Comments from package users (A)
Comments on using the package to enhance a math methods course
for pre-service elementary teachers (by Beatriz D'Ambrosio)
The following comments are provided by Beatriz D'Ambrosio, a faculty member at Indiana University/Purdue University at Indianapolis responsible for teaching several mathematics education courses at both undergraduate and graduate level. Professor D'Ambrosio is also involved in the design and delivery of professional development for in-service mathematics teachers in her role as Principal Investigator in an NSF-funded "Local Systemic Change Project." Professor D'Ambrosio found several possible ways in which the materials in this package could enhance her practice as a teacher educator -- including using the materials to enhance her math content and math methods courses for elementary pre-service teachers, to design some professional development experiences for in-service teachers, and even assigning them as a reading within a seminar for doctoral students in mathematics education.
In this commentary, she reports on how she used the package to enhance her math methods course for elementary teachers.
After many years of teaching elementary pre-service math methods courses I had many questions about the effectiveness of the course I had developed. I was uncomfortable with the students' levels of understanding of inquiry-based teaching. I was troubled by the contradictions between their lived experiences with mathematics and the image of inquiry-based teaching we were trying to create. I was discouraged by the lack of powerful examples of inquiry-based teaching that would help illustrate inquiry-based teaching for future teachers.
As I examined the materials in the Borasi and Fonzi (1998) package I realized what a wonderful resource these materials could be for the restructuring, updating, and innovating of my course. The framework was aligned with my beliefs about teacher preparation and the sample syllabi provided me with ideas of ways to achieve many of my goals for an elementary math-methods course. Throughout the materials I found new, refreshing activities to incorporate into my teaching.
The samples of students' work gave me a perspective on what to expect from the assignments proposed in the package. They helped me to anticipate the reactions and responses of students engaging in the inquiry-based illustrative units.
I have incorporated the illustrative units in my math methods course. The mathematical challenge of the tasks has helped students renegotiate their beliefs about themselves as learners of mathematics. The engagement in an inquiry-based unit as learners has helped students create an image of the role of the learner in this learning community. The video-tape of the classroom of children working with the tessellation unit has helped students create an image of the role of the teacher and the vision of the dynamics of the inquiry-based learning community.
Through students' writing assignments we have raised and challenged their beliefs about the nature of mathematics and the nature of mathematical teaching. Opportunities have surfaced for the discussion of the choice of tasks for mathematics instruction, the nature of inquiry-based tasks, the need to elicit student understanding in order to build on that knowledge, and the use of student questions to guide the design of a lesson. Many of the topics that I want to address in this course have emerged as students engage in the inquiry-based illustrative units in the package and question how the inquiry-based approach can lead to their further construction of mathematical ideas.
In summary, I have found the materials to be useful on two levels, both in my planning for instruction and in fostering my students' inquiry about teaching. It has been very satisfying to incorporate these materials into my teaching and to see how stimulating the resulting discussions have turned out to be. Motivated by the skillful design of these materials, students have more readily raised questions that get at the heart of constructing meaning for inquiry-based mathematics teaching.