The intersection of a plane and a cone is a conic section and rotating the plane leads to a family of conics. What happens to the foci of these conics as the plane rotates? A classical result gives the locus of the foci as an oblique strophoid when the plane rotates about a tangent to the cone. The analogous curve when the plane intersects a…

The Sequences and Series calculus course (S&S) can be structured to provide students with a unique opportunity to build their proofs skills prior to or concurrently with a bridge course. This article offers a framework for S&S which places logical reasoning on equal footing with content, by employing the theorems and convergence tests as axioms,…

We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

A simple nonstiff linear initial-value problem is used to demonstrate the amplification of round-off error in the course of using a second-order Runge-Kutta method. This amplification is understood in terms of an appropriate expression for the global error. An implicit method is then used to show how the roundoff error may actually be suppressed.…

Scores on state standards-based assessments are readily available and may be an appropriate alternative to traditional placement tests for assigning or accepting students into particular courses. Many community colleges do not require test scores for admissions purposes but do require some kind of placement scores for first-year English and math…

What is the evidence that teachers who return to learn more mathematics are better teachers? Over more than a decade we have been involved in six different projects giving teachers the opportunity to reengage with mathematics. We have returned to them to ask the teachers about the long-term impact and to give us examples. The result extends…

This article discusses a writing project that offers students the opportunity to solve one of the most famous geometric problems of Greek antiquity; namely, the impossibility of trisecting the angle [pi]/3. Along the way, students study the history of Greek geometry problems as well as the life and achievements of Carl Friedrich Gauss. Included is…

This article discusses ways in which improvisational comedy games and exercises can be used in college mathematics classrooms to obtain a democratic and supportive environment for students. Using improv can help students learn to think creatively, take risks, support classmates, and solve problems. Both theoretical and practical applications are…

Students are entering college having earned credit for college Calculus 1 based on their scores on the College Board's Advanced Placement (AP) Calculus AB exam. Despite being granted credit for college Calculus 1, it is unclear whether these students are adequately prepared for college Calculus 2. College calculus classes are often taught from a…

The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem-solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

In this investigation, we examined the college readiness in math of Texas community college students using archival data from the Texas Higher Education Coordinating Board. Data analyzed were the rate of all first-time in college (FTIC) developmental education students who scored below the Texas college readiness standards in math and the rates of…

The present study aimed to investigate in what way and to what extent Taiwanese college students' epistemological views of mathematics had evolved during a history-based liberal arts mathematics course titled: "When Liu Hui Meets Archimedes--Development of Eastern and Western Mathematics." The course was designed to help college students…

This paper proposes and discusses how to use an assignment based on "Freakonomics" as a way to foster critical thinking and statistical literacy skills within the classroom.

This article presents a problem-based approach that prepares students for future learning in the classroom. In this approach, students complete problem-based activities before coming to class to familiarize themselves with the topics to be covered. After the discussion on how the use of these activities relate to the learning and transfer…

This paper reports a study on retention of differential and integral calculus concepts of a second-year student of physical chemistry at a Danish university. The focus was on what knowledge the student retained 14 months after the course and on what effect beliefs about mathematics had on the retention. We argue that if a student can quickly…