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Before ItŐs Too Late:
Glenn Commission Report
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"Michigan State University"
 Michigan State University
 University of Missouri
 Western Michigan University
 University of Chicago

To advance the research base and leadership capacity supporting K-12 mathematics curriculum design, analysis, implementation, and evaluation.
Doctoral Program
Goals:
Increase the number and diversity of professionals prepared in doctoral programs in mathematics education at CSMC institutions.
Strengthen the quality of doctoral programs through collaboration and program enhancement.
Prepare doctoral graduates to assume leadership roles in scholarly work related to mathematics curriculum.

Conference Announcement
DOCTORAL PROGRAMS IN MATHEMATICS EDUCATION: A DECADE OF PROGRESS
Marriott Country Club Plaza
Kansas City, Missouri
September 23-26, 2007
Register at: mathcurriculumcenter.org
Deadline:  March 31, 2007

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"Course lecture responsibilities shared between..."
Course lecture responsibilities shared between doctoral students and instructor (some students worked in pairs and others went solo)
Each class period involved presentations, discussions, questions, conjectures and proofs
Besides daily lecture responsibilities, students prepared three papers:
1) Curriculum analysis of current high school textbook treatments of polynomials
2) A detailed lesson plan and presentation of higher degree polynomial       applications for secondary teachers
3) A detailed paper on a polynomial topic not covered in this class but important for doctoral students in mathematics education

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"The polynomial x2+5x+3..."
The polynomial x2+5x+3 in R[x] induces the function f:R¨R defined
by the rule: f(a) = a2+5a+3 for each a in R.  This assignment defines an surjective ring homomorphism R[x] ¨R[a] = ring of polynomials in the variable a.
Remark:  There is a distinction between polynomials and polynomial functions (these rings are not isomorphic in general).
Example:  Consider the unequal polynomials x4+x+1 and x3+x2+1 in
Z3[x] and the induced functions
 f: Z3¨Z3 , f(a)= a4+a+1 for each a in Z3
 g: Z3¨Z3, g(a)=a3+a2+1 for each a in Z3
 f(0)=1=g(0); f(1)=3=0, g(1)=3=0; f(2)=19=1, g(2)=13=1
Therefore, f=g, but the polynomials that induced these functions are not equal, (i.e., the above homomorphism is not always injective).
Note:  The existence of such an example is clear, since the polynomial ring Z3[x] is infinite, but there are only a finite number of functions f: Z3¨Z3.
Question:  Is there a similar example if the coefficient field is infinite?
Answer: NO!!!   R[x] isomorphic to R[a] iff R is infinite.

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