The presence of a bilingual educator is proving pivotal to the success of technology initiatives aimed at developing Spanish-speaking students' grasp of both the concepts and the language of mathematics. This article features Ginny Badger, a teaching assistant at Glenwood Springs High School in Glenwood Springs, Colorado, who sacrificed her…

Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

This article describes several enrichment activities that connect mathematics to science in an algebra 1 curriculum. It provides a basis and suggestions for teachers to include student-produced essays about the role of mathematics in the history of civilization. (Contains 6 figures and 1 table.)

Let R be an associative ring which has a multiplicative identity element but need not be commutative. Let f(X) = a[subscript n]X[superscript n] + a[subscript n-1]X[superscript n-1] + ... + a[subscript 0] [is a member of] R[X] and [alpha] [is a member of] R. It is known that there exist uniquely determined q(X) = b[subscript n-1]X[superscript n-1]…

Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took individual mathematics…

This article presents an activity for middle-grades students that explores using an expansion of the algebraic expression as the basis for weaving plaids. (Contains 8 figures.)

This article presents the mathematics involved in finding and tracking celestial objects with an electronically controlled telescope. The essential idea in solving this problem is to choose several different coordinate systems that simplify the various motions of the earth and other celestial objects. These coordinate systems are then related by…

Since most students "hate" the concept of limit, in order to make them "happier," this article suggests a couple of naive "lim (h[right arrow]0)-is-missing" problems for them to try for fun. Indeed, differential functional equations that are related to difference quotients in calculus are studied in this paper. In particular, two interesting…

Today's generation does not always have its clever ways of writing algebraic equations and expressions. This paper attempts to trace how this system has developed since the dawn of civilization. The author looks at a few snapshots taken at distinct times to illustrate this progress. (Contains 4 tables.)

This note considers a family of piece-wise linear functions that can be used in the classroom to illustrate various concepts involved in iteration theory such as periodicity. These functions require minimal background on the part of the student. (Contains 2 figures.)

This article describes how all students can apply the algebra skills they have learned to problem solving through investigation, along with different levels of proving the conjectures algebraically.

Middle school teachers' use of digital curricula incorporating dynamic technology has been found to support student learning of complex algebraic concepts. This article reports on pilot research involving collaboration among faculty from a public university's college of education, educational researchers from a nonprofit research organization, and…

In this article, the author describes a lesson he observed involving a function machine. This function machine was a box with a slot at the top of one side and a large cut-out hole at the bottom of the opposite side. A card with a number written on it (the input) was pushed into the slot and the teacher put their hand through the hole of the other…

The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it is a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use…

In order to consider whether a course in college algebra should be a prerequisite for taking psychology statistics, we recorded students' grades in elementary psychology statistics and in college algebra at a 4-year university. Students who earned credit in algebra prior to enrolling in statistics for the first time had a significantly higher mean…