What is Mathematics?
To most people, mathematics is about calculating numbers. Some may even expand the definition to include the study of quantity (arithmetic), space (plane and solid geometry), and change (calculus). But even this definition does not encompass the many areas where mathematics and mathematicians are found. A broader definition of mathematics comes from W. W. Sawyer. In the 1950s, he
described mathematics as the “classification and study of all possible patterns.” He explained that pattern was meant “to cover almost any kind of regularity that can be recognized by the mind” (Sawyer, 1982).
Other mathematicians who share Sawyer’s view have shortened the definition even further: Mathematics is the science of patterns. Devlin (2000) not only agrees with this definition but has used it as the title of one of his books. He explains that patterns include order, structure, and logical relationships and go beyond the visual patterns found in tiles and wallpaper to patterns that occur everywhere in nature. For example, patterns can be found in the orbits of the planets, the symmetry of flowers, how people vote, the spots on a leopard’s skin, the outcomes of games of chance, the relationship between the words that make up a sentence, and the sequence of sounds we recognize as music. Some patterns are numerical and can be described with numbers, such as voting patterns of a nation or the odds of winning the lottery. But other patterns, such as the leopard’s spots, are visual designs that are not connected to numbers at all.
Devlin (2000) further points out that mathematics can help make the invisible visible. Two thousand years ago, the Greek mathematician Eratosthenes was able to calculate the diameter of Earth with considerable accuracy and without ever stepping off the planet. The equations developed by the eighteenth-century mathematician Daniel Bernoulli explain how a jet plane flying overhead stays aloft. Thanks to Isaac Newton, we can calculate the effects of the unseen force of gravity. More recently, linguist Noam Chomsky has used mathematics to explain the invisible and abstract patterns of words that we recognize as a grammatical sentence.
If mathematics is the science of patterns and if visible and invisible patterns exist all around us, then mathematics is not just about numbers but about the world we live in. If that is the case, then why are so many students turned off by mathematics before they leave high school? What happens in those classrooms that gives students the impression that mathematics is a sterile subject filled with meaningless abstract symbols? Clearly, educators have to work harder at planning a mathematics curriculum that is exciting and relevant and at designing lessons that carry this excitement into every day’s instruction.
I will leave the discussion of what content to include in a Pre K to 12 mathematics curriculum to experts in that area. My purpose here is to suggest how the research in cognitive neuroscience that we have discussed in the previous chapters can be used to plan lessons in mathematics that are more likely to result in learning and retention.
Devlin, K. (2000). The math gene: How mathematical thinking evolved and why numbers are like gossip. New York: Basic Books.
Sawyer, W. W. (1982). Prelude to mathematics. New York: Dover Publications.