Developing Undergraduate and Graduate Mathematics Courses and Materials for Mathematics Education Majors as Part of Two

1. We propose the establishment of a Center for Teaching and Learning that focuses on mathematics curriculum. The Center will serve the K-12 educational community by focusing scholarly inquiry, leadership development, and teacher learning around issues of mathematics curriculum. We propose the establishment of a Center for Teaching and Learning that focuses on mathematics curriculum. The Center will serve the K-12 educational community by focusing scholarly inquiry, leadership development, and teacher learning around issues of mathematics curriculum.

4. Before It’s Too Late: Glenn Commission Report

13. Michigan State University University of Missouri Western Michigan University University of Chicago The proposed Center includes a team that has the expertise and commitment to take on this mission. It includes: institutions with doctoral programs, K-12 school partners, and groups with experience in curriculum development and development of evaluation tools and methods. The Center’s team includes active curriculum developers, users, and researchers as well as teacher leaders, mathematics educators, and mathematicians. While aspects of the work that the Center proposes are underway within various partner sites, the structure, shared commitment, and resources offered by the Center will add tremendous value to the work and will accelerate it’s progress. The proposed Center includes a team that has the expertise and commitment to take on this mission. It includes: institutions with doctoral programs, K-12 school partners, and groups with experience in curriculum development and development of evaluation tools and methods. The Center’s team includes active curriculum developers, users, and researchers as well as teacher leaders, mathematics educators, and mathematicians. While aspects of the work that the Center proposes are underway within various partner sites, the structure, shared commitment, and resources offered by the Center will add tremendous value to the work and will accelerate it’s progress.

14. To advance the research base and leadership capacity supporting K-12 mathematics curriculum design, analysis, implementation, and evaluation.  Specifically, we intend to advance the research base and leadership capacity supporting K-12 mathematics curriculum design, analysis, implementation, and evaluation. We believe that curriculum matters and that only by examining and characterizing the role and influence of curriculum on both teaching and learning can we improve student learning opportunities. There is also a pressing need to help prepare the next generation of mathematics curriculum developers, professional development leaders who know how to use curriculum as a central focus of teacher study, and curriculum researchers who can help generate knowledge for new development cycles. Specifically, we intend to advance the research base and leadership capacity supporting K-12 mathematics curriculum design, analysis, implementation, and evaluation. We believe that curriculum matters and that only by examining and characterizing the role and influence of curriculum on both teaching and learning can we improve student learning opportunities. There is also a pressing need to help prepare the next generation of mathematics curriculum developers, professional development leaders who know how to use curriculum as a central focus of teacher study, and curriculum researchers who can help generate knowledge for new development cycles.

15. 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.

16. 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

17. Ideal curriculum Intended curriculum Enacted curriculum Attained curriculum Ideal curriculum Intended curriculum Enacted curriculum Attained curriculum

18.

19.

20. 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

22. 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.