We present a calculation involving a wide class of real integrals by means of integration in the complex plane. Some particular cases where Euler numbers and Bell polynomials appear are discussed and a generalisation of some previous results is also provided. (Contains 1 table and 1 figure.)

A major challenge faced by teachers nowadays relates to the usage of proper educational technology to achieve a true and meaningful learning experience involving time for reflection. Teachers constantly seek new ways to improve instruction, but in virtual learning environments they often find themselves in a new role, interacting in a dynamic…

Making the transition from arithmetic to mathematics, especially algebra, is critical to future academic and economic success, yet many students find this transition difficult and success in algebra elusive. This paper reports on the outcomes achieved from a three year course of professional development, POWERSOURCE[c], that helped teachers apply…

The purpose of this study was to determine the impact of an integrated learning system on students who were considered at-risk of academic failure on the Texas Assessment of Knowledge and Skills (TAKS) mathematics assessment. Voyager Math (VMath), an integrated learning system had been implemented to address the needs of students at-risk of…

To better support students' conceptual understanding of algebra in the information age, we need an improved understanding of how students interpret connections between multiple representations using CAS as a representational toolkit. This research centers on the development of an analytic framework for categorizing students' connections between…

The current study investigated the effects of an undergraduate mathematics content course for pre-service elementary teachers. The participants' content knowledge was quantitatively measured using an instrument comprised of items from the Mathematical Knowledge for Teaching Measures (Hill, Schilling, & Ball, 2004). Using a one-group…

Although mathematical pattern tasks are often found in elementary school curricula and are deemed a building block for algebra, a recent report (National Mathematics Advisory Panel, 2008) suggests the resources devoted to its teaching and assessment need to be rebalanced. We examined whether children's developing proficiency in solving algebraic…

The study we report here examines parts of what Chevallard calls the "institutional" dimension of the students' learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To…

Research has shown that prediction has the potential to promote the teaching and learning of mathematics because it can be used to enhance students' thinking and reasoning at all grade levels in various topics. This article addresses the effectiveness of using prediction on students' understanding and reasoning of mathematical concepts in a middle…

Logistic growth displays an interesting pattern: It starts fast, exhibiting the rapid growth characteristic of exponential models. As time passes, it slows in response to constraints such as limited resources or reallocation of energy. The growth continues to slow until it reaches a limit, called capacity. When the growth describes a population,…

Case studies of two high schools that have been turned around from failing to successful show different ways in which failing high schools can be made to succeed. Both high schools concentrated on first helping incoming freshman, and both reforms were driven by data. They differed in staffing and the focus of their first year of reform.

This study compares the respective achievement of students in an integrated algebra course taught with two different types of handhelds over a period of one year. The experimental group was taught with TI-Nspire[TM] handhelds and was compared to the control group taught with TI-84 Plus graphing calculators. The teachers of each group received…

When developing online classrooms it is necessary to ensure that all learners will be successful in the course regardless of the topic or discipline that is being discussed. This becomes especially important when the class involves numerical data. This paper outlines the difficulty of delivering online classes such as algebra, accounting, and…

A possible contributing factor to students' difficulty in learning advanced mathematics is the conflict between students' "natural" learning styles and the formal structure of mathematics, which is based on definitions, theorems, and proofs. Students' natural learning styles may be a function of their intuition and language skills. The purpose of…

USM piloted the Math Zone in Spring 2007, a computer-based program in teaching MAT 101 and MAT 099 in order to improve student performance. This research determined the effect of the re-design of MAT 101 on student achievements in comparison to a traditional approach to the same course. Meanwhile, the study investigated possible effects of the…