A Better Use of Tests in Mathematics

W. D. Reeve

doi:10.5951/mt.17.3.0140

A Better Use of Tests in Mathematics

Mathematics Teacher ◽

10.5951/mt.17.3.0140 ◽

1924 ◽

Vol 17 (3) ◽

pp. 140-147

Author(s):

W. D. Reeve

Keyword(s):

Diagnostic Tests ◽

Mathematical Work ◽

Prognostic Tests ◽

Mathematical Career ◽

Innate Ability

Tests in mathematics may be classified under two main heads, namely, prognostic tests, and achievement or diagnostic tests. Prognostic tests are those which may be given by the teacher early in the pupil's mathematical career the results of which are supposed to measure innate ability to do mathematical work. By their use one is supposed to be able to predict how the pupil will probably perform in his later mathematical work. These tests must, in the nature of things, be more comprehensive than any which have been devised for particular fields.

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The Mathematical Work of S.C.Kleene

Bulletin of Symbolic Logic ◽

10.2307/420945 ◽

1995 ◽

Vol 1 (1) ◽

pp. 9-43 ◽

Cited By ~ 9

Author(s):

J.R. Shoenfield

Keyword(s):

Recursion Theory ◽

Mathematical Work ◽

Church’S Thesis ◽

Recursive Functions ◽

Close Relationship ◽

Church's Thesis ◽

Mathematical Career ◽

Definable Functions ◽

Class Of Functions ◽

Computable Functions

§1. The origins of recursion theory. In dedicating a book to Steve Kleene, I referred to him as the person who made recursion theory into a theory. Recursion theory was begun by Kleene's teacher at Princeton, Alonzo Church, who first defined the class of recursive functions; first maintained that this class was the class of computable functions (a claim which has come to be known as Church's Thesis); and first used this fact to solve negatively some classical problems on the existence of algorithms. However, it was Kleene who, in his thesis and in his subsequent attempts to convince himself of Church's Thesis, developed a general theory of the behavior of the recursive functions. He continued to develop this theory and extend it to new situations throughout his mathematical career. Indeed, all of the research which he did had a close relationship to recursive functions.Church's Thesis arose in an accidental way. In his investigations of a system of logic which he had invented, Church became interested in a class of functions which he called the λ-definable functions. Initially, Church knew that the successor function and the addition function were λ-definable, but not much else. During 1932, Kleene gradually showed1 that this class of functions was quite extensive; and these results became an important part of his thesis 1935a (completed in June of 1933).

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Clinical decision analysis methods applied to diagnostic tests in dentistry

Journal of Dental Education ◽

10.1002/j.0022-0337.1983.47.11.tb01729.x ◽

1983 ◽

Vol 47 (11) ◽

pp. 708-714 ◽

Cited By ~ 12

Author(s):

CW Douglass ◽

BJ McNeil

Keyword(s):

Decision Analysis ◽

Diagnostic Tests ◽

Clinical Decision ◽

Analysis Methods

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Images of Aging in the Psychotherapeutic Context

GeroPsych ◽

10.1024/1662-9647/a000129 ◽

2015 ◽

Vol 28 (2) ◽

pp. 47-55 ◽

Cited By ~ 10

Author(s):

Eva-Marie Kessler ◽

Catherine E. Bowen

Keyword(s):

Old Age ◽

Diagnostic Tests ◽

Aging Process ◽

Developmental Psychology ◽

Mental Representations ◽

Later Life ◽

Future Research ◽

Psychotherapeutic Process ◽

Images Of Aging ◽

Client Communication

Both psychotherapists and their clients have mental representations of old age and the aging process. In this conceptual review, we draw on available research from gerontology, social and developmental psychology, and communication science to consider how these “images of aging” may affect the psychotherapeutic process with older clients. On the basis of selected empirical findings we hypothesize that such images may affect the pathways to psychotherapy in later life, therapist-client communication, client performance on diagnostic tests as well as how therapists select and apply a therapeutic method. We posit that interventions to help both older clients and therapists to reflect on their own images of aging may increase the likelihood of successful treatment. We conclude by making suggestions for future research.

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Statistics training that works with our innate ability to assess the likelihood of events can help doctors and patients figure the odds of illness better

PsycEXTRA Dataset ◽

10.1037/e307072004-001 ◽

2001 ◽

Author(s):

Keyword(s):

Innate Ability

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NIDCD Working Group Considerations for Developing and Implementing Genetic Diagnostic Tests for Hereditary Hearing Impairment and Other Communication Disorders

PsycEXTRA Dataset ◽

10.1037/e606942012-001 ◽

1998 ◽

Keyword(s):

Hearing Impairment ◽

Diagnostic Tests ◽

Working Group ◽

Communication Disorders ◽

Hereditary Hearing Impairment

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The present state of aspirin and clopidogrel resistance

Hämostaseologie ◽

10.1055/s-0037-1617036 ◽

2009 ◽

Vol 29 (03) ◽

pp. 285-290 ◽

Cited By ~ 2

Author(s):

K. E. Guyer

Keyword(s):

Diagnostic Tests ◽

Arterial Thrombosis ◽

Cardiovascular Events ◽

Treatment Success ◽

Antiplatelet Agents ◽

Antiplatelet Drug ◽

Coronary Syndrome ◽

Testing Method ◽

Pharmacological Response ◽

Platelet Physiology

SummaryAntiplatelet therapy has demonstrated significant clinical benefit in the treatment of acute coronary syndrome. However, as with any treatment strategy it has been unable to prevent all cardiovascular events. This is far from surprising when considering the complexity of arterial thrombosis and more specifically platelet physiology. This lack of treatment success has provoked the introduction of various diagnostic tests and testing platforms with the intent of guiding and optimizing clinical treatment. Such tests have resulted in the generation of clinical data that suggest suboptimal response to antiplatelet agents such as aspirin and clopidogrel.In the case of both aspirin and clopidogrel, this suboptimal response has been termed resistance. Drug resistance would imply a lack of pharmacological response that has not been specifically investigated in many of the clinical studies performed to date. Rather, the term resistance has been used to describe various facets of platelet activation and aggregation relative to the testing method. Many of these measured parameters are not addressed in the therapeutic intent of the antiplatelet drug in question.

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Optimizing Diagnostic Test Sequences: The Probability Modifying Plot

Methods of Information in Medicine ◽

10.1055/s-0038-1634143 ◽

1999 ◽

Vol 38 (01) ◽

pp. 50-55 ◽

Cited By ~ 2

Author(s):

P. F. de Vries Robbé ◽

A. L. M. Verbeek ◽

J. L. Severens

Keyword(s):

Urinary Tract Infection ◽

Urinary Tract ◽

Tract Infection ◽

Decision Trees ◽

Diagnostic Tests ◽

Test Sequence ◽

Optimal Sequence ◽

Specific Test ◽

Total Cost ◽

Modelling Techniques

Abstract:The problem of deciding the optimal sequence of diagnostic tests can be structured in decision trees, but unmanageable bushy decision trees result when the sequence of two or more tests is investigated. Most modelling techniques include tests on the basis of gain in certainty. The aim of this study was to explore a model for optimizing the sequence of diagnostic tests based on efficiency criteria. The probability modifying plot shows, when in a specific test sequence further testing is redundant and which costs are involved. In this way different sequences can be compared. The model is illustrated with data on urinary tract infection. The sequence of diagnostic tests was optimized on the basis of efficiency, which was either defined as the test sequence with the least number of tests or the least total cost for testing. Further research on the model is needed to handle current limitations.

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