Is Review Really Necessary?

Joseph ToddNewton D. Baker Junior High School, Cleveland, Ohio

Most educators are agreed that with the rise of science and tech-nology something beyond ordinary arithmetic may be needed for theworker of tomorrow. Many students without present college aspira-tions will find themselves forced by economic pressures to extendtheir educational resources through technical school or college, yet donot elect the algebra courses currently offered. Consider the followingpupils:

Joe A., I.Q. 105, arithmetic achievement 8.8. Joe is planning to take an auto-motive mechanics course and does not see why he should take algebra.John B., I.Q. 95, arithmetic achievement 8.1. John failed algebra last semester

and decided upon the advice of his teacher to change to general mathematics.He would like to go into radio and television repair.June C., I.Q. 110, arithmetic achievement 9.7. June can see some need for

mathematics but decides to take the easier course.

A typical general mathematics course begins with a six to eightweek review of the fundamental operations in natural numbers, com-mon fractions and decimals and contains, in the first semester, a studyof percentage. This is as it should be, since many pupils profit fromthis review7. But what of the pupils mentioned above? How can weavoid wasting their talents? Perhaps an intermediate offering betweenthe algebra designed to prepare for further study in mathematics andthe arithmetic review is the answer.The writer visualizes a course of study designed to be terminal�

containing a survey of interest, installment buying, insurance, andother aspects of business mathematics needed for consumer life�butincluding enough algebra to enable those finishing to handle formulasencountered in a high school level chemistry or physics course. Thisshould be ample for future technical courses these pupils may en-counter.The material w^ould center upon the formula and equations result-

ing from substitution into formulas. From a regular algebra coursefactoring, some complex fractions, all quadratic equations not of theform ax^-^-c^O, much of the manipulation of literal numbers such asmultiplication and division of polynomials by polynomials, mostword problems, radicals, considerable wwk with exponents, and pos-sibly signed numbers could be omitted.The purpose of the unit wwild be to enable the student to solve

formulas similar to F== kwiW^/d2 or V^v-^-^at2 tor any variable wherevalues are given for all others. This w^uld have equations as difficultas o= bcd/x2 or a~=b/2{x-\-c). A program leading to sufficient skill andunderstanding would include:

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Is Review Really Necessary? 69

1. Algebraic notation including a+&, a�by ab, a’/b, a (6+^), and a2.2. The equations ax=b, y/a=by a/x=b, x2=a, x�a=b, and com-

binations.3. Substitution and evaluation of V==v-}-^af2 for a, when F=20,

^=4, and ^=3.The commutative, associative, and distributive laws must be

stressed; it has been this writers experience that the student forwhich this course is aimed has difficulty recognizing x-\-a=b anda-{-x==b as equations for which similar methods of solution are used.The fact that "equals^ is a symmetric relationship must also bestressed; too many pupils who have learned to solve .05^= 15 cannotfind p in i==prt where i= 15, r== .05 and t= 1. No understanding canbe assumed.

Since a semester w^uld be sufficient time to allot for this, schoolswhich have separate semesters would not have to set up an entireyearns program. If the present semesters are labeled General Math Iand II, a new offering, General Math III, could be devised. Studentscould be admitted to III�which would be taken in lieu of I�on thebasis of I.Q. and arithmetic achievement; those lacking fundamentalskills, the majority, would be placed in I. A common General Math II,including needs of terminal students, could be offered the secondsemester. Any material besides fundamental review found in GeneralMath I, such as geometric mensuration, could be studied on a formulabasis in General Math III.

Besides the advantage mentioned of preparing a heretofore neg-lected group for higher technology, the challenge of new materialwhich is in the pupil’s grasp may put some vitality into a sometimesmoribund course. The general mathematics student is often not well-disposed towards school. While creating a new course is not the onlyanswer to the problem of individual differences, these students canuse all the help the curriculum can offer.

"IMPOSSIBLE" COMPOUND MADE WITHINERT GAS BY CHEMISTS

A chemical reaction, previously thought impossible, has been made byscientists at Argonne National Laboratory.Xenon, an inert gas, has been combined with a single element, fluorine, to

form a stable compound, xenon tetrafluoride. The discovery was made in rela-tion to atomic energy programs with fluorine.

Dr. Winston M. Manning, director of the chemistry division at Argonne,said: "A whole new area for the study of chemical bonding has been openedup."

Drs. John G. Malm and H. Henry Selig of the Argonne Laboratory with con-sultant, Dr. Howard H. Claassen, were responsible for the achievement.