Learning To Teach Through Making

“Curriculum ceases to be a thing, and it is more than a process. It becomes a verb, an action, a social practice, a private meaning, and a public hope. Curriculum is not just the site of our labour, it becomes the product of our labour, changing as we are changed by it.” 

– Pinar et al., 1995

We think about Curriculum in two ways:

        1. 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.

        2. Curriculum as experience refers to the range of educative experiences through which prospective teachers construct knowledge for teaching mathematics. For us, these involve 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.

Curriculum is typically conceived as a thing (#1), like a textbook or a collection of readings. For us, that’s where it starts. But then the thing becomes a process (#2) – 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.

This website represents a curriculum module we’ve developed for mathematics teacher educators. It provides and explains both the content and experience dimensions of our Making for Learning experience. This is an experience that was iteratively tested within teacher preparation and that tasks prospective teachers with designing, fabricating, and evaluating new physical manipulatives to support mathematics teaching and learning. It has now progressed through several iterations of a design cycle 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 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. Constructivism recognizes 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 (Halverson & Sheridan, 2014). 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 21st century STEM interests and capacities. Multiple iterations of Making experiences with prospective mathematics teachers has yielded a viable curriculum module that is now available through this website for widespread use in mathematics teacher preparation.

We also believe that mathematics should be a process of corporeal investigations (de Freitas & Sinclair, 2020) – that is, one where we explore, create, discover, and understand mathematics by doing mathematics with our bodies. Our work is also influenced by the theory of an enactivist approach to cognition and learning, which states that we are all bodies in a constant state of perception and reaction in the world. This perceptually guided activity (Varela, Rosch, & Thompson, 1992) is how we come to learn, and the process of learning mathematics is no exception. In other words, “knowing is doing and doing is knowing” (Reid & Mgombelo, 2015, p. 172), and problem posing and solving are an emergent and embodied phenomenon (Proulx, 2013) that are shaped by one’s environment, culture, body, and lived history. Humans aren’t simply input/output machines, we are embodied beings whose senses and movements are inherent to our learning, knowing, and reasoning (Abrahamson & Bakker, 2016). By including activities like the Maker Project into our mathematics curricula, we get to ask and see what kinds of authentic mathematics our body/minds do, and therefore, know.

Check out the video below for more information on the importance of design, creativity, and embodied interaction in meaningful mathematical learning! It features Dor Abrahamson, PhD, who is a Professor of Cognition and Development at University of California, Berkeley. He is also an advisory board member for the ReMaking Teaching for Mathematical Learning project and has served as a major source of inspiration and insight for our team! Learn more about Dor’s work here.