An algebra teacher changes the dynamics of her classroom by recognizing the conflict between students wanting the freedom to make their own decisions and teachers wanting to limit that freedom and wanting to control the students. The adoption of self-paced classroom instruction where students had to master each concept before proceeding to the…

States the principal-agent theory is difficult to teach because of its technical complexity and intractability. Indicates the equilibrium in the contract space is defined by the incentive parameter and insurance component of pay under a linear contract. Describes a graphical approach that students with basic knowledge of algebra and…

Carry Groups are a wonderful collection of groups to introduce in an undergraduate Abstract Algebra course. These groups are straightforward to define but have interesting structures for students to discover. We describe these groups and give examples of in-class group projects that were developed and used by Miller.

Interesting problems sometimes have surprising sources. In this paper we take an innocent looking problem from a calculus book and rediscover the radical axis of classical geometry. For intersecting circles the radical axis is the line through the two points of intersection. For nonintersecting, nonconcentric circles, the radical axis still…

The benefits of visualizing mathematics by using technology such as TI-92+ and mathematically oriented software (DERIVE 5 and CABRI II) are indisputable. On the basis of some examples we would like to show that visualizing techniques can help students to analyse certain mathematical problems better and give them strong support in finding formal…

One of the most important connections that must be made during the middle school years is the relationship between scientific inquiry and algebraic thinking. Fortunately, there are plenty of ways in which teachers in both mathematics and science can make this intrinsically important association for students. One way is by studying rate of change,…

The card game SET has attracted the attention of math and game enthusiasts alike. In this article, I present a first semester Abstract Algebra project that guides the students through an algebraic formulation of the game. There are many interesting mathematical questions that one can ask about the game, and I illustrate how the project can be used…

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…