Question: Who wrote the defintions that were given up front? Question: To what "community" do these definitions belong?
I tend to use student-generated definitions, so that there is agreement within the classroom community of what words mean. As a teacher, I serve a role in making sure there is general agreement between their defintions and those of larger communities in order to allow communication with folks outside our classroom.
At times students will rely on outside sources for their defintions. Not often is this really helpful. First, the definitions themselves use terms the students may not be familiar with. Second, different sources yield widely varying definitions. (Example: Does a trapezoid have exactly one pair of parallel sides? Or at least one pair? I have seen both answers, and also "sometimes" in a math dictionary.)
Thus, the CLASS makes a decision on how they want to define something: o Where do we draw the lines? Given that there is some idea we want to look at, how broad or narrow should it be? (Frequently a troublesome question! My class had continuing discussions on the definiton of a trapezoid.) o How do we want to express this in a way that makes sense, so that we know what we mean when we use this term?
Some students find this troubling. (What is the REAL answer?) But bottom-line, there is no real answer. Meanings are always negotiated. Unfortunately, in many mathematical classrooms this negotiation is pretty one-sided.
Looking forward to hearing more discussion on this topic!
<...> >Also, I would like to learn a little more about the use of definitions. >Several years ago our faculty went through some training in group work, >presentation skills and teaching provided by the educational outreach >program of Boeing Computer Division. One of their strategies is to post >all definitions so that all participants are using the same language. > >It is in this sense that I said that we put our definitions upfront. > >In my (still developing) mind, there is a big distinction between >definitions and concepts and applications. Each is important and each >must be addressed directly.
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