We detail a student project that incorporates the story of the 1918 Influenza Pandemic, which, between the summer of 1918 and the spring of 1919, infected one-fifth to one-half of the world's population and killed more U.S. soldiers fighting in World War I than the war itself. The project uses Susceptible, Infected, Recovered, and Dead (SIRD)…

The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…

The authors propose the idea of threaded cognition, an integrated theory of concurrent multitasking--that is, performing 2 or more tasks at once. Threaded cognition posits that streams of thought can be represented as threads of processing coordinated by a serial procedural resource and executed across other available resources (e.g., perceptual…

Accuracy is often analyzed using analysis of variance techniques in which the data are assumed to be normally distributed. However, accuracy data are discrete rather than continuous, and proportion correct are constrained to the range 0-1. Monte Carlo simulations are presented illustrating how this can lead to distortions in the pattern of means.…

We confronted 151, 5th and 6th elementary grade pupils with a quantitative problem in a mathematics or religion class, to examine the influence of the context on pupils' understanding and solution of such problems inside and outside the mathematics class. Pupils were first asked to solve a problem about fair sharing either during a mathematics or…

This paper discusses an attempt to examine pre-service teachers' mathematical modelling skills. A modelling project investigating relationships between temperature and time in the process of cooling of coffee was chosen. The analysis was based on group written reports of the cooling of coffee project and observation of classroom discussion.…

This article reports on the findings of a research project whose aim was to support and enhance the teaching of risk at Key Stage 4. An innovative and cross-curricular approach has been used, based on modelling socio-scientific issues using new technological tools, designed specifically to enable the consideration of ethical and social issues,…

We have been investigating university student conceptions of mathematics over a number of years, with the goal of enhancing student learning and professional development. We developed an open-ended survey of three questions, on "What is mathematics" and two questions about the role of mathematics in the students' future. This…

The material presented here was used for a semester-long capstone project for a first semester freshman course entitled Mathematical Modeling and Introduction to Calculus. The goals for the students in this work were twofold: first, enable the students to gain insight into an actual problem that affects millions of people in the United States and…

A simple rocket can be made using a plastic bottle filled with a volume of water and pressurized air. When opened, the air pressure pushes the water out of the bottle. This causes an increase in the bottle momentum so that it can be propelled to fairly long distances or heights. Water rockets are widely used as an educational activity, and several…

Metaphors and analogies are more than figurative language suitable only for English classes and standardized test questions. They are "power tools" that can electrify learning in every subject and at all grade levels. Metaphors show students how to make connections between the concrete and the abstract, prior knowledge and unfamiliar concepts, and…

A unifying theory of subject-centered scalability is offered that is grounded in structural true score modeling, is conceptually distinct from internal consistency and homogeneity as determined by item correlations, and is empirically confirmable. Scalability holds when item true scores are perfectly correlated but differ in their individual scale…

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…

The study explored the effects of a computer-assisted COnceptual Model-based Problem-Solving (COMPS) program on multiplicative word-problem-solving performance of students with learning disabilities or difficulties. The COMPS program emphasizes mathematical modeling with algebraic expressions of relations. Participants were eight fourth and fifth…

Computer-based mathematical modeling in physics is a process of constructing models of concepts and the relationships between them in the scientific characteristics of work. In this manner, computer-based modeling integrates the interactions of natural phenomenon through the use of models, which provide structure for theories and a base for…