This paper discusses a result of Li and Shen which proves the existence of a unique periodic solution for the differential equation x[dots above] + kx[dot above] + g(x,t) = [epsilon](t) where k is a constant; g is continuous, continuously differentiable with respect to x , and is periodic of period P in the variable t; [epsilon](t) is continuous…

At the pre-college and first-year college level of physics instruction, Kepler's laws are generally taught as empirical laws of nature. Introductory physics textbooks only derive Kepler's Second law of areas. It is possible to derive all of Kepler's laws mathematically from the conservation laws, employing only high-school algebra and geometry.…

The normal equations discussed in this paper for a least-squares parabolic fit have a unique solution if and only if there are at least three different x-values in the observations. This requirement is satisfied by most real sets of quantitative observations. For particular data sets, the appropriateness of parabolic fits should be assessed with…

This paper is written on a level accessible to college/university students of mathematics who are taking second-year, algebra based, mathematics courses beyond calculus I. This article combines material from geometry, trigonometry, and number theory. This integration of various techniques is an excellent experience for the serious student. The…

This report presents empirical findings from the analysis of the performance of 85 students from Madison Park High School, Boston, Massachusetts, on the Boston Public Schools City Algebra Test (BPSCAT) in June and August 2000, and how their participation in Jobs for Youths Boston PLATO computer-based instruction in the intervening months may have…

Brooks (1999) compared algebra achievement of students enrolled in the intervention group (I CAN Learn[R] classes) to that of students enrolled in the comparison group (traditional classes) at pretest, midyear, and posttest. Brooks found that students in the I CAN Learn[R] classes achieved higher scores in algebra than students in traditional…

"Transition Mathematics" aims to increase 7th- through 12th-grade students' skills in applied arithmetic, pre-algebra, and pre-geometry. This one-year curriculum also addresses general application to different wordings of problems, types of numbers, and contexts for problems and aims to promote mathematical reading skills. The curriculum…

Fundamental to statistical analyses is the comparison of means of one variable from two or more populations. Population samples may be constructed (i.e., experimental and control groups), or they may be natural groupings (i.e., students at a particular grade in different years). If the populations are similar, the mean comparisons are…

This article describes ways in which digital imagery can be used to enhance mathematics instruction. (Contains 6 figures.)

The Department of Mathematics at the University of Food Technology, Plovdiv, Bulgaria, has introduced the Computer Algebra System DERIVE into the Mathematics courses with a view to increasing student motivation and understanding of the material taught as well as the efficiency of the teaching process. With the aim of investigating the effect of…

This article will share results from research that investigated how sixth-, seventh-, and eighth-grade students who had not been exposed to formal algebraic methods approached word problems of an algebraic nature. Student use of systematic guess and check, the predominate approach taken by these students, is the focus. The goal is to consider the…

Findings from an on-going design experiment within a year-long graduate course for middle school teachers of mathematics are reported. The purpose of the course was to help teachers assist students in transitioning from arithmetic to algebraic reasoning. Goals included developing teachers' ability to interpret, compare, and generalize across…

This article deals with the investigation of the psychometric quality and constructs validity of algebra word problems generated by means of a schema-based version of the automatic min-max approach. Based on review of the research literature in algebra word problem solving and automatic item generation this new approach is introduced as a…

This article describes a teaching experiment conducted in a seventh-grade classroom. It explores ways that students used four types of problem-solving knowledge through writing their responses to algebraic problems. The problems were presented to students in the geometric contexts of growth and change and size and shape. It was found that writing…

Manufacturing engineering provides a relevant context from which to envision interdisciplinary learning experiences because engineers integrate their knowledge and skills of manufacturing and algebra processes in order to plan the efficient manufacture of products. In this article, the author describes an interdisciplinary learning activity that…