The aim of this series of four articles is to look critically, and in some detail, at the primary strategy approach to written calculation, as set out on pages 5 to 16 of the "Guidance paper" "Calculation." The underlying principle of that approach is that children should use mental methods whenever they are appropriate, whereas for calculations…

This article describes the use of a Dutch pyramid model that may help teachers design assessment problems that go beyond reproduction and need mathematization, generalization, and insight. (Contains 4 figures.)

This article analyses the modeling approach used by one student in a business problem. It is argued that if we use previous frameworks we are not able to classify the students' approach to modeling as purely theoretical or empirical. Instead the student used a theoretical approach when constructing a real model, but abandoned it when she had to…

We focus on the problem of ignoring statistical independence. A binomial experiment is used to determine whether judges could match, based on looks alone, dogs to their owners. The experimental design introduces dependencies such that the probability of a given judge correctly matching a dog and an owner changes from trial to trial. We show how…

The paper reports on studies of the impact of harvesting on a prey-predator system with non-monotonic functional response and intra-specific competition in the predator growth dynamics. The existence of its steady states and their stability are studied using eigenvalue analysis. The possibility of the existence of bionomic equilibria has been…

Purpose: The purpose of this paper is to present a computational approach and a toolset to infer spatial displacements as they occur in route narrative documents and report on first experiments done to produce computer-aided learning (CAL) applications and instructional design editors that exploit the inferred georeferenced itineraries.…

"Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…

When the highest-way association is present in a 3-way cross-classification of frequencies, standard logit and loglinear models have an many parameters as there are cells in the table; that is, the models are "saturated." Extensions of logit and loglinear models are described here that provide more parsimonious alternatives to saturated…

This study analytically examined the multiple comparison procedures for testing a combined set of planned and post hoc comparisons. To establish a practical guideline, the following issues were investigated: (1) when the generalized sequentially rejective Bonferroni method (GSRB) is and is not applicable; (2) the required alpha levels for the GSRB…

A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. Numerical examples were…

Among the criticisms of Micko's Halo Model are: 1) it is too restrictive to fit empirical data, 2) it misrepresents unrelated percepts as bipolar structures, 3) it requires all dimensions to be bipolar, and 4) it causes the interpretations of orthogonality of factors and factor loadings to become problematic. (Author/BJG)

In some situations where reliability must be estimated it is impossible to divide the measuring instrument into more than two separately scoreable parts. In such a case, neither Cronbach's coefficient alpha nor Kristof's three-part approach are satisfactory. A technique is developed for estimating reliability in such situations. (Author/BJG)

Peay presented a class of grouping methods based on the concept of the r-clique for symmetric data relationships. The concepts of the r-clique can be generalized readily to directed (or asymmetric) relationships, and groupings based on this generalization may be found conveniently using an adoption of Peay's methodology. (Author/BJG)

The indexing depth in several documentation systems is shown to have a mixed Poisson distribution. (PF)

This paper demonstrates that a meta-analysis technique applied to the Solomon Four-Group Design (SFGD) can fail to find significance even though an earlier "weaker" test may have found significance. The meta-analysis technique was promoted by Braver and Braver as the most powerful single test for analyzing data from an SFGD. They…