Learning To Teach Through Making
We think about Curriculum in two ways:
1. Curriculum as experience refers to the range of educative experiences through which prospective teachers construct knowledge for teaching mathematics. For us, these look like open-ended mathematical tasks, analyses of videos of children’s problem solving, crafting essential questions to formatively assess children’s mathematical thinking, and conceiving of a physical tool that might help a child learn something new.
2. Curriculum as content refers to the material resources that mediate those educative experiences. These include topic outlines, lesson presentations, articles, videos, in-class problem-solving activities, and assignments.
Curriculum is typically conceived as a thing (#2), like a textbook or a collection of readings. For us, that’s where it starts. But then the thing becomes a process (#1) – a matrix of actions, activities, and experiences that are generated from – not defined by – curricular problems as they’re posed, and that offer prospective teachers a site for mathematical, pedagogical, and curricular transformation.
We are in the process of developing a curriculum module for teacher educators that provides and explains both the content and experience dimensions of our Making for Learning experience. This is an experience that is being tested within teacher preparation and that tasks prospective teachers with designing, fabricating, and evaluating new physical manipulatives to support mathematics teaching and learning. By the time we share the module here, it will have progressed through several iterations of a design cycle in order to demonstrate its utility in helping prospective teachers become effective designers of mathematical instruction.
My interest is in the process of invention of “objects-to-think-with,” objects in which there is an intersection of cultural presence, embedded knowledge, and the possibility for personal identification (Seymour Papert, Mindstorms, 1980).
The Learning Philosophy behind Prospective Teachers Making for Mathematical Learning is founded with the purpose of prompting the teacher education community to think in new ways about teacher preparation. Recognizing the potential of technology to transform education, our evolving vision of enabling prospective math teachers (PMTs) to use 3D design and fabrication technology to make manipulatives for student learning is what we refer to as Teachers Making for Mathematical Learning (TMML). TMML opportunities will encourage PMTs to apply knowledge in ways that emphasize the complex relationships between mathematics, technology, and student learning which, in turn, can assist in addressing elementary teachers’ ongoing struggles with mathematics.”
Our theoretical background is organized around the learning theories of constructivism and constructionism. Both of these theories recognize that learners actively construct knowledge, with constructionism adding the dimension that the learning is particularly effective during the process of making a shareable object. One part of Making is the activity of designing, or the purposeful. Imagining, planning, and intending that precedes and interacts with Making. Teachers are called upon to actively engage in inquiry, research, and design so that they can make tangible, meaningful artifacts that represent the end products of the learning process.
As technologies like 3D printing become more prevalent in schools, teachers whose pedagogies have been informed by Making experiences will be well positioned to develop these experiences for their students and cultivate their peers’ and students’ 21st century STEM interests and capacities. Multiple iterations of Making experiences with prospective mathematics teachers will permit the development of a viable curriculum module that will be made available for widespread use in mathematics teacher preparation.