Despite repeated discussions and practice, algebra students continue to make variable errors, in many ways, year after year. This same problem appeared thirty years ago in a list of common errors that math teachers today would immediately recognize, many involving exponents and distribution (Marquis 1988). Similar complaints even appeared in the…

In the criminal justice system, defendants accused of a crime are presumed innocent until proven guilty. Statistical inference in any context is built on an analogous principle: The null hypothesis--often a hypothesis of "no difference" or "no effect"--is presumed true unless there is sufficient evidence against it. In this…

The mathematics that students see in their textbooks is highly polished. The steps required to solve a problem are all clearly laid out. Thus, students are denied what could be a valuable learning experience. Often when students meet a problem that differs only slightly from the ones in the book, they are unable to proceed and afraid to "play…