ABSTRACT
This chapter shows that formulating theories to account for data is absolutely essential to scientific progress and that theory are most crucial in difficult areas such as mathematics education. Humans have only very limited reasoning capacities. If experiments are reported together with their connection to existing theory, then the scientists who write the reports are telling readers clearly what they think the experiments mean and how they relate to other knowledge. Stating theoretical implications is an excellent way to suggest what information others might use. When scientists run an experiment, they do other scientists a great service by communicating their best judgment as to what parts of the results are general and might be applicable elsewhere, and what parts are not. The readers need not agree but, as the persons most knowledgeable about the experiment, scientists should make their judgments available. But mathematics education is a young field, and the study of algebra learning is even younger.
