There is tremendous excitement around makerspaces for deepening and enriching curricula across subjects, as well as engaging traditionally marginalized learners in new ways. To address the lack of translation of maker education projects to mathematics learning, we propose that educators aspire to create a “Mathland” when designing maker educational activities. Mathlands are environments envisioned by Seymour Papert where mathematics are learned alongside ways of doing mathematics in self-selected contexts, leading to an epistemology and natural language of mathematics that pervades all experiences. To imagine a Mathland where women’s participation in mathematics is lifelong and lifewide, we explore traditionally female-dominated fiber crafts where long-term engagement, mathematics, and heritage intersect. As part of a longitudinal embedded multi-year ethnographic study, we conducted cohort analyses as well as grounded, iterative, and thematic coding of semi-structured interview data, augmented with crafting artifacts from 65 adult fiber crafters. Using qualitative analytical techniques, we asked: How does math occur in craft? How do crafters observe the intersection between math and craft in process? Fiber crafts were found to present a “Mathland,” a lifelong context for immersive math engagement. We present crafters’ math insights in the craft, as well as multiple aspects of the crafts and surrounding communities that supported the crafters in sustaining their engagement with mathematics throughout their lifetime. This study has implications for the design of inclusive and lifelong maker educational environments for mathematics learning.
more »
« less
This content will become publicly available on June 12, 2024
To Quilt is to Math: Investigating the Breadth and Depth of Mathematics in Fiber Crafts
This study investigates connections between fabric crafts and the breadth and depth of mathematics involved in pursuing the crafts with a particular focus on quilting. The authors became participant observers in crafting circles, conducted 65 semi-structured interviews to investigate crafters’ mathematical insights in their projects, and analyzed artifacts through close manual examination and photographs to deepen these insights. We ask the questions: (1) How do crafters observe the interplay between mathematics and the process of a craft? (2) How can crafters’ products illuminate the breadth and depth of mathematics? The findings suggest that the different ways in which mathematics and craft intersect either bear the form of a craftforward approach, as crafters produce patterns and explore it through changes in the patterns or in the form of a math-forward approach, in which crafting directly draws on mathematical concepts guiding the work toward the improved performance or modeling of math concepts.
more »
« less
- Award ID(s):
- 1647150
- NSF-PAR ID:
- 10431785
- Date Published:
- Journal Name:
- International Conference of the Learning Sciences (ICLS)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This article examines how fiber crafting can develop mathematics learning and learners. Extending the constructionist paradigm with relational materialist principles, this paper advances the notion of “materialized action,” which describes the natural inquiry process that results through emergent patterns between learners and the materialized traces of their actions. This paper takes a qualitative approach, combining a design and intervention phase examine fiber crafts (here knitting) and engagement in a “powerful idea” (i.e., unitizing in multiplicative proportional reasoning) as an illustration of how we can better understand micro-developmental learning processes, and advance constructionist theory.more » « less
-
Researchers support race, gender, and age diverse groups of people to create with maker electronics. These groups include older adults, who are often overlooked as not interested or capable of learning new technologies due to ageist stereotypes. One approach, often involving e-textiles, leverages crafting as a bridge to broaden participation in making. We investigated ways to broaden participation in maker electronics for older adults by remotely co-designing e-textile projects with 6 older adult crafters over the course of 5 workshop sessions for a total of 45 hours. We developed a deeper understanding of their practices, identifying a Planner-Improviser Spectrum for how they approached their craft, and created medium fdelity prototypes. Our design implications draw on our participants’ crafting experience and their experience in the workshop to highlight what e-textile toolkit designers can learn from skilled older adult crafters, such as selecting familiar materials, supporting aesthetic goals, and making electronics more attainable.more » « less
-
null (Ed.)Communication of ideas involves the simultaneous efforts of verbal, physical and neurological processes (Sherr, 2008). In elementary classrooms where young students are in the process of developing their verbal capacities, gestures from both the teacher and students serve as a key component of communication of new ideas and the processing of social information (Foglia & Wilson, 2013). Thus far, research efforts to understand how students utilize gestures in the communication and understanding of ideas have focused primarily on mathematics and the physical sciences (see Nemirovsky & Ferrara, 2009; Nuñez, Edwards & Matos, 1999; Shapiro, 2014; Sherr, 2008). With the introduction of the Next Generation Science Standards (NGSS Lead States, 2013), students engineering is now included in K-12 instruction. Engineering education centers around designing and optimizing solutions to engineering challenges. The creation of a design solution differentiates engineering education from other classroom subject areas. Current work in engineering education focuses mostly on students’ words or drawings, leaving out gestures as an important component of students' communication of engineering designs. This study aimed to contribute to the general understanding of students’ use of gestures and manipulatives when discussing their engineering design solutions and is part of a larger NSF-funded project. Students participated in pre- and post-field trip classroom activities that extended learning done on an engineering-focused field trip to the local science center into the classroom. For this study, we focused on a module that challenged students to design a craft that either slowed the fall of a penny (classroom engineering design challenge) or hovered in a column of upward moving air (field trip engineering design challenge). We analyzed six videos (3 from the classroom and 3 from the field trip) of first-grade student explanations of their crafts to identify their use of gestures and prototyped craft design solutions in communicating. In this paper, we explore how student use of gestures and use of prototyped design solutions overlap and differentiate to understand how student sense-making can be understood through each.more » « less
-
The process of synthesizing solutions for mathematical problems is cognitively complex. Students formulate and implement strate- gies to solve mathematical problems, develop solutions, and make connections between their learned concepts as they apply their reasoning skills to solve such problems. The gaps in student knowl- edge or shallowly-learned concepts may cause students to guess at answers or otherwise apply the wrong approach, resulting in errors in their solutions. Despite the complexity of the synthesis process in mathematics learning, teachers’ knowledge and ability to anticipate areas of potential difficulty is essential and correlated with student learning outcomes. Preemptively identifying the common miscon- ceptions in students that result in subsequent incorrect attempts can be arduous and unreliable, even for experienced teachers. This pa- per aims to help teachers identify the subsequent incorrect attempts that commonly occur when students are working on math problems such that they can address the underlying gaps in knowledge and common misconceptions through feedback. We report on a longi- tudinal analysis of historical data, from a computer-based learning platform, exploring the incorrect answers in the prior school years (’15-’20) that establish the commonality of wrong answers on two Open Educational Resources (OER) curricula–Illustrative Math (IM) and EngageNY (ENY) for grades 6, 7, and 8. We observe that incor- rect answers are pervasive across 5 academic years despite changes in underlying student and teacher population. Building on our find- ings regarding the Common Wrong Answers (CWAs), we report on goals and task analysis that we leveraged in designing and develop- ing a crowdsourcing platform for teachers to write Common Wrong Answer Feedback (CWAF) aimed are remediating the underlying cause of the CWAs. Finally, we report on an in vivo study by analyz- ing the effectiveness of CWAFs using two approaches; first, we use next-problem-correctness as a dependent measure after receiving CWAF in an intent-to-treat second, using next-attempt correctness as a dependent measure after receiving CWAF in a treated analysis. With the rise in popularity and usage of computer-based learning platforms, this paper explores the potential benefits of scalability in identifying CWAs and the subsequent usage of crowd-sourced CWAFs in enhancing the student learning experience through re- mediation.more » « less
