Arithmetic without sets

1976 ◽  
Vol 60 (413) ◽  
pp. 165-170
Author(s):  
R. L. Goodstein
Keyword(s):  
School Mathematics ◽  
Mathematical Research ◽  
Mathematical Concepts ◽  
Mathematics Courses ◽  
Primary Level ◽  
The Past ◽  
The Many

During the past 20 years the notion of set has been introduced into school mathematics courses not only at the secondary but also at the primary level. When one considers that neither Newton nor Gauss made any explicit use of the concept, it is rather remarkable that teachers have thought it desirable to teach the concept so early in their school courses. I should like to consider briefly some of the many possible reasons, historical and pedagogic, why “set” has become a school topic. One reason is, of course, the belief which Russell and Whitehead fostered in their Principia mathematica in the first decade of the century, that all mathematical concepts can be reduced to the concept of set. I don’t intend to discuss here the extent to which they failed to justify that belief, although I shall have occasion to mention some of the difficulties which their programme ran into. A second reason is the important part which sets have played in mathematical research this century.

scholarly journals Features of applying Maple in school mathematics course

2020 ◽  
Vol 26 (4) ◽  
pp. 82-91
Author(s):  
Nursaule Baimakhan ◽  
◽  
Raskul Ibragimov
Keyword(s):  
Teaching Method ◽  
School Mathematics ◽  
Full Time ◽  
Mathematical Concepts ◽  
Mathematics Courses ◽  
Course Content ◽  
State Pedagogical ◽  
Independent Work ◽  
Maple Package ◽  
Mathematics Course

This article discusses the features of using the Maple package in a school math course. The school mathematics course consists of basic mathematical concepts, ideas and principles. The scientific nature of the course content and the abstract nature of the topics studied make this course difficult to study in the classroom. The current situation with the coronavirus pandemic has completely eliminated full-time education and made distance education more relevant. The share of independent work of students has increased significantly. This negatively affects the ability to read and understand very complex material. In this regard, the choice of the Maple package as a method of computer technology and its technological possibilities for the organization of independent work of students in school mathematics courses are justified. The authors of the article developed a technology of teaching using the Maple package for school mathematics courses on the basis of the South Kazakhstan State Pedagogical University. This teaching method is aimed at organizing the independent work of students in the study of school mathematics. Examples of the use of the Maple package to solve some problems in a school math course are presented. Taking into account the specifics of the tasks of teaching mathematics at school, the possibilities and advantages of the technology of organizing students' independent work with the help of the Maple package are considered in detail.

scholarly journals UNDERSTANDING OF BASIC CONCEPTS FOR MASTERING COMPETENCES OF SCHOOL MATHEMATICS

2016 ◽  
Vol 2 ◽  
pp. 330
Author(s):  
Anita Sondore ◽  
Elfrīda Krastiņa ◽  
Pēteris Daugulis ◽  
Elga Drelinga
Keyword(s):  
Elementary Schools ◽  
Problem Solving ◽  
Life Quality ◽  
School Failure ◽  
School Mathematics ◽  
Mathematical Concepts ◽  
Mathematics Courses ◽  
Mathematical Competence ◽  
Basic Concepts ◽  
University Level

Mathematical competence as a universal and fundamental competence is essential for everyone as a problem solving and life quality improving tool. It is also essential for future teachers who will implement competence based teaching processes starting from elementary schools and preschools. The goal of this research is to discuss typical errors about certain basic mathematical concepts which are taught in school. Failure to grasp these concepts cause problems for learning subsequent mathematics courses and dealing with practical problems. This research will help to improve studies at university level. Experience analysis of university educators related to oral and written answers of students in tests is used in this research. Observations show that many errors get repeated year by year.

The Improvement of High School Mathematics Courses as Recommended by the Commission on Post-War Plans

1946 ◽  
Vol 39 (6) ◽  
pp. 269-275
Author(s):  
James H. Zant
Keyword(s):  
High School ◽  
School Mathematics ◽  
High School Mathematics ◽  
Mathematics Courses ◽  
Mathematical Instruction ◽  
The Past ◽  
Post War

The Commission on Post-War Plans conceives the problem of improving mathematical instruction as one which should bethought of in its entirety, that is, from grades one through fourteen and not broken into fragments as has been done so often in the past. It is our opinion that the program throughout all of these grades is in need of a thoroughgoing reorganization and the Second Report of the Commission makes a number of specific recommendations which it hopes will be of aid in such a reorganization.

On Future Directions in Pathology

1982 ◽  
Vol 40 ◽  
pp. 274-277
Author(s):  
Benjamin F. Trump ◽  
Irene K. Berezesky ◽  
Raymond T. Jones
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Clinical Pathology ◽  
Future Directions ◽  
Diagnostic Pathology ◽  
The Past ◽  
Transmission Electron ◽  
Organ Systems ◽  
The Many

The role of electron microscopy and associated techniques is assured in diagnostic pathology. At the present time, most of the progress has been made on tissues examined by transmission electron microscopy (TEM) and correlated with light microscopy (LM) and by cytochemistry using both plastic and paraffin-embedded materials. As mentioned elsewhere in this symposium, this has revolutionized many fields of pathology including diagnostic, anatomic and clinical pathology. It began with the kidney; however, it has now been extended to most other organ systems and to tumor diagnosis in general. The results of the past few years tend to indicate the future directions and needs of this expanding field. Now, in addition to routine EM, pathologists have access to the many newly developed methods and instruments mentioned below which should aid considerably not only in diagnostic pathology but in investigative pathology as well.

A 200-Year History of the Study of Childhood Language Disorders of Unknown Origin: Changes in Terminology

2020 ◽  
Vol 5 (1) ◽  
pp. 6-11 ◽  
Author(s):  
Laurence B. Leonard
Keyword(s):  
Language Impairment ◽  
Specific Language Impairment ◽  
Scientific Literature ◽  
Language Disorder ◽  
Language Disorders ◽  
Unknown Origin ◽  
Developmental Language Disorder ◽  
The Past ◽  
History Of ◽  
The Many

Purpose The current “specific language impairment” and “developmental language disorder” discussion might lead to important changes in how we refer to children with language disorders of unknown origin. The field has seen other changes in terminology. This article reviews many of these changes. Method A literature review of previous clinical labels was conducted, and possible reasons for the changes in labels were identified. Results References to children with significant yet unexplained deficits in language ability have been part of the scientific literature since, at least, the early 1800s. Terms have changed from those with a neurological emphasis to those that do not imply a cause for the language disorder. Diagnostic criteria have become more explicit but have become, at certain points, too narrow to represent the wider range of children with language disorders of unknown origin. Conclusions The field was not well served by the many changes in terminology that have transpired in the past. A new label at this point must be accompanied by strong efforts to recruit its adoption by clinical speech-language pathologists and the general public.

The Many Pasts of Detective Fiction

2020 ◽  
Vol 1 (2) ◽  
pp. 157-172
Author(s):  
Thomas Leitch
Keyword(s):  
Detective Fiction ◽  
Golden Age ◽  
Public History ◽  
Detective Novel ◽  
Sherlock Holmes ◽  
Detective Story ◽  
The Past ◽  
Wide Range ◽  
Detective Novels ◽  
The Many

Building on Tzvetan Todorov's observation that the detective novel ‘contains not one but two stories: the story of the crime and the story of the investigation’, this essay argues that detective novels display a remarkably wide range of attitudes toward the several pasts they represent: the pasts of the crime, the community, the criminal, the detective, and public history. It traces a series of defining shifts in these attitudes through the evolution of five distinct subgenres of detective fiction: exploits of a Great Detective like Sherlock Holmes, Golden Age whodunits that pose as intellectual puzzles to be solved, hardboiled stories that invoke a distant past that the present both breaks with and echoes, police procedurals that unfold in an indefinitely extended present, and historical mysteries that nostalgically fetishize the past. It concludes with a brief consideration of genre readers’ own ambivalent phenomenological investment in the past, present, and future each detective story projects.

Law as a Field of Tension

2018 ◽  
Author(s):  
Andrea Gamberini
Keyword(s):  
Public Authority ◽  
The Public ◽  
The Past ◽  
Political Cultures ◽  
The Many

As it had been in the communal age, so, in the Visconti-Sforza era, law was the instrument that the public authority relied upon in order to subordinate the many actors present and to subjugate their political cultures. There is, therefore, the attempt to tighten a vice around competing powers—a vice that is at the same time legislative, doctrinal, and judicial. And yet, it is difficult to escape the impression of an effort whose outcomes were somewhat more uncertain than had been the case in the past. The chapter focuses on all these aspects of the deployment of legal and other stratagems to consolidate or to wrest power.

Evidence-based Assessment

2010 ◽  
pp. 76-98
Author(s):  
John Hunsley ◽  
Eric J. Mash
Keyword(s):  
Decision Making ◽  
Clinical Assessment ◽  
Assessment Process ◽  
Evidence Based ◽  
The Past ◽  
Specific Assessment ◽  
The Many ◽  
Selection Of ◽  
Made In

Evidence-based assessment relies on research and theory to inform the selection of constructs to be assessed for a specific assessment purpose, the methods and measures to be used in the assessment, and the manner in which the assessment process unfolds. An evidence-based approach to clinical assessment necessitates the recognition that, even when evidence-based instruments are used, the assessment process is a decision-making task in which hypotheses must be iteratively formulated and tested. In this chapter, we review (a) the progress that has been made in developing an evidence-based approach to clinical assessment in the past decade and (b) the many challenges that lie ahead if clinical assessment is to be truly evidence-based.

CPT-based liquefaction case histories compiled from three earthquakes in Canterbury, New Zealand

2021 ◽  
pp. 875529302199636
Author(s):  
Mertcan Geyin ◽  
Brett W Maurer ◽  
Brendon A Bradley ◽  
Russell A Green ◽  
Sjoerd van Ballegooy
Keyword(s):  
New Zealand ◽  
Case History ◽  
Prediction Models ◽  
Free Field ◽  
Case Histories ◽  
Cone Penetration ◽  
History Data ◽  
The Past ◽  
Surface Manifestation ◽  
The Many

Earthquakes occurring over the past decade in the Canterbury region of New Zealand have resulted in liquefaction case-history data of unprecedented quantity. This provides the profession with a unique opportunity to advance the prediction of liquefaction occurrence and consequences. Toward that end, this article presents a curated dataset containing ∼15,000 cone-penetration-test-based liquefaction case histories compiled from three earthquakes in Canterbury. The compiled, post-processed data are presented in a dense array structure, allowing researchers to easily access and analyze a wealth of information pertinent to free-field liquefaction response (i.e. triggering and surface manifestation). Research opportunities using these data include, but are not limited to, the training or testing of new and existing liquefaction-prediction models. The many methods used to obtain and process the case-history data are detailed herein, as is the structure of the compiled digital file. Finally, recommendations for analyzing the data are outlined, including nuances and limitations that users should carefully consider.

Research trends in sociological studies on social security and welfare

2021 ◽  
pp. 026858092110053
Author(s):  
Koichi Hiraoka
Keyword(s):  
Social Security ◽  
Research Trends ◽  
Important Research ◽  
Research Results ◽  
The Past ◽  
Active Research ◽  
The Many ◽  
Sociological Studies ◽  
Broad Overview

This article reviews the research trends in welfare sociology (sociological studies on social security and welfare), one of the many subfields of active research in sociology in Japan. For this purpose, several research streams formed from the 1970s to the 2000s are described, and some of the most important research results produced within these in the past two decades are introduced. In the latter part of this article, a broad overview of the research trends in Japanese welfare sociology is attempted by focusing on the contents of the journal published by the Japan Welfare Sociology Association (JWSA).

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