Spreadsheets were invented in the 1970's as tools for business calculation, principally financial calculation. They consist of large arrays in which numerical and textual data can be entered and on which various calculations can be performed efficiently. The calculations can take many forms, but these days tend to include arithmetic, 'scientific', statistical, financial, calendar and logical functions. It is the ability of spreadsheets to be programmed with formula commands that gives them their power, allowing for financial projections to be made (so-called what-if analyses). Of particular significance is the ability to 'fill down' or 'copy down' a formula easily and efficiently from one cell to a range of others, thus giving rise to recursive functions.
Spreadsheets first became evident in secondary schools in the 1980's, especially in the educational computing areas of schools. For a time, there was a common view of the 'computer as a tool', perhaps first popularized by Robert Taylor's trichotomy of computer as 'tutor, tool, tutee'. The 'tools' most commonly used in school computing have been word processing, databases and spreadsheets. Similarly, integrated computer packages (such as Microsoft Works, Excel, ClarisWorks and Apple Works) include at least a word processor, a database facility and a spreadsheet as integral parts. (These days they also include drawing, painting and telecommunications facilities as well.) A consequence of all this is that spreadsheets are available in many homes and in all schools in affluent countries like Australia.
In the early 1980's, the possibility of using spreadsheets for relatively sophisticated mathematical tasks was explored (most notably by Deane Arganbright's Mathematical Applications of Electronic Spreadsheets, McGraw-Hill 1985) and the possibilities of using spreadsheets as tools for mathematics education was also discussed in some circles. However, many people regarded the spreadsheet as a solution in search of a problem, at least educationally speaking, and of less value than computer (and later, calculator) software developed with the needs of student learners in mind. In recent times, spreadsheets have become increasingly sophisticated, and now routinely include significant graphing capabilities as well as numerical capabilities. A recent very interesting publication is David Sjöstrand's Mathematics with Excel, Chartwell-Bratt 1994).
Mathematically speaking, spreadsheets have considerable potential. They can be used for tabulating functions, graphing functions, statistical analysis, simulation and financial mathematics, in each case requiring some expertise by the user to manipulate the inbuilt spreadsheet functions efficiently to achieve a desired end. A small example of using a spreadsheet to explore the idea of chaos is given in a paper I wrote some years ago. Another example is given in the fractions file, exploring what happens when a series of fractions is constructed using various rules and various starting points. Yet another example is given in the division file, which provides the decimal expansion of fractions to an (almost!) unlimited number of places.
The two most significant educational disadvantages of spreadsheets for mathematics is that they don't deal directly and conventionally with algebraic variables and they require a computer to operate them. Thus, to use a spreadsheet to draw a graph of, say, y = sin x requires that first a set of replacement values of x be generated (using a 'fill down' type of command) and then the associated y-values are generated (by obtaining the sine of each of the x-values in turn - again using a fill down command). Once the data are generated in this way, the graphing facility needs to be invoked to draw the graph. This is somewhat more cumbersome and tedious than a computer grapher or a graphics calculator, and uses cell names (such as A1, A2, A3, ... and B1, B2, B3, ...) instead of the variables x and y. While a sophisticated user may not find these differences worrying, it is less likely that this will be the case for unsophisticated users. The tabulation capabilities of spreadsheets can be put to good use for learning algebra, nonetheless. There are some examples in Access to Algebra Book 3 (Curriculum Corporation), where the numerical solution of equations using spreadsheets is demonstrated and students are expected to acquire this as one of a number of ways of thinking about and dealing with elementary equations.
Of even more practical significance is the need to access a computer to operate a spreadsheet. One consequence of this is that students will not be permitted to use a spreadsheet in high stakes public examinations, because there will not be enough computers to go around, and there will be lingering unease about other information available on computers, to say nothing of the difficulties associated with computer malfunctions (hardware or software) during examinations.
A second consequence of needing a computer is that it is often difficult to arrange enough computers to be available in most schools when and where they are needed. While many homes in countries like Australia these days have a computer (indeed, many homes have more than one computer!), there are many other homes that do not have computers, and are unlikely to acquire one in the foreseeable future. Students in homes that have recently purchased computers probably have a spreadsheet available to them, but this is not always the case. There are also problems associated with the differences between home spreadsheet software and school software, as they will normally be different, sometimes significantly. Inequities of this kind are difficult for schools to deal with. While schools frequently have access to computer laboratories and classroom computers, these are not always available when needed, particularly if the need cannot be programmed in advance (which is of course usually the case in practice).
As far as accessibility is concerned, graphics calculator still are more available (or potentially so) for educational purposes than anything that requires a computer. When issues of student affordability, home use, portability, use across the curriculum and examination use are considered carefully, the spreadsheet is still a very poor second to a graphics calculator.
Here are some links to web sites that deal with various aspects of using spreadsheets for mathematics. Further contributions here would be welcome.
A beginner's guide to the nature and use of spreadsheets is available at the Math Forum .
The University of Vienna site contains many references to uses of spreadsheets and spreadsheet resources on the web.
Maths Net has much interesting material and includes some references to spreadsheets and to Excel in particular. The A to Z of spreadsheets answers most operational questions.
The Spreadsheet User Journal is published by Sheffield Hallam University in the UK.
Spreadsheets in Education is an electronic journal founded recently, devoted to the place of spreadsheets in education.
The Math Forum Spreadsheets page has some examples and advice.
Some examples for GCSE have been developed by Brian Fitzsimmons and Ken Houston:
"The purpose of this article is to share some ideas on the use of spreadsheets in the teaching of GCSE mathematics and to inform the reader of the availability of a software package (Mac or PC) which can be obtained from the first author (BF) for the price of a disc plus postage. The resource provided is a simplified guide to getting started with spreadsheets together with some simple applications. Our survey of teachers indicated that they would welcome a self-instructional pupil workbook on getting started, which would also be useful to teachers themselves. The survey indicated that teachers' main criticism of currently available materials on the use of spreadsheets is that the manuals go into far too much detail to start with, and most non IT teachers find this daunting and offputting."
Interactive Excel projects from the Center for Technology and Teacher Education, University of Virginia, show some excellent examples of spreadsheets used for learning activities.