Card sorting has the potential to provide opportunities for exploration of a variety of topics and levels. In a card-sorting task, each participant is presented with a set of cards--each of which depicts a relationship--and is asked to sort the cards into categories that make sense to him or her. The concept of function is critical to…

All common fractions can be written in decimal form. In this Discovery article, the author suggests that teachers ask their students to calculate the decimals by actually doing the divisions themselves, and later on they can use a calculator to check their answers. This article presents a lesson based on the research of Bolt (1982).

In this article, the authors show how students can form familiar geometric figures on the calculator keypad and generate numbers that are all divisible by a common number. Students are intrigued by the results and want to know "why it works". The activities can be presented and students given an extended amount of time to think about…

In this culture of instantaneous technology, students are familiar with immediate feedback. To maintain student engagement, it is vital for teachers to create similarly interactive experiences. Student-centered instruction is important in connecting students to key mathematical concepts. If the connection is not obvious, they may be unaware of…

The senior school Mathematics syllabus is often restricted to the study of single variable differential equations of the first order. Unfortunately most real life examples do not follow such types of relations. In addition, very few differential equations in real life have exact solutions that can be expressed in finite terms. Even if the solution…

Derivation of the law of radioactive decay is considered without prior knowledge of calculus or the exponential series. Calculus notation and exponential functions are used because ultimately they cannot be avoided, but they are introduced in a simple way and explained as needed. (Contains 10 figures, 1 box, and 1 table.)

Dynamic/interactive graphing applets can be used to supplement standard computer algebra systems such as Maple, Mathematica, Derive, or TI calculators, in courses such as Calculus, Differential Equations, and Dynamical Systems. The addition of this type of software can lead to discovery learning, with students developing their own conjectures, and…

The financial calculator is incorporated in finance education. In class, the instructor shows students how to use the financial calculator's function keys to solve time value of money (TVM) related problems efficiently. The fundamental finance course is required for all majors in the business school. Some students, especially…

In Part Three, the author reviews the basic ideas presented in Parts One and Two while arguing why the traditional equation-solving developmental algebra curricula is not a good choice for implementing neural response strategies presented in the first two parts. He continues by showing that the developmental algebra student audience is simply…

Quantitative literacy has been recognized as an important skill in the higher education and workforce communities, focusing on problem solving, reasoning, and real-world application. As a result, there is a need by various stakeholders in higher education and workforce communities to evaluate whether college students receive sufficient training on…

It seems rather surprising that any given polynomial p(x) with nonnegative integer coefficients can be determined by just the two values p(1) and p(a), where a is any integer greater than p(1). This result has become known as the "perplexing polynomial puzzle." Here, we address the natural question of what might be required to determine a…

The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were…

Student activities focused on discovering mathematics play an important role in the teaching and learning process. WebMathematics Interactive (WMI2) was developed to offer a fast and user-friendly on-line web interface to enhance the quality of both theoretical and applied mathematics courses. For the teacher, in the classroom, it provides…

For thousands of years before the invention of reliable clocks, humans measured their days by the motion of the sun. Astronomically, one day was the length of time it took for the sun to return to the same position in the sky. With the advent of precise mechanical chronometers such as Harrison's timekeepers (Sobel and Andrewes 1998), which ran at…

Before the advent of microcomputer-based labware (MBL), "time-of-flight" measurements for the speed of a transverse pulse on a string required elegant apparatus. This paper describes how to use an off-the-shelf MBL force sensor and a computer to perform the measurement. The data shown in this paper were collected using Vernier Software's wireless…