Homer W. Austin

Sample size: How much is enough?

SummaryThe question of sample size—how much is enough—has no simple answer. Magical numbers do not exist.Sample size must be considered in terms of confidence 1 — α, accuracy (or error) E, and variance

Calculus and its teaching: an accumulation effect

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An assessment of mathematical implication in college students

(or standard deviation σ). In order to approach sample size in this way, the researcher must know how closely he or she wants to estimate, with what confidence the estimation is required, and something about the variance of the population being sampled.The example described herein applies only to the estimation of a population mean. There are many other parameters a researcher may desire to estimate. He or she is again faced with the same problem: how large a random sample should be selected? Methods not unlike the ones described here might help the researcher process information more easily, maybe even to the point where he or she can decide how much is enough.

Preservice Elementary Teachers' Understanding of Logical Inference.

Colleges and universities which admit students with diverse backgrounds in mathematics must devise ways to place these students in courses for which they are prepared. At Salisbury State College, a self‐assessment test is used. Although the test is far from perfect, it is beneficial in placing students in appropriate courses. The test appears to have acceptable levels of both validity and reliability.

Classroom note: An equivalence relation

The teaching of elementary calculus during the last twenty‐five years in the United States is comparable to the development of the calculus. The development of the calculus and the teaching of calculus share a similar background in that both are characterized by periods of time in which ideas slowly accumulate, awaiting the arrival of some person, who will, with a new method of discovery, synthesize the fragmentary pieces and lift the subject to a higher plane.

Making statistics a full partner in mathematical sciences programs

ABSTRACT Colleges and universities across the nation offer instruction in elementary statistics. Most of these courses are taught in departments of mathematics by mathematicians. The perspective from which a course is taught governs the direction the course will take. The authors share their perspective on teaching a course in elementary statistics.

The Fermat machine

Mathematical implication is misunderstood by a large proportion of students at the college level. An inventory of the level of understanding of the conditional statement can be informative to professors of mathematics to the point where change in the teaching of the subject might occur.

A problem to foster critical thinking in mathematics

Abstract This article reports on the logical reasoning efforts of five prospective elementary school teachers as they responded to interview prompts involving nonsense, natural, and mathematical representations of conditional statements. The interview participants evinced various levels of reliance on personal relevance, linguistic contextualization, and time-dependent interpretation in working through reasoning tasks. Different kinds of affective and cognitive demands, dependent on personal history, may be needed for the depersonalization, decontextualization, and detemporalization required by abstract logico-deductive reasoning. Implications for college instruction with future elementary school teachers include suggestions for logical argument analysis activities aimed at enriching learners’ reasoning situation images.