George Cobb … posted … on how statistics differs from mathematics and how that impacts the teaching of statistics by mathematics teachers. It was a great note but I felt that the “bad guy” was perhaps not entirely mathematics but the way in which mathematics has often been taught. While everyone the world over gets the same answer to a long division problem, if you look at other cultures and other times, you will find that the algorithms used have varied widely. Each has it’s justification, but those are rarely taught to children. This is why I refused to learn it in fourth grade;-) While some lament the substitution of an electronic device for the hallowed algorithm of their youth, both that algorithm and the plastic calculator are cultural artifacts that come and go while mathematical truth remains. In graduate level mathematics, definitions are chosen for a reason, though again that is rarely shared with the learner. What are the pros and cons and historical roots of the definitions of “real number” given by Cantor and Dedekind? So George’s comments made me think of a quote from another of my mentors that used to hang on my office door. It’s taken me this long to find it on an old Windows backup and move it to my Linux computer.
Robert B. Davis was an MIT-trained mathematician who gave up research to work with inner city children. The paragraphs below I assembled from a variety of his writings over the years — most of them never widely available.
“Whereas science and creative mathematics are essentially and necessarily tentative, uncertain and open-ended, the traditions of elementary school teaching in many instances are authoritative, definite, absolute, and certain.
Such a view is incompatible with science, with mathematics — or, for that matter, with nearly any serious body of thought. In fact many questions have no answer, some questions have many (equally good) answers, and some questions have approximate answers but no perfect answers. The “tolerance of ambiguity” that is required of anyone who would see the world realistically is a severe demand for some teachers.
It should be emphasized that the difficulty here is with some teachers, not with children. Children know that they live with incompleteness and uncertainty; scientists know that no other state is available to living human beings. Unfortunately, teachers have all too often been taught that every question has exactly one right answer, and that the child is entitled to know what it is — or, perhaps, should even be required to know what it is.”
One reason to learn and teach statistics is so we can become better mathematics teachers.