Reasoning

Virtually all of mathematics is related to reasoning in one form or another. Perhaps you use the word reasoning in the same way you use the word thinking. However, we will be examining several specific kinds of mathematical reasoning, and each of these kinds of reasoning will have a name. Recent research on the brain suggests that each different kind of reasoning is handled by different parts of the brain or by different combinations of parts of the brain. Therefore, each of these different kinds of reasoning will probably have a different feel to the student of mathematics. It is likely that each learner will find some forms of reasoning to be easier than others, and each person will differ in which areas he or she finds to be difficult. One of the most powerful features of mathematics is that many mathematical problems can be solved using various forms of reasoning. One person will easily find a visual way to solve a problem, while another person will easily find a symbolic way to solve the same problem. By studying and becoming very familiar with many forms of reasoning, the student of mathematics will discover which ways are her preferred ways and will know to use those ways deliberately whenever she is faced with a difficult problem.