This article provides an overview of a modeling sequence that culminates in student reinvention of a bifurcation diagram. The sequence is the result of years of classroom-based research and curriculum development grounded in the instructional design theory of Realistic Mathematics Education. The sequence of modeling tasks and examples of student…

The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave,…

Contemporary case studies rely on verbal arguments and set theory to build or evaluate theoretical claims. While existing procedures excel in the use of qualitative information (information about kind), they ignore quantitative information (information about degree) at central points of the analysis. Effectively, contemporary case studies rely on…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…

In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence…

When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date,…

In this article, the author focuses on possible ways to develop the concepts of joint variation and function through the upper primary and lower secondary years of education. The examples demonstrate the building of a range of important mathematical ideas by modelling life-related situations using students' informal and intuitive knowledge. Over…

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

Two ideal-point probabilistic choice models from the external analysis of preferences are presented that allow for more flexible distributions of ideal-points. The first extends the probit model of W. Kamakura and R. Srivastava. The second is based on simplifying assumptions that lead to a multidimensional histogram of ideal-points. (SLD)

Compares probabilistic models of same-different and identification judgments concerning their sensitivity to perceptual dependence or the degree to which underlying psychological dimensions are correlated. Results support a perceptual independence assumption when using these models and pertain to studies of different decision rules used at…

Mathematical analysis and computer simulation methods are used to show that interactive models of context effects can exhibit classical context effects if there is variability in the input to the network or the network itself. Interactive models represent hypotheses about information-processing dynamics leading to the global asymptotic behaviors…

New methods of analysis--equations and graphs for iso-r(sup 2) contours--were introduced and used to illustrate location effects for pooled data sets. The "r(sup 2)" is the coefficient of determination. Results are used to highlight imprecise statements in the literature about the behavior of the correlation coefficient for pooled data…

Confidence envelopes for one-parameter, two-parameter, and three-parameter logistic item response models are illustrated. M-line plots showing the genesis of the envelope and the density of lines in the confidence region are described and illustrated. (Author/SLD)

This paper makes the point that descriptive and inferential measures of nonnormality and graphic displays of the frequency distribution of important variables should be routine in research reporting. This point is particularly true for research involving measures with nonarbitrary metrics where the distribution shape is unaffected by measurement…