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Making & Caring


Making is defined as designing, building and innovating with tools to create an object that solves practical problems (Halverson & Sheridan, 2014).

Constructionism adds that knowledge is constructed during the process of making a shareable object (Halverson & Sheridan, 2014).

With much of the Maker literature centered on interactions between the Maker and the tool (see Schon, 1992), we also focus on the personal experiences of the Maker (a prospective mathematics teacher or PMT) sharing their object with a user (a child).

By attending to caring-centered relationships, we illustrate how together, a teacher educator (TE), a PMT, and a child redefine values associated with Making, traditional mathematics and what can get celebrated as learning.

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Accepting Responsibility:  a Moment of Discomfort

David’s original design was a copy of a pre-made manipulative that he and his partner found online. After witnessing the recording of David’s interview with Vincent, the TE was struck by David and Vincent’s warm interactions and the careful calibrations of each other’s movements on the classroom floor. As a result, the TE invited David to abandon this original design and instead create something specifically for Vincent.

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Accepting Responsibility:  
a Moment of Listening


After meeting with the TE, David shifts from the pre-made manipulative design and creates a new direction for a manipulative that utilizes Vincent's knowledge and love of diverse shapes.

He wants to experiment with designing 2-dimensional shapes that can challenge Vincent to tessellate. But before undertaking the design challenge, he brings pattern blocks to a session with Vincent and discovers that Vincent can already tessellate.

Instead of taking the easy way out, David accepts responsibility for Vincent's care, and takes the initiative in shifting away from a tessellation manipulative design even though he still doesn't know what he will do.

We viewed this design and pedagogical decison through the lens of Davis's conception of listening, which embraces listening not merely as an "act" but as an "orientation" toward Vincent and where he is in his learning (Davis, 1994; p. 6).

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Accepting Responsibility:  a Moment of Celebration

David ultimately designs and creates geometric prisms with variously shaped holes and inserts. In a final mathematics interview, Vincent begins exploring as expected, attempting to match kindred inserts and holes. Eventually, he breaks with this and plays with the possibility that not every shape and insert must match to fill the holes (e.g., he drops hexagonal inserts into the square hole).

Vincent's explorations culminate when he aligns the hexagonal and square prisms with unlike holes to peer through them. David responds by arranging the pieces between himself and Vincent so that they form a telescope! Together, they lock eyes and exchange laughter and words of affirmation in a mathematical caring relationship where David decenters from the intended activity to literally see his child’s point of view (Hackenberg, 2005).

Here, we see David accepting responsibility by abandoning his original intentions and expectations of Victor's interactions with the manipulative. Rather than dismiss Victor's inquiries and realign him with an intended goal, David celebrates Victor's novel discovery, making space for Victor to explore and recognize the mathematical concepts of topological equivalence!

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Outsiders to Making/ Insiders to Caring

Typically recognized as a male, “adult, white, middle-class pursuit,” Making culture can feel closed to entrants who do not fit these stereotypes (Barton, Tan & Greenberg, 2017, p. 5). The subject of mathematics also carries an exclusionary culture.

The current study concentrates on three participants who, in some way, were outsiders to the project context:

  • A teacher educator (TE) and a presenter who is a Cuban female with caring-centered pedagogies and identified as a novice and interloper to the Making culture.
  • A PMT-student, David, who was student teaching in a kindergarten class and brought a lived history with caring teachers to the project course. Even though he is a white male, David did not feel like a “Maker,” bringing anxiety over the project’s technological aspects.
  • A kindergartner, Vincent, another white male who is also atypical within mathematical communities: as a student with Autism Spectrum Disorder, his bustling, energetic and physical ways of engaging and learning are not commonly “tolerated” in traditional mathematics classrooms where procedural knowledge and efficiency are privileged (Lambert, 2015).

We now turn to three moments in which the TE and PMT accept responsibility for the kind of learning that disrupts traditional conventions, makes space for caring, and supports meaningful mathematics learning for Vincent.

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Takeaways

We explored Making and designing as a novel opportunity to facilitate these same connections “through the process of jointly negotiating the meaning of concepts and activity,” allowing our teachers to “demonstrate care for individual students and for the subject matter itself” (Bartell, 2011, p. 54) in a way that embraces mathematical struggle, surprise and discovery.

In a typical mathematics classroom, Vincent (a student with disabilities, or SWD) might be considered a “disturbance” because of his animated physical enthusiasm towards learning. Instead, the TE and David’s caring-centered pedagogies supported opportunities to celebrate Vincent’s inclination to learn with his body, and explore open-ended mathematical ideas together. In doing so, David defied the limited notions that SWDs should not participate in conceptual thinking and problem solving and welcomed the unexpected (but worthwhile) mathematical interpretations that open-ended investigations can bring.

By inviting David to substitute a more open-ended investigation for his initial “easy” project solution, the TE set in motion a ripple effect that challenges traditional notions of mathematics learning in which authentic and sometimes uncomfortable discoveries are dismissed as divergent from intended tasks (Lampert, 1990).

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Abstract

Our study presents findings from a Maker project as it was enacted through a caring pedagogy in a course for preservice and practicing mathematics teachers. We focus on the cases of three individuals - outsiders to the traditionally exclusionary cultures and spaces of Making and mathematics - as we explore the questions: How does enacting a caring pedagogy during a Making-centered experience impact and broaden opportunities for meaningful mathematics learning? How does this challenge traditional notions of who can and cannot Make or do mathematics? We suggest a pedagogy of caring, sharing, and Making as one way to accept the educational responsibility of celebrating such marginalized and often excluded individuals, and centering them in meaningful mathematical learning within these spaces.

Our study presents findings from a Maker project as it was enacted through a caring pedagogy in a course for preservice and practicing mathematics teachers. We focus on the cases of three individuals - outsiders to the traditionally exclusionary cultures and spaces of Making and mathematics - as we explore the questions: How does enacting a caring pedagogy during a Making-centered experience impact and broaden opportunities for meaningful mathematics learning? How does this challenge traditional notions of who can and cannot Make or do mathematics? We suggest a pedagogy of caring, sharing, and Making as one way to accept the educational responsibility of celebrating such marginalized and often excluded individuals, and centering them in meaningful mathematical learning within these spaces.

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