Introduction: Research on university-level academic performance has significantly linked failure and dropping out to formal reasoning deficiency. We have not found any papers on formal thought in Argentine university students, in spite of the obvious shortcomings observed in the classrooms. Thus, the main objective of this paper was exploring the…

Many academics like to isolate a piece of the world to study: an important social issue, a central philosophical problem, a key moment in history. They know they're oversimplifying but they do it anyway--it's the only way to make progress, and what's more, their little worlds are often more beautiful than the real one. This paper shares a story of…

Using case study analysis and a cognitive theoretical orientation, we examine elements of knowledge for teaching needed by a mathematician to orchestrate whole-class discussions in an undergraduate mathematics classroom. The instructor, an experienced teacher and mathematics researcher, used an inquiry-oriented curriculum to teach a differential…

This textbook is a course in differential calculus, integral calculus, and calculus of variations.

This note offers a derivation of the Euler-Maclaurin formula that is simple and elementary. In addition, the paper shows that the derivation provides Euler-Maclaurin formulas for a variety of functionals other than the trapezoid rule.

This paper deals with a brief historical introduction to fractional calculus with basic ideas, definitions and results of fractional order integration and differentiation of arbitrary order.

When first-year calculus students are interested in studying double integrals, they can find, in standard textbooks, a detailed description of the different regions of integration. The aims of this paper are: to give a criterion to select the plane that will be projected, to classify the projections, and to give a simple rule to obtain them.…

The Bernoulli polynomials are generalized and some properties of the resulting generalizations are presented.

This study sought to compare the performance of students in the College Board Advanced Placement Program® (AP®) compared to non-AP students on a number of college outcome measures. Ten individual AP Exams were examined in this study of students in four entering classes (1998-2001) at the University of Texas at Austin. The four main groups of…

This submission contains the Proceedings of the 2014 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of Alberta in Edmonton, Alberta. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

I report on the findings from research and literature on (a) use of symbols in mathematics, (b) algebraic/trigonometric expressions, (c) solving equations, and (d) functions and calculus. From these, some insights and implications for teaching and learning are derived.

This paper reports on students' errors in performing integration of rational functions, a topic of calculus in the pre-university mathematics classrooms. Generally the errors could be classified as those due to the students' weak algebraic concepts and their lack of understanding of the concept of integration. With the students' inability to link…

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,…