconserting to those who are good at, and generally enjoy mathematical theory. Pure mathematicians often find "real life" application as irrelevant to the study of mathematics. Mathematics is worthy of study in its own right, and not contingent on its practical use. This, clearly, is upsetting to those who have devoted their lives to applying mathematical theories to real life. Personally, my own philosophy of mathematics education is a synthesis of both. There are certain topics and subjects which must be taught. Certain abilities must be mastered. Applications must be tied into theory, but theory does not necessarily have to be tied into application. I.e. application must have basis, but theory needs no ornaments. I also feel very strongly that mathematics education must also teach students what mathematicians do. Notation, proofs, reasoning, skill, memorization, and much more that, unfortunately, most students do not see the importance of. With this in mind, using calculators to teach multiplication facts is bad. Using calculators to calculate standard deviations is good. Daniel J. Vande Bunte dvbunt86@calvin.edu (stuff I can access on campus or at home)* DanVandeBunte@msn.com (stuff I can only access from home) danvandebunte@hotmail.com (stuff I can access on campus or at home)* * = your best bet of having me see your message before 11pm. ---------------------------- message approved for posting by k12.ed.math moderator k12.ed.math is a moderated newsgroup. charter for the newsgroup at www.wenet.net/~cking/sheila/charter.html submissions: post to k12.ed.math or e-mail to k12math@sd28.bc.ca 3. Article: 1 of 2 From: Sbehel1234 Subject: Calculators in the Classroom 4th grade Date: Mon, 31 May 1999 16:27:43 GMT I want to use both drill and calculators in the classroom for teaching math. I love math and patterning(great book called Mathographics by Robert Dixon) and the whole "game." What are the general knowledges of the professional readers on this subject? Have there been research studies on this subject to your knowledge? Please include experiences with the abacus. Enlighten me. ---------------------------- message approved for posting by k12.ed.math moderator k12.ed.math is a moderated newsgroup. REPLY: Article: 2 of 2 From: Thomas W. Cowdery Subject: Re: Calculators in the Classroom 4th grade Date: Mon, 31 May 1999 17:33:40 GMT My first reaction is YOU ARE GOING TO ROT THEIR BRAINS! OK, now that the blood pressure is back to normal, an occasional project using calculators in the 4th grade probably won't do any lasting damage, but PLEASE actively discourage using them on a regular basis. Check out www.coe.ilstu.edu/jabraun/students/cowdery/titlepage.htm for a paper I once wrote for a grad class about using calculators in elementary school (putting it out as a web page was also part of the class). -- _.-'`'-._.-'`'-._.-'`'-._.-'`'-._.-'`'-._.-'`'-._.-'`'-._.-'`'-._.-'`'-._.-' `'-. "We Have Met The Enemy, And He Is Us" Walt Kelley's Pogo tcowdery@usa.net (work) cowderyt@district87.org ---------------------------- message approved for posting by k12.ed.math moderator k12.ed.math is a moderated newsgroup. charter for the newsgroup at www.wenet.net/~cking/sheila/charter.html submissions: post to k12.ed.math or e-mail to k12math@sd28.bc.ca 4. Article: 1 of 2 From: Doug Porter Subject: Reply to "Influence of Calculators" Date: Thu, 03 Jun 1999 13:30:39 GMT I believe calculators should be limited in the high school classroom. From geometry through calculus, calculators are necessary and important tools. But those students who are taking algebra or pre-algebra, the use of calculators should be limited. Many of these students cannot do basic fraction operations, nor can they perform computations with positive and negative integers. My pre-algebra students never use calculators and my algebra students only use them with radicals and scientific notation. One big problem is the fraction key. Many middle school teachers in our system let the students use this key. Thus, the students do not learn the basic rules of fractions. ---------------------------- message approved for posting by k12.ed.math moderator k12.ed.math is a moderated newsgroup. charter for the newsgroup at www.wenet.net/~cking/sheila /charter.html submissions: post to k12.ed.math or e-mail to k12math@sd28.bc.ca 5. Article: 2 of 2 From: Mark Bouwmeester Subject: Re: Reply to "Influence of Calculators" Date: Thu, 10 Jun 1999 01:07:03 GMT IMHO, the problem here is that kids learn to do questions like 3/4 + 1/2 on a calculator (which is what a calculator is for) but never learn the rules for adding (or subtracting, or multiplying, or dividing) fractions. Then they get to a question like (x+5)/(2x-3) + x/(x+1). Calculator can't help here. You need to know how to do addition and subtraction of fractions to simplify this correctly. The answer is certainly not (2x+5)/(3x-2), although I bet this is a very common error. (Of course some of the Newest, most advanced calculators may be able to do this, but how many students have access to these calculators?) A possible list of 4 most important things to know: addition, subtraction, multiplication and division of fractions Pythagorean Theorem how to set up a proportion addition, subtraction, multiplication and division of polynomials Howard L. Hansen wrote in message news:37597656.43223807@news.gte.net... Doug, Please tell me more about the "basic rules of fractions" and "fraction operations." What do you believe are the 5 most important things a pre-algebera student should learn in your class? Ditto for algebra. 6 Article: 4 of 4 From: William L. Bahn Subject: Re: Use of calculators Date: Tue, 08 Jun 1999 03:21:07 GMT And, just in time to illustrate the points that many of us have been trying to make, here is a post from one of the electronics newsgroups. It is quite typical of far too many many posts. RBanks wrote in message <7jg63s$knu$1@topsy.kiva.net>... I am stuck on this problem in my electronics class. Can someone please help me? _______1_______ fr = 6.28 * sqrt LC I need to solve for L. How do I get it by itself? This person needs to be sent back to about 6th grade (or further) and when they have actually learned the stuff that they should have learned the first time through, then they should be allowed to pursue their education in electronics. William L. Bahn wrote in message <375b4c1d.28187701@news.gte.net>... And then, some day, this person gets to the point where they need to use a microcontroller that can add and subtract single byte values and write a program to multiply two bytes together. They will be clueless. I've seen it happen. And when they need to divide two bytes they might as well drop out of college and go get a job at Burger King so that they can rely on Burger King's cash register to do their math for them (saw that happen once, too). I think it's pretty sad when you have college seniors in electrical engineering and the instructor has to spend several class periods teaching the basics of what a positional numbering system is, how you perform multi-digit multiplication using only single-digit multiplication and addition and how you perform long-division - i.e., fourth and fifth grade math. Your recommendation of only drilling them to the "fives" means that you are expecting and actively encouraging that we make sure that people cannot multiply ANYTHING without using a calculator. They buy lunch someplace and the bill totals $6.00 and they can't figure out how much money to leave for a tip because that involves multiples of 6 and we don't teach that anymore. Sbehel1234 wrote in message <37589d83.53254152@news.gte.net>... Objective: To get on with math applications and stretch the students' quantitative skills......... Why would one not teach the concept of multiplication to the "fives," drill >and memorize them, and leave it at that, going on to the calculator? The long .