In the 1970s, the movement to the metric system (which has still not completely occurred in the United States) and the advent of hand-held calculators led some to speculate that decimal representation of numbers would render fractions obsolete. This provocative proposition stimulated Zalman Usiskin to write "The Future of Fractions" in 1979. He…

Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…

A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third-year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from one problem that involved solving a set of three linear equations of…

Many popular mathematical software products including Maple, Mathematica, Derive, Mathcad, Matlab, and some of the TI calculators produce incorrect graphs because they use complex arithmetic instead of "real" arithmetic. This article expounds on this issue, provides possible remedies for instructors to share with their students, and demonstrates…

In this article, the authors describe how a Java applet can help to build learners' intuitions about basic ideas of algebra. "Matchbox Algebra" is a Java applet the authors have designed to enable learners to grasp a key idea in learning algebra: that the letter "x" may be thought of as representing an as-yet-unknown number. They describe the…

One of the main problems in undergraduate research in pure mathematics is that of determining a problem that is, at once, interesting to and capable of solution by a student who has completed only the calculus sequence. It is also desirable that the problem should present something new, since novelty and originality greatly increase the enthusiasm…

In this paper we describe a strand of activities for teachers of mathematics that we used with two cohorts of participants in a professional development program called Revitalizing Algebra (REAL). We first discuss our goals and describe the participants, and then we describe the construction and selection of the tasks followed by teacher…

Characteristic polynomials are used to determine when magic squares have magic inverses. A resulting method constructs arbitrary examples of such squares.

Based on a sequence of number pairs, a recent paper (Mauch, E. and Shi, Y., 2005, Using a sequence of number pairs as an example in teaching mathematics, "Mathematics and Computer Education," 39(3), 198-205) presented some interesting examples that can be used in teaching high school and college mathematics classes such as algebra, geometry,…

Montgomery County Public Schools (MCPS) "Special Education at a Glance," which includes a copy of the "Guide to Planning and Assessing School-Based Special Education Programs," provides in a single document, information about the special education population at each Montgomery County (Maryland) public school, including…

The study sought to test the hypotheses that effective, guided discussions that facilitate meaningful dialogue about math anxiety would reduce levels of math anxiety in college algebra students, and would enhance course performance and course retention at a large community college in South Texas. The study was quantitative with a qualitative…

In the Singapore primary school Mathematics curriculum, students are taught the model method that uses bar diagrams to visualize the problem structure in a given word problem. When these students progress to secondary school, they learn the algebraic way of solving word problems. Studies (e.g. Ng et al.) have shown that poor bridging of students…

The authors examined an association between mathematical content in college-level curricula and beginning salaries of graduating students on the basis of data collected from a public university in the southern region of the United States. The authors classified the mathematical content requirements of the curricula into the following 5 groups…

This study is a qualitative analysis of data collected during a yearlong series of teacher learning community meetings and classroom observations. The participants are middle and high school mathematics teachers from 2 school districts. Teachers were introduced to the research behind formative assessment and how to apply that research to their…

In teaching primary teacher trainees, an awareness of the characteristic features, especially commutativity and associativity of basic operations play an important role. Owing to a deeply set automatism rooted in their primary and secondary education, teacher trainees think that such characteristics of addition are so trivial that they do not need…