First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)

The classical problem of the brachistochrone asks for the curve down which a body sliding from rest and accelerated by gravity will slip (without friction) from one point to another in least time. In undergraduate courses on classical mechanics, the solution of this problem is the primary example of the power of variational calculus. Here, we…

A sample of 127 high school Advanced Placement (AP) Calculus students from two schools was utilized to study the effects of an engineering design-based problem solving strategy on student performance with AP style Related Rate questions and changes in conceptions, beliefs, and influences. The research design followed a treatment-control multiple…

The Black-White achievement and participation gap in mathematics is a major concern for educators in America. In order to understand why these gaps exist and have continued to exist over the years, it is important to identify some of the factors that may contribute to them. However, one of the limitations in identifying factors that influence the…

Nowadays, many technological means are available to support teaching, such as the interactive whiteboard, class sets of laptop or netbook computers, and high speed internet access. For mathematics education there are advanced software packages for geometry, algebra, calculus, and statistics, which in many cases are available on line at no cost.…

This experiment was designed to determine which assessment method: continuous assessment (in the form of daily in-class quizzes), cumulative assessment (in the form of online homework), or project-based learning, best predicted student learning (dependent upon post-test grades) in an undergraduate mathematics course. Participants included 117…

The authors sought to better understand the relationship between students participating in the Advanced Placement (AP) program and subsequent performance on the Scholastic Aptitude Test (SAT). Focusing on students graduating from U.S. public high schools in 2010, the authors used propensity scores to match junior year AP examinees in 3 subjects to…

The integration of technology into modern classrooms has enhanced learning opportunities for students. With increased access to educational content, students gain a better understanding of the concepts being taught. "Flipped Instruction: Breakthroughs in Research and Practice" is a comprehensive reference source for the latest scholarly…

The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…

Over the past several years, we have been exploring and researching a phenomenon that occurs among undergraduate students that we called extension of linear models to non-linear contexts or overgeneralization of linear models. This phenomenon appears when some students use linear representations in situations that are non-linear. In a first phase,…

This paper discusses a possible solution to a problem frequently encountered by educators seeking to use computer-based or multiple choice-based exams for mathematics. These assessment methodologies force a discrete grading system on students and do not allow for the possibility of partial credit. The research presented in this paper investigates…

"Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…

Many empirical investigations concerning the use of computer algebra systems (CAS) and symbolic calculators (SC) are restricted to a period of only a few weeks. They do not show long-term effects on students understanding. Therefore, a long term project (2003-2012) was started to test the use of symbolic calculators in Bavarian…

This article presents material that has been used as a classroom activity in a calculus-based probability and statistics course. The application was used in the first few lessons of this course. Students had three previous semesters of math, including calculus (single and multivariable), differential equations, and a course in mathematical…

An account is made of the relationship between the convergence behaviour of a sequence and the accumulation points of the underlying set of the sequence. The aim is to provide students with opportunities to contrast two types of mathematical entities through their commonalities and differences in structure. The more set-oriented perspective that…