The Trouble With Transfer: Insights From Microgenetic Changes in the Representation of Numerical Magnitude

Abstract

Spontaneous transfer of learning is often difficult to elicit. This finding may be widespread partly because pretests proactively interfere with transfer. To test this hypothesis, 7-year-olds' transfer was examined across 2 numerical tasks (number line estimation and categorization) in which similar representational changes have been observed. As predicted, children given feedback on numerical estimates learned to use a linear representation of numerical quantity instead of a logarithmic one, but providing practice on a categorization pretest led children to continue using a logarithmic representation on the same task, which they otherwise abandoned with surprising frequency. These findings imply unsupervised practice of inappropriate representations impedes transfer, and studies of learning can greatly underestimate children's potential for transfer if pretest effects are uncontrolled.

Development of Quantitative Thinking

“…To test this hypothesis, Opfer and Thompson (2008) presented kindergartners who initially produced number line estimates that were more logarithmic than linear with feedback designed to improve the linearity of number-line estimates and tested both number line estimation and categorization. As expected, after the feedback experience, the linear function provided a better fit to the mean category judgments of children who received feedback on their number-line judgments than for those who did not receive such feedback.…”

Dynamic testing and transfer: An examination of children's problem-solving strategies

“…According to Holyoak (1984), transfer requires individuals to perceive the underlying relationship between two problems with some level of similarity (see also Brown, 1982;Brown, Bransford, Ferrara, & Campione, 1983). This is often difficult to accomplish, particularly for young children, and many cognitive training studies since then have shown that children do not easily generalize newly learned strategies to other problems and contexts (e.g., Detterman, 1993;Opfer & Thompson, 2008). Holyoak described transfer as the process of finding an analogy between a base (trained task) and a target problem (transfer task).…”

“…Dynamic testing can result in significant gains but the effects appear to be restricted to the domain in which training took place and to tasks that are not very different from the original ones. Current procedures appear not to encourage children to spontaneously search for relational similarities between the new and previously learned tasks (e.g., Goswami, 1992;Opfer & Thompson, 2008). Future studies should stress this relationship more directly, for instance by using a second adaptive training procedure during the assessment of transfer.…”

The log–linear response function of the bounded number-line task is unrelated to the psychological representation of quantity

“…Traditionally, researchers have assumed that a participantÕs response function to the bounded number-line task provides a direct window on their psychological understanding of quantities (Booth & Siegler, 2006;Opfer & Siegler, 2012;Opfer, Thompson, & Kim, 2016;Siegler & Booth, 2004; we term this a direct response strategy). Researchers who accept the direct response strategy have interpreted the bounded number-line data as indicating that childrenÕs psychological understanding of quantities is logarithmic, whereas older children and adults psychological understanding of quantities is linear (Booth & Siegler, 2006;Laski & Siegler, 2007;Opfer & Siegler, 2005Siegler & Opfer, 2003, Siegler & Booth, 2004Siegler & Ramani, 2006;Siegler, Thompson & Opfer, 2009). …”