Teaching elementary mathematics to the current math standards involves helping
children learn how to reason about mathematical ideas. Instruction is intended
to be child-centered and focused on problem solving. In preparing preservice
teachers to teach mathematics to children in these ways, we must help them find
effective ways to come closer to children’s processes of thinking and
understanding, at the same time as they strive to learn more deeply the content
of mathematics and the art of instruction.
Students must become willing to engage in a constant balancing act and improvisation. In this chapter, the authors describe how they added documentation into an innovative program of elementary mathematics teacher preparation at the University of Nebraska-Lincoln as one means of accomplishing our goals.
The program is based on the collaborative work of a mathematics educator and mathematician aimed at integrating mathematical content, pedagogy, and field experiences for the purpose of developing outstanding elementary teachers who excel in the area of teaching mathematics. In the context of this program, the mathematics educator and mathematician along with an expert in early childhood education and child development drew on their collective expertise in pedagogy, mathematics, and children’s understandings to construct a learning opportunity for preservice teachers.
The opportunity involved preservice teachers’ work with individual children on a math problem involving the creation of all possible shapes from four congruent isosceles right triangles, analysis of the product and process of preservice teachers’ work with children, and construction of documentation panels representing stories of children’s mathematical understandings and preservice teachers’ emerging understandings of mathematics, teaching, and children.
In constructing
the documentation panels to be displayed at the elementary school and university,
students and faculty had to think through issues of narrative, communication,
audiences, collaboration, subjectivity, and multiple perspectives. The chapter
will include a description of the original math problem, the assignment given
to preservice teachers, how the authors used the process of documentation to
transform the preservice teachers’ work with individual children into
documentation panels representing children as mathematical knowers, and the
authors’ understandings of the potential of documentation as a tool in
the process of learning to teach elementary mathematics.