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Senior High School Mathematics Marc A. Laframboise University of Detroit,, Detroit/ Michigan Recent developments in the world picture of science have been causing some concern over the educational potential of the high school years. There has been an increasing realization in some instances that the secondary educational pattern is not accomplishing what it might and could, especially in the field of science including mathematics. High School teachers are asking the colleges what kind of preparation should be given the budding scientist or mathematician. Some High Schools are realizing that their science programs in some areas arc inadequate. We shall be concerned here with the question of mathematics in the High School and the preparation in mathematics for those stu- dents pursuing this discipline in college. In the past, secondary school courses in mathematics have usually included courses through intermediate algebra, trigonometry and solid geometry. This was and is a very satisfactory program pro- vided the courses are substantial in content and well attended. A significant cause for recrimination however lies in the fact that these courses are optional and elective even for the better students as well as for those bound for college. Work in many instances is haphazard and superficial in view of the duplication of these courses in the col- lege freshman year. This writer is inclined to remark at this point that the first year of college mathematics should be devoted to a good substantial course in calculus and that the entering freshman student with an interest or need for mathematics be prepared for this to the extent of a fairly complete preparation in college algebra, trigonometry and solid and analytic geometry in the high school years. Such a program would necessitate of course separating the able student from those of modest ability, otherwise the program will be geared to the mediocre student. A separation can and should be ef- fected as soon as possible and certainly no later than the end of the second High School year. It is apparent to all those who wish to sec that many students are more facile and more able in learning. Are all students to be deluded from this distinction until the college years? An early separation according to performance could have a salutary effect on the lackadaisical. The first two high school years need not change basically as re- gards mathematics. At present these years are devoted to the rudi- ments of algebra and plane geometry. However from the third year on the work should become earnest and intensive. 565

Senior High School Mathematics

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Senior High School Mathematics

Marc A. LaframboiseUniversity of Detroit,, Detroit/ Michigan

Recent developments in the world picture of science have beencausing some concern over the educational potential of the high schoolyears. There has been an increasing realization in some instances thatthe secondary educational pattern is not accomplishing what it mightand could, especially in the field of science including mathematics.High School teachers are asking the colleges what kind of preparationshould be given the budding scientist or mathematician. Some HighSchools are realizing that their science programs in some areas arcinadequate.We shall be concerned here with the question of mathematics in

the High School and the preparation in mathematics for those stu-dents pursuing this discipline in college.

In the past, secondary school courses in mathematics have usuallyincluded courses through intermediate algebra, trigonometry andsolid geometry. This was and is a very satisfactory program pro-vided the courses are substantial in content and well attended. Asignificant cause for recrimination however lies in the fact that thesecourses are optional and elective even for the better students as wellas for those bound for college. Work in many instances is haphazardand superficial in view of the duplication of these courses in the col-lege freshman year.

This writer is inclined to remark at this point that the first year ofcollege mathematics should be devoted to a good substantial coursein calculus and that the entering freshman student with an interestor need for mathematics be prepared for this to the extent of a fairlycomplete preparation in college algebra, trigonometry and solid andanalytic geometry in the high school years.Such a program would necessitate of course separating the able

student from those of modest ability, otherwise the program will begeared to the mediocre student. A separation can and should be ef-fected as soon as possible and certainly no later than the end of thesecond High School year. It is apparent to all those who wish to secthat many students are more facile and more able in learning. Are allstudents to be deluded from this distinction until the college years?An early separation according to performance could have a salutaryeffect on the lackadaisical.The first two high school years need not change basically as re-

gards mathematics. At present these years are devoted to the rudi-ments of algebra and plane geometry. However from the third yearon the work should become earnest and intensive.

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566 School Science and Mathematics

The first semester of the third year could be devoted to a course inintermediate algebra to be followed in the second semester by acourse in trigonometry with emphasis on the analytical aspects.The first semester of the fourth year could be devoted to a course

in what is presently called college algebra starting from the theory ofquadratics and embracing such topics as mathematical induction,complex numbers and ending with the elements of the theory ofequations and determinants.The second semester of the fourth year could be devoted to the

rudiments of plane analytic geometry followed by solid geometry withthe analogies of plane to solid analytic geometry.

If college mathematics were to start with calculus the High Schoolswould, in all probability, do a more thorough job in algebra, geometryand trigonometry, knowing that there would be no repetition incollege. Further, if remedial work in college is necessary, if givenwithout college credit, it would place the responsibility for such prep-aration upon the High School. Actually is this not where it belongs?This preparation for calculus should certainly not be beyond thecapabilities of a serious senior high school student.Such a program would move the mathematics work in college ahead

one full year. The High School would have an objective and definitecommitments.The program herein suggested would comprise the following:

(A one-semester course implies 5 meetings weekly over a semester ofsome 18 weeks more or less)

YEAR I: The rudiments of algebra, plane geometry, and generalmathematics.

YEAR II: A continuation of the first year algebra and geometry withan introduction to solid mensuration.Here, at the latest, the students are separated.

YEAR III: Stress algebra and graph work1st Semester�Intermediate algebraNumbers, Products, Factoring, Fractions, Exponents, Radicals,Equations, Functions, Graphs, Linear Equations, SimultaneousEquations, Quadratic Formula.

Hnd Semester�TrigonometryUsual topics. Stress analytic trigonometry, equation solving,logarithmic properties.

YEAR IV: Stress algebra and function sketching.1st Semester�^College Algebra^

1958 Convention Program 567

Theory of Quadratics, Ratio, Proportion, Variation, Progres-sions, Binomial Theorem, Inequalities, Mathematical Induction,Complex Numbers, Permutations, and Combinations, Interestand Annuities, Logarithms, An Introduction to the Theory ofEquations and Determinants.

lind Semester�Plane Analytic Geometry and Solid GeometryEquations of Lines and Conies, Distance Formulae, ElementaryProperties, Analogies in Three Dimensions from the SolidGeometryMensuration Formulae, Areas and Volumes of Parallelepipeds,Cylinders, Pyramids, Cones. The Prismatoid. The Sphere andZones.

The graduating high school senior would now be ready for calculus.This would be a big step in the right direction, moving the collegemathematics program forward one full year for the better and betterprepared student.

HIGHLIGHTS OF THE 1958 CONVENTION PROGRAMGENERAL OUTLINE

Clyde T. McCormickVice-Presidenf, CASMT, Illinois State Normal University,

Normal, Illinois

It is our wish to keep members and friends of Central Association of Scienceand Mathematics Teachers well informed in advance of the program and activitiesof the forthcoming 58th annual convention (November 27-29, Claypool Hotel,Indianapolis). Here, in very brief outline, are some of the highlights of the 1958convention program.

1. The convention opens Thursday evening with a program centered aroundthe general theme of the convention, "The Challenge of Science and Mathe-matics in a Free World." Dr. Thomas P Carney, Vice-Prcsidcnt, Eli Lillyand Company, Indianapolis, will speak on "What is the Challenge ofScience and Mathematics?" This will be followed by a panel on the theme,"How is CASMT to meet the Challenge on the Elementary, Secondary, andAdvanced Levels?" Dr. Rose Lammcl, Professor of Science Education,Wayne State University, will represent the elementary level. Professor PaulKlinge, Coordinator for School Science, Indiana University, will representthe secondary level. Professor Ralph C. HufTer, Chairman, Department ofMathematics and Astronomy, Beloit College, will represent the advancedlevel.

2. Governor Harold W. Handley of Indiana will extend Greetings and Wel-come to the first general session on Friday morning. This will be followedby an address by Professor E. H. C. Hildebrandt of Northwestern Univer-sity. He will address the Association on "Our Debt to the Middle East�Can it be Repaid?" Following this address, Mr. Wayne H. Kincaid, In-dianapolis, will demonstrate "Simple Devices for Teaching Atomic Struc-ture." The presentation consists of a series of experiments and flannelboards explaining in a fascinating fashion some of the fundamental ideas