The role of spreadsheets in an investigation of Fibonacci numbers

We introduce a function Z(k) which measures the number of distinct ways in which a number can be expressed as the sum of Fibonacci numbers. Using a binary table and other devices, we explore the values that Z(k) can take and reveal a surprising relationship between the values of Z(k) and the Fibonacci numbers from which they were derived. The article shows the way in which standard spreadsheet functionalities makes it possible to reveal quite striking patterns in data.

Spreadsheets and Bulgarian goats

We consider a problem appearing in an Australian Mathematics Challenge in 2003. This article considers whether a spreadsheet might be used to model this problem, thus allowing students to explore its structure within the spreadsheet environment. It then goes on to reflect on some general principles of problem decomposition when the final goal is a successful and lucid spreadsheet implementation.

Applications of Spreadsheets in Education : The Amazing Power of a Simple Tool

This e-book is devoted to the use of spreadsheets in the service of education in a broad spectrum of disciplines: science, mathematics, engineering, business, and general education. The effort is aimed at collecting the works of prominent researchers and educators that make use of spreadsheets as a means to communicate concepts with high educational value. The e-book brings some of the most recent applications of spreadsheets in education and research to the fore. To offer the reader a broad overview of the diversity of applications, carefully chosen articles from engineering (power systems and control), mathematics (calculus, differential equations, and probability), science (physics and chemistry), and education are provided. Some of these applications make use of Visual Basic for Applications (VBA), a versatile computer language that further expands the functionality of spreadsheets. The material included in this e-book should inspire readers to devise their own applications and enhance their teaching and/or learning experience.

Discrete phase-locked loop systems and spreadsheets

This paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40 years, may exhibit extremely complicated behaviour interpreted in contemporary terms as transition from global asymptotic stability to chaos through period-doubling bifurcations. The authors argue that embedding advanced mathematical ideas in the technological tool enables one to introduce fundamentals of discrete control systems in tertiary curricula without learners having to deal with complex machinery that rigorous mathematical methods of investigation require. In particular, in the appropriately designed spreadsheet environment, one can effectively visualize a qualitative difference in the behviour of systems with different types of non-linear characteristic.

Some unusual applications of the `Error-bar` feature in Excel spreadsheets

This paper demonstrates how the "error-bar" feature can be used to extend the utility of "worldware" spreadsheet packages in producing high-quality graphs for university teaching and learning, and for research. To further utilize the advantages of spreadsheets in university education, this paper seeks to overcome some of the earlier reservations about the lack of scientific plotting capabilities of spreadsheet applications. Specific examples of educational material in the areas of enzyme kinetics, vibrational spectroscopy, vibronic spectroscopy, and mass spectrometry are discussed. It is argued that, where practical, university educators should use "worldware" packages to prepare teaching aids, since these would better prepare their students for future employment. The use of software features for purposes that were not envisioned by the programmers has additional educational benefits in fostering flexibility and innovation. Other graphing packages can also use the "error-bar" feature in a manner similar to that described here for Excel.

A survey of first-year university students`ability to use spreadsheets

Universities are using more information and communication technologies (ICT) in their teaching and learning environments. An anonymous multiple-choice survey self-assessed the spreadsheet skills of students enrolled in first-year units at the beginning of 2003. The results of the survey indicate significant deficiencies in the use of spreadsheets. There is a significant proportion of students who are unable to use spreadsheets as part of their education at the start of their university studies. The implications for tertiary education are discussed.

Using spreadsheets in chemical education to avoid symbolic mathematics.

Traditionally, quantum theory has traditionally relied heavily on the use of  mathematics. However, there is a significant cohort of students who are  weak in mathematics, for example, students who are majoring in   biochemistry, biological sciences, etc. This paper reports on the use of  spreadsheets to generate approximate numerical solutions and visual  (graphical) descriptions as a method of avoiding or minimizing symbolic  manipulations, mathematical derivations and numerical computation. A  specific example from quantum theory is provided. Some aspects of  educational pedagogy of spreadsheet usage are discussed.

Differentiation from first principles using spreadsheets

The article demonstrates the ability of spreadsheets to fit a polynomial to a set of discrete points. It is noted that such an ability enables students to not just evaluate a gradient at a single point, but at a whole family of points, which generates the analytical global gradient function of secants without doing any algebraic manipulations. One of the advantages of such an approach is that it enables the class to focus on the concepts being taught, rather than being hindered by the mechanics of trying to factorise a cubic polynomial.

Using graphics calculators and spreadsheets in chemistry : solving equilibrium problems

Discusses tabular and graphical approaches to equilibrium calculations.

Scaling a Dataflow Testing Methodology to the MultiparadigmWorld of Commercial Spreadsheets

Spreadsheets are widely used but often contain faults. Thus, in prior work we presented a data-flow testing methodology for use with spreadsheets, which studies have shown can be used cost-effectively by end-user programmers. To date, however, the methodology has been investigated across a limited set of spreadsheet language features. Commercial spreadsheet environments are multiparadigm languages, utilizing features not accommodated by our prior approaches. In addition, most spreadsheets contain large numbers of replicated formulas that severely limit the efficiency of data-flow testing approaches. We show how to handle these two issues with a new data-flow adequacy criterion and automated detection of areas of replicated formulas, and report results of a controlled experiment investigating the feasibility of our approach.