Published on

11-Jan-2017View

212Download

0

Transcript

A mathematical treasure huntAuthor(s): Richard CrouseSource: The Mathematics Teacher, Vol. 80, No. 2 (FEBRUARY 1987), p. 81Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27965251 .Accessed: 16/06/2014 16:12Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp .JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org. .National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Mathematics Teacher.http://www.jstor.org This content downloaded from 129.174.21.5 on Mon, 16 Jun 2014 16:12:07 PMAll use subject to JSTOR Terms and Conditionshttp://www.jstor.org/action/showPublisher?publisherCode=nctmhttp://www.jstor.org/stable/27965251?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jspPBflllCP PB|l6C|?0nS Reactions to articles and points of view on teaching mathematics _____mm _^^^^^^^M^^^^^^^%4t^?^^^? A mathematical treasure hunt While teaching a course for new students at our university, I real ized that they did not know their way around the campus. To help them, I introduced the idea of a treature hunt using mathematical problems. The eighteen students were divided into six groups of three, and each group was given a copy of the campus map on which the buildings were numbered. The treasure hunt began when the fol lowing problem was put on the chalkboard : The number you want is the minimum value of y = 2 ? 4x + 105. The students were told to solve the problem and that the correct answer (101) was the number of a building on campus. They were to use the map to locate the building and then proceed to that building, where another prob lem, taped on the front door, would be waiting for them. They were then to solve the problem and find the next building. The group that came in first at the last building with all problems solved by all the students in that group would re ceive a prize. The problems used for this trea sure hunt covered material they had just learned. Variations of this activity could be used for locations within a classroom or outside a school. Richard Crouse University of Delaware Newark, DE 19716 Double your identities Running out of identities and tired of working them backward to make Because of space limitations, letters may be subject to abridgment. Although we are unable to acknowledge those letters that cannot be published, we appreciate the interest and value the views of those who take the time to send us their com ments. Readers who are commenting on articles are encouraged to send copies of their correspondence to the authors. Please double-space all letters that are to be considered for publication. up new ones? Merely exchange the functions with the cofunctions, and vice versa. That way, you double your pool of exercises with mini mal effort. The given identity 1 + sin cos -1-:? = 2 sec cos 1 + sin becomes 1 + cos sin -:-h-= 2 esc . sin 1 + cos Vincent J. Hawkins University of Hartford West Hartford, CT 06117-0395 American eyes As a mathematics supervisor, I've circulated the article "British Eyes on American Mathematics" in the December 1985 issue. It has done wonders to convince our teachers of the foibles of our present cur riculum. Naturally, I was appalled when I read Norma Cummings's letter (September 1986, p. 408-9). The implication that students going on to higher education need such wonderful things as 2| 4?? and long division is totally ludi crous because (1) it is not for the college bound that these items are in our curriculum ; (2) I doubt that 50 percent of our student popu lation goes on to higher education (and these people need thinking skills, not rote repetition of drills) and (3) what options are kept open by mindless algorithms? Surely Cummings is not implying that long division teaches thinking. But the crowning blow was the " appli cability of logarithms" to piano tuning. I really would like to see educa tors pay more than lip service to problem solving, estimation, and creativity in mathematics. For the most part, mathematics consists of those boring forty-five to sixty min utes in the day when students get yet another worksheet with yet an other set of fifty exercises in long division or fabulous fraction addi tion (e.g., 3/59 + 7/65). Such a "hard-nosed single track" leads our students to boredom, hatred of mathematics, and the belief that mathematics occurs nowhere once they step out of the classroom. It is not the " opportunity to compare teaching philosophies" that is important. It's the lessons we should be gleaning from these philosophies. Hector Hirigoyen Dade County Public Schools Miami, FL 33135 Norma Cummings responds : I ap preciate the opportunity to reply to Hirigoyen's comments. 1. My description of the gener al exams used in Britain indicates a widespread use of multiple-choice tests. 2. Many students are unable to solve equations with fractional co efficients because they cannot multiply or divide fractions. Also, long division skills are necessary to do polynomial division. College bound students do need to master these operations. I agree com pletely with your statement that thinking skills are of paramount importance, but if one cannot do elementary arithmetic and alge braic manipulations, problems will remain unsolved. 3. According to the 1984 U.S. Census, 13 million people aged eighteen to twenty-four had com pleted only high school and 9.5 mil lion had completed one to four years of college, indicating that 42.2 percent of high school gradu ates pursue further education. This is far higher than the 12 percent in Britain. 4. I quoted my piano tuner only to note that one cannot always assume that old aproaches are ob solete. I spent a month in China this summer and saw the abacus used everywhere with great ef ficiency. I would not recommend that we throw away our calcu lators or computers, but there may be places where old techniques are appropriate. 5. The strength of the British system lies in its individualized programs. I wish more of this were February 1987-81 This content downloaded from 129.174.21.5 on Mon, 16 Jun 2014 16:12:07 PMAll use subject to JSTOR Terms and Conditionshttp://www.jstor.org/page/info/about/policies/terms.jspArticle Contentsp. 81Issue Table of ContentsThe Mathematics Teacher, Vol. 80, No. 2 (FEBRUARY 1987), pp. 81-167Front Matterreader reflectionsA mathematical treasure hunt [pp. 81-81]Double your identities [pp. 81-81]American eyes [pp. 81-82]Reuleaux polygons II [pp. 82-82]Summer experience [pp. 82-82]Factor wars [pp. 83-83]Mathematical trivia [pp. 83-84]Much ado about canceling [pp. 84-84]Student discovery [pp. 84-84]Prime number theorem [pp. 84-85]Keep up with the Joneses [pp. 85-86]APL prime-number generator [pp. 86-86]The Shortest Route [pp. 88-93, 142]You Can't Get There from Herean Algorithmic Approach to Eulerian and Hamiltonian Circuits [pp. 95-98, 148]Two Views of Oz [pp. 100-101]A Matrix Method for Generating Pythagorean Triples [pp. 103-108]applicationsTHE EXPONENTIAL-DECAY LAW APPLIED TO MEDICAL DOSAGES [pp. 110-113]sharing teaching ideasTHE CHAIN LETTER: AN EXAMPLE OF EXPONENTIAL GROWTH [pp. 114-115]BOX TECHNIQUE FOR FACTORING [pp. 115-118]INTEGRATING THE INVERSE OF A FUNCTION WHOSE INTEGRAL IS KNOWN [pp. 118-120][February Calendar] [pp. 122-124, 121]activitiesPERIODIC PICTURES [pp. 126-137]Game Theory: An Application of Probability [pp. 138-142]Studying Decimal Fractions with Microcomputers [pp. 144-148]Teaching ProbabilitySome Legal Applications [pp. 150-153]microcomputer-assisted mathematicsLESSONS LEARNED WHILE APPROXIMATING PI [pp. 154-159]NEW publicationsFrom NCTMReview: untitled [pp. 161-161]From Other PublishersReview: untitled [pp. 161-161]Review: untitled [pp. 161-161]Review: untitled [pp. 161-162]Review: untitled [pp. 162-162]Review: untitled [pp. 162-162]Review: untitled [pp. 162-162]Review: untitled [pp. 162-163]Review: untitled [pp. 163-163]Review: untitled [pp. 163-164]Review: untitled [pp. 164-164]Review: untitled [pp. 164-164]Review: untitled [pp. 164-164]Review: untitled [pp. 164-165]Review: untitled [pp. 165-165]Review: untitled [pp. 165-165]Review: untitled [pp. 165-166]Review: untitled [pp. 166-166]Review: untitled [pp. 166-166]Review: untitled [pp. 166-166]NEW Projects [pp. 166-167]Back Matter