Abrahamson, D., Gutiérrez, J. F., Charoenying, T., Negrete, A. G., & Bumbacher, E. (2012, April). Fostering mathematical discovery: one tutor’s strategies for ushering the construction of proportional schemas via mediated embodied interaction.

In J. Radinsky (Chair) & J. Lemke (Discussant), Emergent methods for studying spatial and embodied dimensions of learning. Symposium presented at the annual meeting of the American Educational Research Association (SIG Learning Sciences), Vancouver, April 13-17.

All perception is constructed, and learning in the STEM disciplines is to a great extent coming to see the world anew. Particularly in mathematics, learning requires re-seeing visual displays, such as situated phenomena and the disciplinary displays purportedly modeling them. Charged with facilitating this process, instructors use a variety of discursive and instrumented techniques to orient, focus, and frame students’ perception of stimuli in domains of scrutiny relevant to the practice (Alibali, Phillips, & Fischer, 2009; Goodwin, 1994; Stevens & Hall, 1998).

Our work expands on this research program along three dimensions in accordance with the peculiarities of our theoretical views, pedagogical leanings, and methodological approach.

First, research on the development of professional vision has predominantly treated explicit instruction that might be characterized as “show and tell” (but see Mariotti, 2009; Radford, 2010). Yet as educators who believe in the cognitive and affective value of discovery learning rather than explicit instruction, we are interested in understanding how instructors usher learners toward noticing and articulating patterns and principles—“show and don’t tell,” if you will.

Second, research within this paradigm often treats processes of conceptual ontogenesis wherein learners develop from not-knowing to knowing, such as in disciplining the novice eye to apprehend the heart of a fetus within an initially inchoate ultrasonogram. Yet as theoreticians developing a model of learning that underscores the cognitive value of coordinating among a set of conceptually viable views on a situation, we are inquiring into moments in which students shift from one stable mode of engagement to the next—from knowing-one-way to knowing-another-way. Instructors ushering this shift do not orient as much as reorient learners’ view toward the visual displays—an objective that plausibly demands more nuanced interaction.

Third, this line of research has predominantly treated cases of passive perception. Yet as designers of interactive learning environments, wherein learners instantiate the data they gather, we recast perception as a cognitively inextricable aspect of perceptuomotor schemas deployed in goal-oriented spatial-temporal activity. We thus analyze what learners are seeing vis-à-vis what they are doing.

We present and interpret a set of empirical episodes selected so as to exemplify a tutor’s multimodal discursive strategies for steering students’ inquiry into an interactive phenomenon (n=22, Grades 4-6). So doing, we revisit theories of professional vision as more centrally conversant with (neo-) Piagetian schema-based genetic epistemology, wherein perceptuomotor interaction precedes and drives reflective abstraction, as well as with (neo-) Vygotskian practice-based theory of social indoctrination, wherein novices learn technoscientific concepts through participating in the reenactment of the situated, multimodal, multimedia choreography of the mundane.

We have reported on discovery via “inadvertent” reinstrumentalization of symbolic artifacts interpolated into a problem-solving space (Abrahamson et al., in press). Returning to these data, we foreground the instructor’s facilitation techniques ushering these cognitive processes.