First, a disclaimer. I am far from an expert on most of the topics which will be illustrated by questions. One of my aims in giving this talk is to let others know about a serious problem which exists beyond the problem of mathematical knowledge of teachers.
I have written about the problem in mathematics and hope that some others will use the resouces which exist to write about similar problems in other areas.
In his American Educational Research Association Presidential Address, which was published in Educational Researcher in 1986, Lee Shulman introduced the phrase “pedagogical content knowledge”. This is a mixture of content and knowing how to teach this content and is the one thing from his speech which has been picked up by the education community. However, there are a number of other points which he made which are important. Here is an early paragraph from this speech:
We begin our inquiry into conceptions of teacher knowledge with the tests for teachers that were used in this country during the last century [the 19th] at state and county levels. Some people may believe that this idea of testing teacher competence in subject matter and pedagogical skill is a new idea, an innovation spawned in the excitement of this era of educational reform, and encouraged by such committeed and motivated national leaders as Albert Shanker, President, American Federation of Teachers, Bill Honig, State Superintendent of Schools, California, and Bill Clinton, Governor of Arkansas. Like most good ideas, however, it’s roots are much older.
It took Wisconsin almost 20 years to adopt this “good idea”.