Joanne Lobato

How Design Experiments Can Inform a Rethinking of Transfer andViceVersa

Limitations with current approaches to the investigation of the transfer of learning in design experiments constrain the type of information that is available to researchers as they make design decisions. This article addresses these limitations by presenting a reconceptualization of transfer, called actor-oriented transfer, which emerged from design experiment work. The merits of this alternative model are considered in terms of the information it provides to design experimenters.

Alternative Perspectives on the Transfer of Learning: History, Issues, and Challenges for Future Research

ion Responding to critiques related to the roles of abstraction and decontextualization in transfer has been more challenging then tackling issues related to metaphor. In mainstream cognitive accounts of transfer, the formation of sufficiently abstract representations is a necessary condition for transfer (Reed, 1993; Singley & Anderson, 1989). Abstraction is typically conceived as the extraction of commonalities from a set of concrete examples (e.g., Rosch & Mervis, 1975). As a result, it is deemed important for learners to engage with multiple situations and to compare problem solutions in order to construct an abstract representation spanning them (Chen & Daehler, 2000; Gentner, Loewenstein, & Thompson, 2003; Reeves & Weisberg, 1994). Abstraction is thus conceived as a process of decontextualization. According to Fuchs et al. (2003), abstractions “delete details across exemplars ... and avoid contextual specificity so they can be applied to other instances or across situations” (p. 294). As mentioned previously, the notion of detaching from concrete experience is problematic from a situated perspective (Hall, 1996). Hence, many situated researchers reject decontextualization and abstraction as epistemologically incompatible with situativity. In his article The Fallacy of Decontextualization, van Oers (1998) argued that if context is defined via personal interpretation of actions and TRANSFER OF LEARNING 439

Quantitative reasoning in a reconceived view of transfer

Abstract This paper extends recent efforts to critique and reconceive transfer by using an empirical study to rethink the surface/structure distinction of the traditional transfer paradigm. The findings suggest that what researchers typically consider a surface feature can present conceptual complexities for students that are more structural in nature than previously understood. In particular, we investigated the quantitative reasoning (meaning reasoning with measurable properties of an object) that is involved in making sense of a typical transfer situation. Two related analyses — one focused on quantitative reasoning and one on transfer — were performed on a case study. The results document how a student reconstructed his understanding of the relationships among quantities in a complex transfer situation in such a way that he was able to see the situation as fundamentally proportional in nature and subsequently make connections with previous proportional-reasoning experiences from a teaching experiment. In our discussion of the findings, we identify four relationships between quantitative reasoning and transfer.

The Teacher's Role in Supporting Students' Connections between Realistic Situations and Conventional Symbol Systems.

We use the notion offocusing phenomena to help explain how a teacher’s actions were connected to her students’ interpretations of a linear equation. This study was conducted in a high-school classroom that regularly emphasised dependency relationships in real-world situations. Seven interviews revealed a majority view ofy = b + mx as astorage container—a place to insert b and m values—rather than as a relationship between x- and y-values. Classroom analysis revealed how the teacher directed attention away from functional relationships with increasing frequency as she moved from realistic situations to conventional representations.

On Learning Processes and the National Mathematics Advisory Panel Report

This article is a response to Foundations for Success: The Final Report of the National Mathematics Advisory Panel (2008) and to one of the task group reports on which it was based, the report of the Task Group on Learning Processes. The author uses Maxwell’s two views of causality—regularity and process—to explore three major issues raised in the report: the nature of what is learned, how learning occurs, and the transfer of learning. She proposes alternative recommendations to those offered by the Panel, by drawing upon the mathematics education literature, which was largely excluded from the reviewed research. Furthermore, by neglecting research grounded in a process view of causality, the report excludes perspectives and findings that would have illuminated what it means to develop conceptual understanding in mathematics—one of three valued outcomes cited by the Panel.