We believe that developing cultural competencies can help students learn mathematics and conversely that learning mathematical content can help students learn about themselves and others. Using frameworks introduced by Rendón (2009) and Gutiérrez (2018), we present a five-part bundle of activities for undergraduate differential equations course…

The paper describes active learning strategies used in undergraduate college algebra and business calculus courses. There are a variety of active learning strategies described in the literature. We wanted to implement a few that together, satisfy the key characteristics of active learning strategies. The active learning strategies described in…

This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to regression and correlation analysis to increase student understanding of the concepts and methods in elementary statistics courses and in courses at the college algebra/precalculus level that…

Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…

One of the most important applications of the definite integral in a modern calculus course is the mean value of a function. Thus, if a function "f" is defined on an interval ["a", "b"], then the mean, or average value, of "f" is given by [image omitted]. In this note, we will investigate the meaning of other statistics associated with a function…

The translation principle allows students to solve problems in different branches of mathematics and thus to develop connectedness in their mathematical knowledge. Successful application of the translation principle depends on the classroom mathematical norms for the development of discussions and the comparison of different solutions to one…

At United States Military Academy, a unit on biological modeling applications forms the culminating component of the first semester core mathematics course for freshmen. The course emphasizes the use of problem-solving strategies and modeling to solve complex and ill-defined problems. Topic areas include functions and their shapes, data fitting,…

Two related sequences of definite integrals are considered. By mixing hand-work, computer algebra system assistance and websurfing, fine connections can be studied between integrals and a couple of interesting sequences of integers. (Contains 4 tables.)

The goals of this note are to derive formulas for the coefficients a and b in the least-squares regression plane y = at + bx + c for observations (t[subscript]i,x[subscript]i,y[subscript]i), i = 1, 2, ..., n, and to present meanings for the coefficients a and b. In this note, formulas for the coefficients a and b in the least-squares fit are…

Certain definitions introduce appropriate concepts, among which are the definitions of the counting functions of the primes and twin primes, along with definitions of the correlation coefficient in a bivariate sample space. It is argued conjecturally that the characteristic functions of the prime "p" and of the quantity "p"+2 are highly…