Niche construction is the modification of components of the environment through an organism's activities. Humans modify their environments mainly through ontogenetic and cultural processes, and it is this reliance on learning, plasticity and culture that lends human niche construction a special potency. In this paper we aim to facilitate…

Predicting student academic performance has long been an important research topic in many academic disciplines. The present study is the first study that develops and compares four types of mathematical models to predict student academic performance in engineering dynamics--a high-enrollment, high-impact, and core course that many engineering…

Samejima hypothesized that non-monotonically increasing item response functions (IRFs) of ability might occur for multiple-choice items (referred to here as "Samejima items") if low ability test takers with some, though incomplete, knowledge or skill are drawn to a particularly attractive distractor, while very low ability test takers…

We present five strategies that mathematics majors can use to improve their proof comprehension. We argue these strategies are effective by presenting qualitative excerpts illustrating the ways in which the employment of these strategies helped four undergraduate students understand the proofs they were reading. Furthermore, we present results of…

In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quantitative data based around the students' approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to…

The relationship between complexity and usefulness can be captured by a U-shaped curve. This comment explores that relationship. Complexity may be useful for one of the main aims of developmental psychology (causal inference) but not for another (description of developmental phenomena). Currently, developmentalists conduct complex analyses that…

We want to apply the geometrical method to a dynamical system of human blood glucose. Due to the educational importance of model building, we show a relatively general modelling process using observational facts. Next, two models of some concrete forms are analysed in the phase plane by means of linear stability, phase portrait and vector…

Normally, a mechanics laboratory at the undergraduate level includes an experiment to verify compliance with Hooke's law in materials, such as a steel spring and an elastic rubber band. Stress-strain curves are found for these elements. Compression in elastic bands is practically impossible to achieve due to flaccidity. A typical experiment for…

In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of…

Mathematical modeling and directed learning groups were employed in a terminal mathematics course to encourage university students to conceptualize real-world mathematics problems. Multiple assessments were utilized to determine whether students' conceptual development is enhanced by participating in directed learning groups conducted in a…

We present epistemological ruptures that have occurred in mathematical history and in the transformation of using technology in mathematics education in the twenty-first century. We describe how such changes establish a new form of digital semiotics that challenges learning paradigms and mathematical inquiry for learners today. We focus on drawing…

In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions…

Using spreadsheets such as Microsoft Excel for building crop models and running simulations can be beneficial. Excel is easy to use, powerful, and versatile, and it requires the least proficiency in computer programming compared to other programming platforms. Excel, however, has several weaknesses: it does not directly support loops for iterative…

I examine the association between the observable physical world and the mathematical models of theoretical physics. These models will exhibit many entities that have no counterpart in the physical world, but which are still necessary for the mathematical description of physical systems. Moreover, when the model is applied to the analysis of a…

This paper introduces the notion of "crystalline concept" as a focal idea in long-term mathematical thinking, bringing together the geometric development of Van Hiele, process-object encapsulation, and formal axiomatic systems. Each of these is a strand in the framework of "three worlds of mathematics" with its own special characteristics, but all…