Trninic, D., Gutiérrez, J. F., Lee, R. G., & Abrahamson, D. (2011, April). Generative immersion and immersive generativity in instructional design. 

Paper presented at the annual meeting of the American Educational Research Association (SIG Research in Mathematics Education). New Orleans, LA, April 8 – 12, 2011.

Design and selection of pedagogically effective mathematical problems raises enduring yet undertheorized problems for educational research. We revisit traditional abstract/concrete and decontextualized/situated dichotomies, questioning their apparent epistemological and ontological assumptions, and evaluate these dichotomies in light of a view of mathematics learning as the mediated cognitive activity of connection building. Orthogonal to traditional dichotomies, we contend, and more pedagogically relevant, are problems’ immersiveness, i.e., capacity to foster personally meaningful situativity, and generativity, i.e., capacity to elicit relevant connections. We illustrate our argument through qualitative analysis of empirical episodes collected in a design-based research study investigating the microgenesis of mathematical meaning.

Meaning… can never be the aim of action and yet, inevitably, will rise out of human deeds after the action itself has come to an end. (Arendt, 1961/2006, p. 78)