Circles and Helices: Two Approaches to Conjecture and Mapping in Design-Based Research

• In Event: Conjecture Mapping: New Approaches to Broadening Processes of Educational Design Research

Abstract

Purpose:
We describe a novel role for conjecture mapping (Sandoval, 2014) in design-based research (DBR): sensitizing researchers to emergent possibilities suggested by participants’ activity. In doing so, add a new meaning to the “mapping” of conjecture mapping—iteratively exploring a design space, and using participants’ responses to conjecture-driven designs to structure this inquiry. As with Expansive Learning (e.g., Engeström, 2016), this approach depends upon researchers’ allowing the intended “outcomes” of design-based research to evolve, attending carefully to participants’ ways-of-engaging, which indicate directions for “orthogonal” development of the objectives of learning and activity. We argue this approach can offer a complement to traditional conjecture-mapping in DBR, and we describe how both approaches coexisted in parallel efforts within a single research project.

Framework:
The word “conjecture” shares with “trajectory” the etymological root of “throwing;” thus a ballistic sense is salient in traditional conjecture mapping. Here, the designers make a series of throws to hit a target (the objective). Here we suggest an alternative framing, in which the “throw” of a “conjecture” is instead a “toss” from designers to participants, who receive the design as a proposal to which they respond (cf Author, 2020).

We depict the traditional approach to DBR as a roughly circular path, perturbed slightly through iterations that explore design changes to bring successive implementations ever closer to a relatively fixed objective (Figure 6A). In contrast, taking a dialogic relation between designers and participants as central, we find that implementation in DBR can be used to explore a multidimensional design space. Participants express their own perspectives and passions through their participation. They introduce motions and motifs that are “orthogonal” to the thrust of the designers’ intentions, and by attending to these we can lift our design trajectory “out of the plane,” illuminating a wider space of new possibilities surrounding the initial design (Figure 6B).

Methods & Data:
Our context was the (NSF #blinded) project, which aimed to support students’ aesthetic engagement with mathematics and computation in week-long summer “Code Your Art” camps. Figure 7 describes the design of one type of activity from our first year’s camp: a “Stadium Cards” activity, in which groups of students constructed images by embodying a pixel grid (Authors, 2019; 2020; 2021c). .

Findings & Significance:
In Year 2 of the project we utilized both traditional, “circular” and exploratory ,“helical” approaches (Figure 7). On one hand, we refined Stadium Cards activities traditionally in creating “Image Camp.” On the other, and in parallel, we used Conjecture Map #2 to build upon learners’ embodied expressivity and conceptualize a new “Action Camp.” Here we shifted from graphic arts and visual composition to creative movement and choreography. Partnering with professional dancers, we developed a camp that amplified learners’ opportunities to explore tensions between disciplinary representations by creating multi-person movement vocabularies. Both camps supported learners in creating art through agent-based programming in NetLogo (Wilensky, 1999), each but pursued a distinctive approach.

Authors

• Corey Brady, Southern Methodist University

• Lauren Vogelstein, New York University