Contemporary teaching and learning approaches expect students--at any level of education--to be active producers of knowledge. This leads to the need for creation of instructional strategies, learning environments and tasks that can offer students opportunities for active learning. Research argues that one of the most meaningful and engaging forms…

This study of fourth-grade students and teachers explores mathematics teaching and learning that focuses on discovering and modeling algebraic relationships. The study has two parts: an investigation of how students learn to construct algebraic statements and models for comparisons and measurement situations in the multiplicative domain, and an…

The Verhulst model can be used to forecast the sequence, which is characterized as non-monotone and fluctuant sequence or saturated S-form sequence. According to the situation of national enrollment scale of college, this paper forecasts the quantity of students taking entrance examination to college with a Verhulst model with remedy based on data…

By means of a simple mathematical model developed by the authors, the apparent movement of the Sun can be studied for arbitrary latitudes. Using this model, it is easy to gain insight into various phenomena, such as the passage of the seasons, dependences of position and time of sunrise or sunset on a specific day of year, day duration for…

Models play an important role in understanding chemical engineering systems. While differential equation models are taught in standard modeling and control courses, Differential Algebraic Equation (DAE) system models are not usually introduced. These models appear naturally in several chemical engineering problems. In this paper, the introduction…

In this article, the authors investigate how the difficulty of a "set shot" at goal varies with position on the field. By "set shot" they mean a player kicking for goal following a mark or free kick. The analysis begins by defining the "angle of opportunity" as a measure of difficulty for kicks at a given distance and…

A number of leaders in technology education have indicated that a major difference between the technological design process and the engineering design process is analysis and optimization. The analysis stage of the engineering design process is when mathematical models and scientific principles are employed to help the designer predict design…

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process--1) use of physical manipulatives, 2) interactive exploration of computer…

The spread of swine flu has been a cause of great concern globally. With no vaccine developed as yet, (at time of writing in July 2009) and given the fact that modern-day humans can travel speedily across the world, there are fears that this disease may spread out of control. The worst-case scenario would be one of unfettered exponential growth.…

Linearization is a standard part of modeling and control design theory for a class of nonlinear dynamical systems taught in basic undergraduate courses. Although linearization is a straight-line methodology, it is not applied correctly by many students since they often forget to keep the operating point in mind. This paper explains the topic and…

Latent interaction models and mixture models have received considerable attention in social science research recently, but little is known about how to handle if unobserved population heterogeneity exists in the endogenous latent variables of the nonlinear structural equation models. The current study estimates a mixture of latent interaction…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos--satisfying an axiom sin[superscript 2] + cos[superscript 2] = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two…

In this article, we examine the use of a new binary integer programming (BIP) model to detect arbitrage opportunities in currency exchanges. This model showcases an excellent application of mathematics to the real world. The concepts involved are easily accessible to undergraduate students with basic knowledge in Operations Research. Through this…

In an effort to assess models of inductive reasoning and deductive reasoning, the authors, in 3 experiments, examined the effects of argument length and logical validity on evaluation of arguments. In Experiments 1a and 1b, participants were given either induction or deduction instructions for a common set of stimuli. Two distinct effects were…