The semiotic approach to mathematics education introduces the notion of "semiotic system" as a tool to describe mathematical activity. The semiotic system is formed by the set of signs, the production rules of signs and the underlying meaning structures. In this paper, we present the notions of system of practices and configuration of objects and…

Sample size determination is an important issue in planning research. In the context of one-way fixed-effect analysis of variance, the conventional sample size formula cannot be applied for the heterogeneous variance cases. This study discusses the sample size requirement for the Welch test in the one-way fixed-effect analysis of variance with…

For beginning chemistry students, the basic tasks of writing chemical formulas and naming covalent and ionic compounds often pose difficulties and are only sufficiently grasped after extensive practice with homework sets. An enjoyable card game that can replace or, at least, complement nomenclature homework sets is described. "Go Chemistry" is…

A good-quality teacher may determines a good-quality learning, thus good-quality students will be the results. In order to have a good-quality learning, a lot of strategies and methods can be adopted. The objective of this research is to improve students' ability in determining the rules of a numeric sequence and analysing the effectiveness of the…

We use a natural experiment to show that the presence of an external examiner has both a direct and an indirect negative effect on the performance of monitored classes in standardized educational tests. The direct effect is the difference in the test performance between classes of the same school with and without external examiners. The indirect…

A cognitive construct that is important when solving engineering design problems is executive control process, or metacognition. It is a central feature of human consciousness that enables one "to be aware of, monitor, and control mental processes." The framework for this study was conceptualized by integrating the model for creative design, which…

Research synthesis of evaluation findings is a multistep process. An investigator identifies a research question, acquires the relevant literature, codes findings from that literature, and analyzes the coded data to estimate the average treatment effect and its distribution in a population of interest. The process of estimating the average…

In school, at least in the US, we were taught to multiply by hand according to a standard algorithm. Most people find that algorithm difficult to use, and many children fail to learn it. We propose a new way to make sense of this difficulty: to treat explicit computation as perceptually supported physical and mental action. Based on recent work in…

We compute closed forms for two multiparameter families of definite integrals, thus obtaining combinatorial formulas. As a consequence, a surprising formula is derived between a definite integral and an improper integral for the same parametric function.

This article considers the relationship between technology, utopia and scholarly life in Hermann Hesse's novel, "The Glass Bead Game." In the first part of Hesse's book, the Glass Bead Game and the society of which it is a part, Castalia, are portrayed in idealistic terms. The second part of the novel chronicles the educational life of Joseph…

Vehicles holding at traffic lights is a typical queuing problem. At crossings the vehicles experience delay in both directions. Longer periods with green lights in one direction are disadvantageous for the vehicles coming from the other direction. The total delay for getting through the traffic point is what counts. This article presents an…

This paper was first motivated by the following question: "A pair of twins, R and S, each gives the "same" hard push on a block. R's block is on a rougher floor than S's. Who does more work?" It is shown that S will do more work on his block if there is no constraint on the distance over which the force is applied. On the other hand, if the…

Pascal's triangle is an arrangement of the binomial coefficients in a triangle. Each number inside Pascal's triangle is calculated by adding the two numbers above it. When all the odd integers in Pascal's triangle are highlighted (black) and the remaining evens are left blank (white), one of many patterns in Pascal's triangle is displayed. By…

Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2]…

A new method for proving, in an immediate way, many combinatorial identities is presented. The method is based on a simple recursive combinatorial formula involving n + 1 arbitrary real parameters. Moreover, this formula enables one not only to prove, but also generate many different combinatorial identities (not being required to know them "a…