This study investigates the relationship between the use of graphing calculators employed as Type II technology and student achievement, as determined by assessing students' problem solving skills associated with the concept of function, at the college algebra and pre-calculus level. In addition, this study explores the integration of graphing…

A perception exists that physics and engineering students experience difficulty in applying mathematics to physics and engineering coursework. While some curricular projects aim to improve calculus instruction for these students, it is important to specify where calculus curriculum and instructional practice could be enhanced by examining the…

How do mathematics teachers introduce the concepts of slope, rate of change, and steepness in their classrooms? Do students understand these concepts as interchangeable or regard them as three different ideas? In this article, the authors report the results of a study of high school Advanced Placement (AP) Calculus students who displayed…

This case study documents the struggles and successes encountered by a pre-calculus teacher while using Classroom Connectivity Technology (CCT) daily in her community college mathematics course. CCT refers to a wireless communication system that connects a teacher's computer with an individual student's handheld calculator and has been associated…

Appropriate use of instructional technology can be an elusive quest for many faculty members. The iTouch is one of the latest technologies available to us, yet there is little literature on its use and effectiveness to support learners in their learning. Six new faculty members from various disciplines elected to integrate the device in their own…

Interactive lecture demonstrations (ILDs) are a powerful tool designed to help instructors bring state-of-the-art teaching pedagogies into the college-level introductory physics classroom. ILDs have been shown to improve students' conceptual understanding, and many examples have been created and published by Sokoloff and Thornton. We have used the…

College students enrolling in the calculus sequence have a wide variance in their preparation and abilities, yet they are usually taught from the same lecture. We describe another pedagogical model of Individualized Additional Instruction (IAI) that assesses each student frequently and prescribes further instruction and homework based on the…

Today's classrooms are much different from those of yesterday. The increased diversity of learners, students' familiarity and attraction to technology, and the improved availability of technology in education have made it increasingly possible for teachers to use various forms of technology in instruction. The responsibility for addressing these…

Engineering technology students can attain a meaningful mathematics learning if they are allowed to actively participate in hands-on activities. However, the current dissemination of knowledge in the classroom still focuses on teacher-centered paradigm of teaching. A study to explore lecturers' views regarding a newly developed integral calculus…

To find the number of distinct real roots of the cubic equation (1) x[caret]3 + bx[caret]2 + cx + d = 0, we could attempt to solve the equation. Fortunately, it is easy to tell the number of distinct real roots of (1) without having to solve the equation. The key is the discriminant. The discriminant of (1) appears in Cardan's (or Cardano's) cubic…

In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…

This study adds momentum to the ongoing discussion clarifying the merits of visualization and analysis in mathematical thinking. Our goal was to gain understanding of three calculus students' mental processes and images used to create meaning for derivative graphs. We contrast the thinking processes of these three students as they attempted to…

This article discusses a three-step method that was used in a college calculus course. The three-step method was developed to help students understand the course material and transition to be more independent learners. In addition, the method helped students to transfer concepts from short-term to long-term memory while lowering cognitive load.…

If students are in an advanced mathematics class, then at some point they enjoyed mathematics and looked forward to learning and practicing it. There is no reason that this passion and enjoyment should ever be lost because the subject becomes more difficult or rigorous. This author, who teaches advanced precalculus to high school juniors,…

In this note, we give an alternative approach to introduce the mean value theorem. By first establishing Cauchy-type Mean Value Theorem, we can easily derive other Mean Value Theorem, and their consequences. We believe this approach is more effective in presenting this topic in a typical calculus class.