To achieve the vision of mathematics set forth in "Crossroads" ("AMATYC," 1995), students must experience mathematics as a sensemaking endeavor that informs their world. Embedding the study of mathematics into the real world is a challenge, particularly because it was not the way that many of us learned mathematics in the first place. This article…

The revolution of technology in education has heralded a new wave of learning styles and in some cases total dependence on technology. Yet, statistics reveal no significant improvement in student performance in Mathematics and a downward trend in basic algebra skills. The major impediment in the learning process is lack of understanding of the…

In this article, the authors discuss the importance of unexpected graphs as a vehicle for encouraging critical classroom dialogue. By examining such graphs more critically, teachers and their students can reexamine beliefs about the authority of technology in their classrooms. (Contains 15 figures.)

Calculus at the secondary school level has traditionally represented the peak of school mathematics in Australia, and has been available only to the most capable students. Until recently, many calculus curricula have focused on developing standard techniques, such as those concerned with differentiation and integration, with an emphasis on…

This article describes investigative calculus projects in which students explore a question or problem of their own construction. Three exemplary pieces of student work are showcased. Investigative calculus projects are an excellent way to foster student understanding and interest in calculus. (Contains 4 figures.)

Research on technology-use for teaching and learning statistics is sparse compared to that in algebra and calculus. This paper addresses the deficiency with regard to teaching and learning about "trend" in bivariate data. Available research findings are reviewed and an empirical inquiry in a year 12 (upper secondary) class is reported. Treatment…

To help struggling seniors with the expectations of a high school precalculus course, their lack of confidence, and the "new" intimidation they feel in the classroom, the teacher discusses additional study skills necessary for performing well in the mathematics classroom. The author compares studying mathematics to the practice necessary to…

The Fundamental Theorem of Calculus is discovered based on the use of data analysis techniques applied to a variety of common families of functions. (Contains 8 figures and 6 tables.)

Issues related to college access and the need for a pipeline of STEM teachers, provided the impetus for the Ohio Board of Regents (OBR) to issue a call for Ohio universities to design pre-college experiences for high school students with three major goals in mind: (a) improvement in mathematics, science, or foreign language learning; (b) increased…

Parametric differentiation is used to derive the partial fractions decompositions of certain rational functions. Those decompositions enable us to integrate some new combinations of trigonometric functions.

At the University of Toronto at Scarborough, we provide enhanced flexibility to our students using a blended learning approach (i.e., the webOption) whereby classes are videotaped as they are offered in a traditional manner, then posted online for subsequent student access. Students can attend lectures live, watch them online at their convenience,…

Because statistical analysis requires the ability to use mathematics, students typically are required to take one or more prerequisite math courses prior to enrolling in the business statistics course. Despite these math prerequisites, however, many students find it difficult to learn business statistics. In this study, we use an ordered probit…

The calculus-based, introductory physics course is the port of entry for any student interested in pursuing a college degree in the sciences, mathematics, or engineering. There is increasing demand for online delivery options that make the course more widely available, especially those that use best practices in student engagement. However,…

Social cognitive research has linked students' perceived academic capabilities, or self-efficacy, to academic choices, self-regulation, and performance in diverse contexts from reading comprehension to mathematical problem solving. This study addressed a need to investigate the interactions among prior achievement, self-efficacy, calibration (the…