Because new learning technologies are enabling students to build and explore probability models, we believe that there is a need to determine the big enduring ideas that underpin probabilistic thinking and modeling. By uncovering the elements of the thinking modes of expert users of probability models we aim to provide a base for the setting of…

The purpose of this study is to analyze the statistical reasoning levels of preservice elementary school teachers. With this purpose, pre-service teachers consisting of 29 groups worked on a model eliciting activity (MEA) in scope of an elective course they were taking. At the end of the class, they were asked to present their solutions while…

Many studies have shown the difficulties of learning and teaching the decimal number system for whole numbers. In the case of numbers bigger than one hundred, complexity is partly due to the multitude of possible relationships between units. This study was aimed to develop conditions of a resource which can help teachers to enhance their teaching…

Topicality of the study is driven by the fact that the new fundamental mathematical ideas and methods of mathematics arise in the new era of mathematization of science and have a great influence on the formation of methodological culture of educational research in recent decades. The aim of the article is to identify the important aspects of the…

Interdisciplinary research in computer science requires the development of computational techniques for practical application in different domains. This usually requires careful integration of different areas of technical expertise. This dissertation presents image and time series analysis algorithms, with practical interdisciplinary applications…

Using meta-analytic techniques this study examined the effects of applying mathematical modelling to support student math knowledge acquisition at the high school and college levels. The research encompassed experimental studies published in peer-reviewed journals between January 1, 2000, and February 27, 2013. Such formulated orientation called…

In this article, the authors discuss a pedagogical approach that connects the cultural aspects of mathematics with its academic aspects in which they refer to as ethnomodeling. Ethnomodeling is the process of translation and elaboration of problems and questions taken from systems that are part of the daily life of the members of any given…

Structural balance theory (SBT) has maintained a venerable status in the psychological literature for more than 5 decades. One important problem pertaining to SBT is the approximation of structural or generalized balance via the partitioning of the vertices of a signed graph into "K" clusters. This "K"-balance partitioning problem also has more…

Presented are the results of a study conducted to develop algorithms for ordering and organizing data that can be presented in a two-dimensional matrix form. The purpose of the work was to develop methods to extract latent data patterns, grouping, and structural relationships which are not apparent from the raw matrix data. The algorithms…

Guttman's "rank-reduction" theorem is employed to demonstrate how most of the algebra and computational work for standard correlational and analysis of variance methods can be examined within a single matrix system. Analyses of both correlational and experimental data are illustrated with an easy-to-use computer program. This application…

This paper develops and illustrates a latent trait approach to constructing an item bank when responses are scored in several ordered categories. This approach is an extension of the methodology developed by Choppin, Wright and Stone, and Wright and Bell for the construction and maintenance of banks of dichotomously scored items. (Author/PN)

This discussion of how the multilevel character of data should influence analyses of the determinants of educational achievement is grounded in the context of planning explanatory analyses for the longitudinal Second International Mathematics Study (SIMS). The intention is to describe how a multilevel perspective in the specification of…

This study was concerned with various schemes for reducing the number of variables in a multivariate analysis. Two sets of illustrative data were used; the numbers of criterion groups were 3 and 5. The proportion of correct classifications was employed as an index of discriminatory power of each subset of variables selected. Of the four procedures…

Metacognition has been accorded a role in both mathematical problem solving and in the learning of mathematics. There has been consistent advocacy of the need for the promotion of metacognitive activity in both domains. Such advocacy can only be effective if the advocated process is well understood. In this paper we have four goals: to describe a…

This guide presents many new experimental designs for data analysis and reviews certain standard procedures. It is hoped that the treatment of the material will stimulate new applications since the emphasis of the guide is on the problems encountered in running experiments rather than on an elaboration of mathematical models. Discussed are:…