Algebra students may often demonstrate a certain degree of proficiency when manipulating algebraic expressions and verbalizing their behaviors. Do these abilities imply conceptual understanding? What is a reliable indicator that would provide educators with a relatively trustworthy and consistent measure to identify whether students learn…

The integration of children's trade books in the mathematics classroom has experienced a dramatic surge in its popularity; yet, though the positive benefits of this strategy have been well documented, these benefits may only be realized if the literature is of high quality. Utilizing a mathematics trade book evaluation instrument, this inquiry…

Numerous researchers have pointed to the potential benefits of providing students with a relevant historical context when introducing new mathematics concepts. This paper discusses the ways in which this approach may be applied to enhance student learning and attitudes in Singapore mathematics classrooms. While evidence on the efficacy of this…

Computer Algebra Systems (CAS) are equipped with rich facilities to show graphics, so the use of CAS to show 3D-graphics on screen is a popular tool for mathematics education. However, showing 3D-graphics in mass printed materials is a different story, since the clarity and preciseness of figures tend to be lost. To fill this gap, we developed…

The "flat" world described by Friedman (2006) is one of global supply chains and economic networks, outsourcing, international personal entrepreneurial opportunities, and nearly unlimited, universal information availability. American children will inherit a world in which their competition and opportunities are international. In light of these…

In this article, the author describes an open-ended drawing task that was used to discover young children's experiences with, and understandings of, the concept of mass. Mass is defined as the amount of matter in an object, and, like time, it cannot be seen (NSW Department of Education and Training Professional Support and Curriculum Directorate…

Dividing by fractions is considered by many to be one of the most complicated procedures in elementary mathematics. The computations are not only complicated but also challenging to explain in the context of a word problem. In this article, the author discusses the role of the divisor in the concept of division by fractions. She examines three…

This project was designed to be used in a freshman calculus class whose students had already been introduced to logistic functions and basic data modeling techniques. It need not be limited to such an audience, however; it has also been implemented in a topics in mathematics class for college upperclassmen. Originally intended to be presented in…

Art uses mathematics in many ways. The author's teaching and involvement with mathematics and art in the Bridges Conference connecting the two have convinced him more and more that concepts for understanding mathematics can be achieved by the use of art. The author states that one reason he believes in teaching mathematics through art is that it…

Unlike old perceptions of algebra as a subject that needs to be taught in the upper grade levels of schooling, much of the recent research reports that young students are capable of reasoning algebraically. It is important to note that the recommendation to include algebraic experiences in the early grades is not made simply to introduce typical…

A math classroom is complex. Teachers navigate through a lesson using a variety of activities and tools that are designed to address students' needs and help them build conceptual understanding. Manipulatives, drawings, and other such concrete representations can help students explore mathematical ideas in physically grounded manifestations.…

This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

Educational institutions receive a disproportionately large share of their gift income from estates. Charitable estate plans often donate a share of the total estate, rather than a specific dollar amount. The value of this type of planned gift depends not only on the value of the estate at the time the plan is signed, but also on the individual's…

The issue of the area of irregular shapes is absent from the modern mathematical textbooks in elementary education in Greece. However, there exists a collection of books written for educational purposes by famous Greek scholars dating from the eighteenth century, which propose certain techniques concerning the estimation of the area of such…

An understanding of fractions is foundational to proportional reasoning and algebra. For example, a direct-variation relationship may include a constant of proportionality that is rational, and linear equations may have solutions that are fractions. Beyond that, a grasp of the concept of proportionality and of rational numbers is necessary for…