Spreadsheets are computerized, numerical record keeping systems which were designed originally to replace paper-based, ledger accounting systems. Essentially, a spread sheet is a grid or matrix of empty cells with columns identified by letters and rows identified by numbers. Each cell is a placeholder for values, formulas interrelating values in other cells, or mathematical functions that mathematically or logically manipulate values in other cells. Functions are small programmed sequences that may, for instance, match values in cells with other cells, look up values in a table of values, or create an index of values to be compared with other cells.

Spreadsheets were originally developed and are most commonly used to support business decision making and accounting operations. They are especially useful for answering "what if" questions, for instance, what if interest rates increased by one percent? Changes made in cell automatically recalculate all of the affected values in other cells. Spreadsheets are also commonly used for personal accounting and budgeting.

Spreadsheets also may be used as cognitive tools for amplifying mental functioning. In the same way that they have qualitatively changed the accounting process, spreadsheets can change any educational process when working with quantitative information. The Working Group for Technology of the National Curriculum Commission (1990), helping to frame the national curriculum in Great Britain, has recognized the role of spreadsheets as tools that enable students to use information technologies to explore patterns and relationships through graphs and charts (see fig. 1) and to develop and test sample hypotheses.

fig. 1 - chart of net worth

Spreadsheets are rule-using tools that require that users become rule-makers (Vockell & van Deusen, 1989). Calculating values in a spreadsheet requires that users identify relationships and patterns among the data that they wants to represent in the spreadsheet. Next, those relationships must be modeled mathematically using rules to describe the relationships in the model. Building spreadsheets requires abstract reasoning by the user.

Spreadsheets also support problem solving activities. Given a problem situation with complex quantitative relationships, spreadsheets can be used to represent those relationships. The "what-if" thinking that is best supported by spreadsheets is essential to Decision Analysis (Sounderpandian, 1989). For example, "What is the interest rate for 1998 is increased to 6%?" (see fig. 2) Such reasoning requires learners to consider implications of conditions or options, which necessarily entails higher order reasoning.

fig. 2 - Financial statement recalculated automatically by entering 6%

Identifying values and developing formulas to interrelate the values in spreadsheets enhances learners’ understanding of the algorithms used to compare them and also the mathematical models used to describe content domains. Students understand calculations (both antecedents and consequents) because they are actively involved in identifying the interrelationships between the components of the calculation. Spreadsheet construction and use demonstrates all steps of problem solutions, showing the progression of calculations as they are performed. The spreadsheet process models the mathematical logic that is implied by calculations. Making the underlying logic obvious to learners should improve their understanding of the interrelationships and procedures.

Numerous educators have explored the use of spreadsheets as cognitive tools. Spreadsheets have frequently been in mathematics classes for such purposes as a calculator to demonstrate multiplicative relationships in elementary mathematics (Edwards & Bitter, 1989), for rootfinding in pre-calculus using synthetic division, Bisection method, and Newton’s Method (Pinter-Lucke, 1992), for helping children to understand the meaning of large numbers (a million) by comparing quantities to everyday things (Parker & Widmer, 1991), and for solving elementary mathematical story problems in math class (Verderber, 1990), for implementing linear system solving algorithms for solving advanced mathematical formulas (Watkins & Taylor, 1989), and for implementing Polya's problem solving plan with arithmetic problems (Sgroi, 1992).

Most often, spreadsheets have been used to calculate quantitative relationships in various chemistry and physics classes, such as: calculating the dimensions of a scale model of the Milky Way in order to demonstrate its immensity (Whitmer, 1990); solving complex chemistry problems such as wet and dry analysis of flue gases, which may be expanded to include volumetric flow rate, pressure, humidity, dew point, temperature, and combustion temperature in an mass and energy balances course (Misovic & Biasca, 1990); modeling the shoichiometric relationships in chemical reactions and calculating how many bonds are broken, the energy required to break bonds, and the new masses and densities of the products and reagents in the reactions (Brosnan, 1990); calculating the force needed to lift various weights in various lever problems (Schlenker & Yoshida, 1991); solving rate equation chemical kinetics problems in a physical chemistry course (Blickensderfer, 1990); calculating and graphing quantum mechanical functions like atomic orbitals to simulate rotational and vibrational energy levels of atomic components in a physical chemistry class (Kari, 1990); solving a number of science problems, including an incline plane, converting protein into energy (Goodfellow, 1990); solving physics laboratory experiments such as time, displacement, velocity and their interrelationships using a free-fall apparatus (Krieger & Stith, 1990); and estimating and comparing the relative velocities of different dinosaurs (Karlin, 1988).

Spreadsheets are also useful in social studies instruction, such as representing Keynesian vs. classical macro-economic models, including savings-investment and inflation-unemployment (Adams & Kroch, 1989); supporting Decision Analysis by helping users to find the best use of available information as well as evaluating any additional information that can be obtained (Sounderpandian, 1989); interrelating demographic variables in population geography courses using population templates (Rudnicki, 1990); tracking portfolio performance in a stock training simulation (Crisci, 1992); and creating and manipulating economic models (e.g. balance of payments, investment appraisal, elasticity, cost benefit analysis) in an economics course (Cashien, 1990).

Spreadsheets have even supported ecology by being used to analyze field data on ecology of tree species (Sigismondi & Calise, 1990) and even analyzing lunchroom trash and projecting annual waste for an Earth Day project (Ramondetta, 1992).

Spreadsheets are flexible cognitive tools for representing, reflecting on, and calculating quantitative information. They can be used to model mathematical processes or the relationships between variables in the sciences and social sciences. They are powerful and flexible tools.

Databases are computerized record keeping systems which were developed originally to replace paper-based filing systems. A database consists of one or more files, each of which contains information in the form of sets of records (e.g. individual's account information). Each record in the database is divided into fields which describe the class or type of information contained therein. The content and arrangement of each field is standardized within the records. Database management systems provide the capability for managing , searching, and sorting the information in a database and creating and defining new database files. Having defined the data structure, information can be entered into or deleted from the file. Any database file can be saved on a disk, deleted, copied, or saved under a new name. These computer file management functions enable the user to make permanent copies of the information in the database. Most applications of databases support administrative purposes. However, the functionality of databases may also be used to analyze and organize subject matter content into databases which can then be searched and sorted to answer specific questions about the content or to identify interrelationships and inferences from the content, that is, use databases as cognitive tools.

The organized and defined nature of databases facilitates the analysis of content domains. The use of databases for engaging thinking has been largely limited to elementary and secondary schools, however, the methods are just as applicable in higher education. McCurry and McCurry (1992) described the use of databases to classify types of sea shells. Rooze (1988-89) described the value of databases to social studies, because students play an active role in learning when they are creating databases. The student prepared database requires students to determine the information that needs to be collected and to organize that information into meaningful categories. Pon (1984) described the use of databases as an inquiry tool to aid higher-level thinking in a fourth-grade American Indian studies course. Building databases involves analyzing, synthesizing, and evaluating information, according to Watson and Strudler (1988-89).

There are three basic activities involved in developing and using knowledge databases, each of which engages a different combination of cognitive processes. The simplest application is filling in an existing database by searching for information that fits into the data structure provided by the instructor. For instance, a database comparing the state of social and economic development of different countries might include fields such as GNP, population, infant mortality rate, personal income, literacy rate, defense spending, and so on (see Fig. 1). Students could consult reference sources to locate information to include in the database. Learners could also use the database to answer or construct questions about the information in it, such as:

Fig. 1. Subject database.

The most demanding application of databases is to identify a content domain, sense an information need, and develop a data structure for accommodating the information to be included, filling in the information, and then writing the kinds of questions that require learners to interrelate fields of information and make inferences. A large number of critical thinking skills are required to use and construct knowledge-oriented databases.

The recommendations for using databases as cognitive tools have provided only anecdotal evidence to support their use. There is no formal research base as yet.