What is the main thing about Prelude to Algebra that makes it unique?
It’s hard to single out just one thing, since it presents many new ideas. But the fundamental difference is the way it explains the basic arithmetic operations. For example, the traditional way of thinking about the sum of 5 and 3 is to think of the two numbers 5 and 3 being combined together by addition to form a third number, their sum 5 + 3 or 8. In the operator approach as developed in Prelude, we think of starting with the number 5 and applying the increase operator + 3 to get the sum 5 + 3 or 8. So we don’t combine two numbers to get a third number, we start with one number and change it into a second number by joining an operator, in this case an increase of 3. While this change of perspective is subtle, it turns out to be really significant in how it simplifies everything from multiplication and exponents to canceling and solving equations. It also anticipates the properties of signed numbers. Long before children encounter -1 as a mysterious negative number, they are already c
