Uses interviews with 72 pupils in grades 2-6 to investigate awareness of the relation between situation and computation in simple quotitive and partitive division problems as informally and formally experienced. Concludes that formal division, understood as related to everyday situations, only depends in interplay with informal knowledge.…

Describes two methods commonly used to calculate achievement gaps and suggests problems in the calculation of achievement gaps. One method uses percentage points as a form of "common currency"; the other calculates the change over time in proportion to the figures that are changing. Discusses reasons the second method may be preferable. (SLD)

Children's number sequence progress through several developmental changes that are brought about through adaptations in the children's counting activities. Introduces key psychological aspects of number sequences, pre-numerical counting schemes, an initial number sequence, a tacitly-nested number sequence, explicitly-nested number sequence, and…

Teaching the art of counting can be quite difficult. Many undergraduate students have difficulty separating the ideas of permutation, combination, repetition, etc. This article develops some examples to help explain some of the underlying theory while looking carefully at the selection of various subsets of objects from a larger collection. The…

Since the game SET[R] was first introduced to the public in 1993, it has stimulated some interesting studies. While the game itself is rather straightforward, a plethora of decent mathematical questions lies beneath the surface. It is perhaps because the game ties in so closely with such an underlying mathematical term that its implications can be…

The present article presents a tutorial on how to estimate and interpret various effect sizes. The 5th edition of the Publication Manual of the American Psychological Association (2001) described the failure to report effect sizes as a "defect" (p. 5), and 23 journals have published author guidelines requiring effect size reporting. Although…

The scholarly and popular debate on the delegation to the private sector of governmental tasks rests on an inadequate empirical foundation, as no systematic data are collected on direct versus indirect service delivery. We offer a simple method for approximating levels of service outsourcing, based on relatively straightforward combinations of and…

Redox calculations have the potential to reinforce important concepts in bioenergetics. The intermediacy of the NAD[superscript +]/NADH couple in the oxidation of food by oxygen, for example, can be brought out by such calculations. In practice, students have great difficulty and, even when adept at the calculations, frequently do not understand…

The presidential election that frequently features the results of political polling is presented. These polls attempt to estimate the popular vote that each candidate would receive as they could predict who would win the elections.

This paper examines the difference between mass and weight, which is discussed very early in most physics courses. Those who indulge in mathematical problems involving weights should know the difference. Mass is often defined as the amount of matter in an object. This usually means the sum of the masses of all the atoms that constitute that…

National Assessment of Educational Progress (NAEP) shows a deficiency in U.S. students' mathematics performance and computation skills. The students using calculators in school classrooms result in lower math scores than students who never use them.

A 2-high-threshold signal detection (HTSDT) model, a mixture distribution (SON) model, and 2-highthreshold (HT) models with responses distributed over 1 or several response categories were fit to results of 6 experiments from 2 studies on associative recognition: R. Kelley and J. T. Wixted (2001) and A. P. Yonelinas (1997). HTSDT assumes that…

T. Trabasso and J. Bartolone (see record 2003-07955-016) used a computational model of narrative text comprehension to account for empirical findings. The authors show that the same predictions are obtained without running the model. This is caused by the model's computational setup, which leaves most of the model's input unchanged.

Given a set of urns, each filled with a mix of black chips and white chips, what is the probability of drawing a black chip from the last urn after some sequential random shifts of chips among the urns? The Total Probability Formula (TPF) is the common tool to solve such a problem. However, when the number of urns is more than two and the number…

This article examines how numerical intuition for prices develops after a major change in currency. University students in Portugal (Study 1) and Austria (Study 2) made price estimates for 40 different items from November 2001 to June 2002, surrounding the time at which these countries switched to the euro. Overall results are more in accordance…