This sounds a bit rigid, doesn’t it? Following rules? Don’t we want to encourage folks to be creative and think outside the box? Yet when we’re learning math, (which really is a science that was discovered rather than invented), the rules are the entire foundation! If you start with the rules, you can discern further relationships and discover more rules and relationships. Virtually the entire structure of Math was built in this manner.
If you learn the rules, and follow them without fail, you can apply these rules in a myriad of ways. If you learn that “a negative multiplied by a negative results in a positive product” then you can apply that rule infinitely many ways. You can multiply integers, fractions, decimals, radicals, and even polynomials, and the rule is applied the same way.
In step 1 you “learn the facts” which is basically the rote-memorization part of your foundation. Now you apply those facts using the rules of math by following those rules, which will take you infinitely further.
In our next post, we’ll tie the first two steps together.