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Positioning Teachers as Designers

  • Positioning teachers as designers of their own curricular resources invites opportunities for their explorations of innovation at the intersection of content, pedagogy, and design.
  • This work explores structures of teacher preparation that cultivate the imagination of more humanistic forms of mathematics teaching and learning by supporting such explorations. 
  • Here, we present an investigation into the nature of prospective teachers’ design activity as they were tasked with the Making of mathematical manipulatives.
  • We share findings from the analysis of this activity that conveys the diversity of design decisions, rationales, and mediating resources that it entailed. 
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Teacher Learning through Making

Hypotheses

  • We present a novel Making experience within mathematics teacher preparation that we hypothesized would inform prospective mathematics teachers' (PMTs) curricular and pedagogical thinking and cultivate images of themselves as agents of curricular and pedagogical reform (Leander & Osborne, 2008; Priestley et al., 2012).  
  • We hypothesized that a pedagogically genuine design experience would be formative for the development of an inquiry-oriented pedagogy that is legitimately responsive to the particular needs and interests of actual learners.

Research Question

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Research Design

Theoretical Framing

  • Constructivism and Constructionism (Papert, 1980) recognize that knowledge is actively constructed by a learner, with constructionism adding the dimension that the knowledge be constructed through the process of making a shareable object.
  • Learning by Design (Koehler & Mishra, 2005) provides a venue for characterizing the interplay between a designer’s knowledge, experiences, intentions, and other resources as they are invoked during the iterative design of the shareable object.

  • We appealed to Schön’s (1992) "Knowing in Action" to characterize and organize the resources that mediate PMTs’ design decisions: 
    • Knowledge is in action as “the designer sees what is ‘there’…, draws in relation to it, and sees what he/she has drawn, thereby informing further designing” (p. 5). 
  • From a constructionist perspective, "reflective conversation with materials" (Schön, 1992) are seen as essential for motivating and facilitating the construction of new knowledge (Ackermann, n.d.). They also permit an analysis that moves beyond a static view of knowledge to a dynamic, blended, and transformative view of knowing (e.g., Scheiner, 2015, 2019).

Methods

  • We took an exploratory case study approach (Yin, 2009) to understand PMTs’ design activity by taking the three elements of each of their design decisions as the unit of analysis: the decision itself, a rationale for making the decision, and the resources that mediated the decision making.
    • The manipulative’s design, transcripts of video-recorded in-class design sessions, and three written project components formed the data corpus.

Unit of Analysis: 3 elements of a design decision

  • We took a grounded theory approach (Corbin & Strauss, 2008) to characterize PMTs' design decisions and their mediating resources as they were revealed in the PMTs’ written work and in the transcripts.
    • Analysis involved the constant comparison of data to ensure coherence across codes as we moved from individual analysis and the generation of codes to collaborative analysis and code consensus.

 

 

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Our Findings

Moira's Fraction Ring

 

Anyango's Fraction Pedestals

 

Learner-Centered Design

  • Moira: “After seeing the student I tutor have issues with solving fraction problems, I decided to create a tool that I believe will help him understand fractions.”
  • Anyango: “The student I am working with said she enjoys fractions… so I want to continue with her interest by learning and playing with a manipulative to gain a deeper understanding.”
  • Both designed a fraction tool, but they provided different rationales for that decision. Moira hoped to help her child make better sense of fractions; Anyango hoped to extend her student’s current thinking about fractions.

Nature of the Tool

  • Moira’s design: “A series of rings that rest on a cylinder... The notches help divide the rings equally up into pieces to represent parts of a whole. Each ring represents a different number of parts, like sixths and eighths.” 
  • Anyango's design: “A 3D version of fraction strips. Each strip was made to be a rectangular/square piece that slides into individual pegs…[the] blocks stack vertically... to indicate height as value and amount.” 
  • For both Moira and Anyango, mathematical knowledge of fractions and technological knowledge mediated their design decisions.

The Role of Aesthetic 

  • Moira: “Rings have the same color,” because if each ring had a unique color, it might “take away reasoning from children. If a student believes that a yellow ring represents 1/6ths, they will immediately reach for yellow the second that they hear sixths.” By giving the rings the same color and leaving them “unmarked,” Moira ensures that children will construct their own meanings in relation to each of the rings, thereby giving her tool the promise that it can “be used in multiple ways.”
  • Anyango: “The colors didn’t matter much.” Giving each fraction block its own color would have been “aesthetically pleasing, but it did not affect how the manipulative worked.” 
  • Knowledge of how learning works mediates a decision that seems to reflect Moira’s commitment to an inquiry pedagogy that affords multiple means of engagement. For Anyango, however, color played a purely aesthetic role.

Intended/Imagined Utilization Scheme

  • Moira’s imagined utilization scheme involves aligning notches so that “the rings are able to be compared, showing how many fifths are in one half.” 

  • Anyango’s scheme is that “all the fractions [can be] mounted on one platform… so that the student could begin to grasp how all the smaller parts can equate and compare to the whole.”

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Takeaways & Next Steps

 

Takeaways

  • At the intersection of digital design and fabrication technologies, student-centered design practices, and inquiry orientations to mathematical learning, a host of new possibilities are afforded to teachers
  • The diversity of design decisions made by the prospective teachers, as well as the breadth of resources they brought to bear upon them, speaks to the generative power of the open-ended and iterative design experience in terms of the agency prospective teachers leveraged throughout their design activity and the wealth of knowledge and experiences that mediated it.

  • Whereas teachers are too often positioned as the implementers of curricula that they neither designed nor approved, this experience has the potential to disrupt such alienating activity by providing prospective teachers with realized visions of themselves re/claiming the authority afforded to teachers as agents of curricular and pedagogical reform.

Next Steps

 

 

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Abstract

Positioning teachers as designers of their own curricular resources invites opportunities for their explorations of innovation at the intersection of content, pedagogy, and design. As researchers accepting greater responsibility for the preparation of teachers for work in diverse contexts, our work explores structures of teacher preparation that cultivate the imagination of more humanistic forms of mathematics teaching and learning by supporting such explorations. This paper reports on an investigation into the nature of prospective teachers’ design activity as they were tasked with the Making of mathematical manipulatives. We share findings from the analysis of this activity that convey the diversity of design decisions, rationales, and mediating resources that it entailed. The implications of these findings for teacher preparation are considered.

Positioning teachers as designers of their own curricular resources invites opportunities for their explorations of innovation at the intersection of content, pedagogy, and design. As researchers accepting greater responsibility for the preparation of teachers for work in diverse contexts, our work explores structures of teacher preparation that cultivate the imagination of more humanistic forms of mathematics teaching and learning by supporting such explorations. This paper reports on an investigation into the nature of prospective teachers’ design activity as they were tasked with the Making of mathematical manipulatives. We share findings from the analysis of this activity that convey the diversity of design decisions, rationales, and mediating resources that it entailed. The implications of these findings for teacher preparation are considered.

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