November 28, 2022

Performing Mathematics Through Crafting: A Workshop From A Constructionist Approach

Categories: Connected Learning, Educational Practice, Featured, Research

Fiber craft textiles have played an important role in the development of technology and the advancement of STEM areas. Crochet contributed to the transformation of non-Euclidean geometry due to the consolidation of hyperbolic planes. Our work has led us to design activities with the intention of recovering fiber crafts as a means of learning and engaging with mathematics and other domains, including computing, reasoning with proportions, and spatial visualization. One example of this is knitting. Knitters create personal units that are multiplying in patterned ways with every stitch. This provides opportunities for developing a deep and embodied sense of unitizing and multiplicative proportional reasoning, both ideas that are challenging to learn yet foundational for later mathematics. In a craft project, it is possible to learn various mathematics concepts, either through occasional participation or with a higher level of experience.

At the 2022 Connected Learning Summit, we had the opportunity to facilitate two math-crafts activities with conference attendees during our workshop “Creating A Doll Skirt Or A Basket: Performing Proportional Reasoning And Spatial Visualizations”. One of the activities was “Create a doll skirt”, in which participants designed a skirt based on a model that was presented on screen, with the aim that it would fit a doll, figurine, stuffed animal, or bottle they had at home. The other activity was “Create a basket”, in which participants looked at a photo of a basket on the slide and tried to reproduce the design to build the same basket.

We designed the activities in the context of the Re-Crafting Mathematics project, an NSF-funded project awarded to Kylie Peppler with the aim to better understand how traditional fiber crafts (including sewing) can inform high-quality mathematics learning. Both activities were designed based on constructionist principles, to make it possible to design personally meaningful projects while engaging with important domain concepts. Both activities require engagement with proportional reasoning and 3-d mental rotation as participants create their own projects. Our challenge was not only to bring together craft and mathematics, but also to consider how to facilitate hands-on activities in an online format.

During the workshop, we asked participants to gather the materials needed for the activities and then shared instructions with them. The instructions are also available as open educational resources.




While crafting, participants shared their thoughts about their ongoing crafting experiences. Some participants mentioned that the basket activity was challenging because the basket included a closing mechanism with a shape and function that they had to mentally visualize before being able to recreate it. This was an intentional part of the activity design. The participants only had access to a picture of the basket, so they had to imagine the basket as an unfolded, flat piece of felt and envision the kind of cuts necessary to fold it. One conclusion was that the activity, if facilitated with youth, would require a high degree of motivational support to explore different prototypes, try out possible hypotheses, and discover how the mechanism works, especially when youth are tasked with figuring out how to fold the basket based only on the photograph.

Making the skirt was perceived as easier. While creating the skirts, the group exchanged ideas about how to approach math through crafts. Participants commented that, sometimes, when people do not achieve well in maths, they tend to question their own abilities. In a task without a lot of direction, like creating a doll skirt, one way to get through this tension is to understand that mistakes are part of the construction process and that the outcomes do not have to be the same for everyone. Participants considered it to be helpful to be able to share their experiences about how they were doing and to encourage others. The crafting culture of sharing and generating community through the craft broke through what may be more typically associated with mathematical doing.  Knowing that other participants experienced similar feelings made it easier to share.

In general, attendees commented that both activities were engaging even when they struggled to complete their projects. We learned a lot about how to facilitate both activities in the future, especially in the context of an online environment. These insights include:

Keep the project instructions and materials flexible. There are different ways to develop the activities, and each person can find a different path. For example, some started directly manipulating paper and materials, while others drew a plan first on paper. Keeping the material list adaptable to the things that participants had at home kept the activities adjustable to the participants’ personal environments, and invited a personal touch to the online activities. It enabled opportunities for participants to learn about each other on a personal level. For instance, one participant created a skirt for a cat figurine, which opened up a conversation about shared experiences with animals.

Identify moments in which to balance an open-ended approach with targeted support. Even with non-instructional activities, by keeping it broad but offering targeted support when needed, facilitators can support participants’ problem-solving processes. In the online format, cues and indirect requests for support by participants are more subtle and easier to miss compared to in-person facilitation. We noticed how important it is to be even more explicit with participant instructions and ask more directed questions. This also included “warm calling” participants in ways that prepared participants about the possibility of being called upon and then giving them time to think of a response without interrupting the conversational flow. Make a plan for sharing progress: In a face-to-face environment, people have the opportunity to see others’ processes and learn from them, but in a virtual environment it is more complex to exchange ideas and procedures. Some strategies that can be useful to give a more collective tone to the virtual space are to make comments about your own experience, invite others to share their process in the chat or through the microphone, ask questions, and invite them to show their finished or in-process products via the camera.

Reflect on the process during and after the activities. It is helpful to have participants reflect and share what they made and how they made it. We also learned that including a sharing component during and at the end of the workshop was useful. Sharing and discussing the making process can support participants in resolving fuzzy points in both activities throughout the process. For instance, one of the participants reflected on using more rigid paper for creating the basket compared to softer tissue paper, fabric, or felt, which then made her able to imagine the needed 3D folds more vividly before approaching the activity. Sharing her process of folding the basket helped another participant get unstuck in her project.

In conclusion, facilitating learning situations where mathematics and the arts come together in a holistic and fluid way requires the design of flexible activities, in which the elaboration of projects or crafts is accompanied by questions and moments of reflection that allow for collective learning. To learn more about similar experiences, we curated a playlist of literature that might be of interest:

  • Eglash, R., Bennett, A., Babbitt, W., Lachney, M., Reinhardt, M., & Hammond‐Sowah, D. (2020). Decolonizing posthumanism: Indigenous material agency in generative STEM. British Journal of Educational Technology, 51(4), 1334-1353.
  • Keune, A. (2022). Material syntonicity: Examining computational performance and its materiality through weaving and sewing crafts. Journal of the Learning Sciences, 1-32.
  • Maynard, A. E., & Greenfield, P. M. (2003). Implicit cognitive development in cultural tools and children: Lessons from Maya Mexico. Cognitive Development, 18(4), 489-510.
  • Peppler, K., Keune, A., & Thompson, N. (2020). Reclaiming traditionally feminine practices and materials for STEM learning through the modern maker movement. In Designing Constructionist Futures. MIT Press.

Guest post by Anna Keune, Daniela Villarreal Bermúdez (Technical University of Munich), Maggie Dahn, Joey Huang, and Kylie Peppler (University of California, Irvine)

The workshop featured in this post, “Creating A Doll Skirt Or A Basket: Performing Proportional Reasoning And Spatial Visualizations” was part of the 2022 Connected Learning Summit. It was led by Anna Keune and Daniela Villarreal Bermúdez of the Technical University of Munich, and Maggie Dahn, Joey Huang, and Kylie Peppler of the University of California, Irvine.