Mastery Of Mathematics Research Articles

Measurement understandings in modern school mathematics

Increasing concern over the mathematics programs in our public schools within the last decade has led to attempts to upgrade the mastery of mathematics. Although such curricular attempts arc presented as an indivisible whole, it has been suggested they are tied together by a few basic strands or fundamental concepts that run through the curriculum. This theme is pursued in the Twenty-fourth Yearbook of the National Council of Teachers of Mathematics.1 In California, these themes or basic strands have been classified as number and operations, geometry, measurement, and applications of mathematics.2 Other strands labeled sets, funct ions and graphing, logic, and the mathematical sentence are seen as topics cutting across various systems. Taking direction from these reports, this study investigates the mastery and undcrstandi ng of one of these strands—measurement—among students enrolled in “modern school mathematics.”

Limitations in the Accuracy of Estimates of Blood Group Gene Frequencies

Summary and Conclusions1. For reporting results of calculations of blood group frequencies no more significant figures should be used than are justified by the size of the series tested.2. Technical and clerical mistakes have been responsible for gross discrepancies in reports on blood group distribution published in the literature, which qualified investigators can recognize by mere inspection of the data.3. Maximum likelihood calculations are complex and laborious and require a mastery of mathematics which few workers possess. Even in the hands of experts gross errors have resulted when carrying out the laborious computations, so that such calculations are not only expensive but impracticable and dangerous.4. The application of maximum likelihood calculations by Boyd to two series of individuals tested for the M-N-S types has yielded estimates of gene frequencies differing only in the third decimal place from the values obtained by the author with the aid of simple square root formulae. When one considers, even disregarding the possibility of technical and clerical errors, that the sizes of these two series justified the use of only two significant figures, it is evident that the maximum likelihood method contributed only a dubious increase in „ accuracy ”. Therefore, such calculations consume misdirected energy and place emphasis on superficialities while disregarding more important factors which can affect the accuracy of the data.5. Many investigators when studying the distribution of the blood groups make the tacit but incorrect assumption that the population is undergoing random mating and is therefore homogeneous. This appears to be one basis for the recent series of fallacious reports on the supposed relationship between the blood groups and various diseases.6. Confusion in the blood grouping field is due to the fact that most of the articles and books which are published have been written by individuals who have only superficial knowledge and understanding of the subject. The widespread use of the incorrect G-D-E notations reflects the lack of mastery of Rh-Hr serology shared by these workers.7. It is significant that the same workers who are enthusiastic for maximum likelihood calculations also endorse the pointless studies on blood group distribution in disease, and the use of the superficially attractive but fallacious C-D-E notations.

Control of Fundamental Mathematical Skills and Concepts by High School Students

The purpose of this study was to answer the following questions concerning the mathematical achievement of the students in grades ten, eleven, and twelve in forty-three selected Iowa high schools: (1) What degree of mastery of the mathematical skills and concepts described as essential for the ordinary citizen in the Final Report of the Joint Commission of The Mathematics Association of America and The National Council of Teachers of Mathematics1 is attained by high school students? This question involved the dual problem of determining the degree of mastery for each defined concept and skill as well as the degree of mastery of the composite of these concepts and skills. (2) What common errors do students make in applying these concepts and skills? (3) Are there significant differences between grade levels in the degree of mastery of this basic mathematics?

Mastery of Mathematics Adapted to Needs and Abilities: A Reply to the Previous Article by Professor Kempner

While naturally I am pleased with the good things Professor Kempner says about me and our book, and while I certainly have no quarrel with the desire to have students come into college classes in mathematics better prepared than they do, I believe that some parts of Professor Kempner's assumptions and reasoning should be challenged and I should like to object strenuously to any criticism of the Doug-lass-Kinney book, Senior Mathematics, for failing to serve a purpose for which it was definitely not intended.

CONDUCTIVITY MEASUREMENTS OF PLANT SAP

The plant physiologist recognizes more and more the importance of the application of physics and physical chemistry to fundamental plant problems, realizing that a mastery of botany, physics, chemistry, and mathematics will aid in the understanding of the living cell. Conductivity measurements have been widely used in the study of plant problems in recent years (7, 8,12,14,15,17, 25,27,28,32). A critical examination of these articles indicates the desirability of reviewing the basic principles of conductivity measurements and of pointing out the various factors that influence the conductivity value of plant sap. This paper will discuss the application and limitation of the measurement of electrical conductivity of plant saps, with particular reference to cold-hardened and unhardened plant tissues.

What Modern School Administration Expects of High School Teachers of Mathematics

Accepting the modern dictum that all school teachers, high or elementary, are teachers of children rather than teachers of subjects, there is the added responsibility of teaching children something. Hence, there exists some 25 per cent of the total high school staff whose efforts are devoted to assisting pupils to a degree of mastery of elementary mathematics. To be able to perform this function the teacher of high school mathematics must make an appropriate preparation.

Mathematics for Service

For a long time mathematics has enjoyed the position of first place in the elementary schools, and in the high schools the time devoted to the subject is nearly as great as that for any other subject. Almost daily for ten years, reaching from the first primary grade up to the conclusion of the second year in the high school, a pupil is required to bend his best energies toward the mastery of mathematics. What are the results? It is needless to state that the average graduate going into business or into any of the learned professions, except engineering, fails to put his mathematics to any use whatsoever. Beyond the requirements of keeping one’s accounts and calculating interest and taxes, the ordinary citizen has no need of formal mathematics. The result is that practically everything in this subject learned in the high school is promptly forgotten.