If we can learn to recognize these patterns, our ability to do mathematics, the science of patterns , is greatly enhanced. For example, when confronted with a jumble of numbers, or data, can we organize the data in ways that help us see the patterns, e.g., how tightly grouped or spread out the numbers are and whether or not there might be one number or pattern of numbers in there somewhere which is fairly representative of all the others. Spotting patterns isn t necessarily simple. It usually takes work. They don t materialize out of the blue and we don t have to try to snatch them out of thin air as they whiz by.
Patterns are by definition repeated.
If we take the time to make some calculations, organize our thinking and calculations into tables so that we can see how what we are doing repeats itself, we can find the patterns. But, quite the contrary, algebraic equations are just a way of representing relationships. They are just a shorthand for representing patterns that happen over and over again, ad infinitim, forever. Similarly with solving problems. These objects are related and these relationships can often be represented with equations.