Vectors have important applications both within and outside mathematics, but the concept of vectors is often taught to students in a less-than-engaging way, leading to students feeling inadequate and frustrated. This article describes the use of a mathematical microworld, "Driving with Vectors," to explore vectors using equitable…

Probabilistic reasoning underpins much of middle school students' future work in data analysis and inferential statistics. Unfortunately for many middle school students, probabilistic reasoning is not intuitive. One specific area in which students seem to struggle is determining the probability of compound events (Moritz and Watson 2000). Research…

In this article, physical quantities related to the motion of a parachute system in the framework of Newton's law of mechanics guide an informal approach to the mathematical concept of function. Furthermore, a graphical simulator that enables visualization of the fall of object-parachutes system is presented. The article is aimed at students and…

Research findings support the use of computer-assisted instruction (CAI) as a curriculum supplement for improving math skills, including math fact fluency. There are a number of websites and mobile applications (i.e., apps) designed to build students' math fact fluency, but the options can become overwhelming. This article provides implementation…

Calculus, perhaps more than other areas of mathematics, has a reputation for being steeped with procedures. In fact, through the years, it has been noticed of many students getting caught in the trap of trying to memorize algorithms and rules without developing associated concept knowledge. Specifically, students often struggle with the…

We present background and an activity meant to show both instructors and students that mere button pushing with technology is insufficient for success, but that additional thought and preparation will permit the technology to serve as an excellent tool in the understanding and learning of mathematics. (Contains 5 figures.)

Proportional reasoning pops up in math class in a variety of places, such as while making scaled drawings; finding equivalent fractions; converting units of measurement; comparing speeds, prices, and rates; and comparing lengths, areas, and volume. Students need to be exposed to a variety of representations to develop a sound understanding of this…

This article describes a vision of student use of dynamically connected representations as they investigate mathematical ideas. Although this article is intended to generate discussion about the potential of dynamically connected representations, we situate the discussion within actual descriptions of its use with students in a newly designed…

Since the dawn of civilization, pictorial representations and symbols have been used to communicate simple statistics. Efficient and effective, they are still used today in the form of pictures and graphs to record and present data. Who can tie their shoes? How many calories are in your favorite food? Make data and graphs relevant and interesting…

We consider two different algebra topics that can be taught in a typical college class. With each topic, we demonstrate how a teacher can delve deeper using a computer algebra system.

This article describes an activity for secondary mathematics students using digital imaging on The Geometer's Sketchpad to model polar functions of flowers. The activity presented in the appendix engages students in learning and exploring the polar coordinate system while helping them analyze a real-world situation. By completing this activity,…

Mathematics teachers at all levels of public school education want their students to understand and apply math concepts. When students use different technologies in the classroom, they will become engaged in meaningful learning that helps them to move from abstract ideas to hands-on applications. Students can "see" math concepts and manipulate…

The study compared the effects of a professional development course delivered in an online and a face-to-face format. The effects examined included changes in teachers' pedagogical beliefs, instructional practices, and understanding of teaching number-sense and related mathematical concepts. The study randomly assigned participants to either the…

Teaching is a complex endeavour that requires teachers to meld knowledge about the nature of learners, pedagogical strategies and discipline content. In recent years an increasing variety of educational technologies are finding their way into the school classroom, including the widespread acceptance of interactive whiteboards (IWBs). The emerging…

This paper describes a high school project where the mathematics teaching and learning software M@th Desktop (MD) based on the Computer Algebra System Mathematica was used for symbolical and numerical calculations and for visualisation. The mathematics teaching and learning software M@th Desktop 2.0 (MD) contains the modules Basics including tools…