Using Spreadsheets to Enhance Understanding of Number Theory

Computer spreadsheets can help elementary school students explore concepts in number theory. We describe a spreadsheet program that can generate all the factors of an integer. To understand how the spreadsheet solves these problems, we use the metaphor of a robot. The robot must interpret data from the real world and respond effectively. Although non-engineers may not understand the details, they can see what the robot types, and can discuss how the robot makes decisions. Students can see mathematical knowledge being used. The robot can add, subtract, multiply, and divide, and determine whether a number is an integer. Based upon this knowledge, the robot can determine the factors of a number. In one method, the robot follows the rules blindly, testing each possible factor. In the second method, the robot uses knowledge of number theory to solve the problem much more efficiently. The activities are extended to include the topic of prime numbers. In the first method, the robot determines that 97 is prime by performing all possible divisions starting with 1. Although the answer is correct, the method is inefficient. It is much more effective to apply knowledge of number theory to determine that only the prime numbers less than ten need to be tested. As a result, only four divisions, rather than 97, are needed to determine the correct answer. With the power of spreadsheets, students can observe different methods that get the correct answer, and discover those that are most efficient.