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…

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 1974, the National Football League (NFL) initiated a sudden death overtime rule for games ending in a tie score at the end of regulation time. The rule states that the sudden death system of determining the winner shall prevail when the score is tied at the end of the regulation playing time of all NFL games. The team scoring first during…

In this research article, I present evidence of the existence of visual templates in pattern generalization activity. Such templates initially emerged from a 3-week design-driven classroom teaching experiment on pattern generalization involving linear figural patterns and were assessed for existence in a clinical interview that was conducted four…

This project served as a capstone event for the United States Military Academy sophomore Calculus II course. This multi-disciplinary problem-solving exercise motivated the link between math and biology and many other fields of study. The seven-lesson block of instruction was developed to show students how mathematics play a role in every…

This article is a project that takes students through the process of forming a mathematical model of bicycle dynamics. Beginning with basic ideas from Newtonian mechanics (forces and torques), students use techniques from calculus and differential equations to develop the equations of rotational motion for a bicycle-rider system as it tips from…

Implementation of emerging technology in sub disciplines of mathematics education provides a potential for educators to elaborate the capacity of digitized learning for human being. Spatial thinking is considered as a factor of scientific deduction from a multi disciplinary point of view. This paper reports a study aimed at exploring the effect of…

Exploring and deriving proofs of closed-form expressions for series can be fun for students. However, for some students, a physical representation of such problems is more meaningful. Various approaches have been designed to help students visualize squares of sums and sums of squares; these approaches may be arithmetic-algebraic or combinatorial…

We define a differential operator for analytic functions of fractional power. A class of analytic functions containing this operator is studied. Finally, we determine conditions under which the partial sums of the linear operator of bounded turning are also of bounded turning.

What is the relationship between addition and subtraction? How do individuals know whether an algorithm will always work? Can they explain why order matters in subtraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organized around two big ideas and supported by…

In recent years, the "street teachers" issue has caused social concern in Taiwan. This study estimates the retirement of and needs for newly hired and public primary school teachers in 2010 using an algebraic model from the paper by Husssar (1999). This recursive methodology predicts the number of newly hired public primary school…