The representational alignment hypothesis of transfer of numerical representations.

摘要

Is transfer of learning universally narrow, slow, gradual, and situation specific, or can it also be broad, fast, abrupt, and cross-cut situations? Whether transferring knowledge from one classroom to another, from early in the school year to later in the school year, or from one example to another example, conceptual representations should allow learners to generalize over situations that differ merely in place, time, and superficial details (Murphy, 2002). I hypothesized that narrow transfer of learning---at least in numerical contexts---can occur automatically. In my representational alignment hypothesis, transfer is facilitated not only through the overlap in identical elements across the training and transfer context, but also through participants' ability to recognize the underlying structural similarity between the two contexts. Numbers are an interesting test case of this theory because surface similarities (e.g., 1 and 7 look more similar than do 1 and 3) as well as relational similarities may be examined (e.g., decimal system; the magnitudes denoted by 1 and 3 are more similar than the magnitudes denoted by 1 and 7). I examined an interesting implication of the representational alignment hypothesis---the implication that representational changes can impose costs as well as benefits for task performance. In my first set of experiments, I investigated the phenomenon of robust transfer and showed that simply highlighting the superficial perceptual details of the contexts in question allowed children to "scale up" a learned linear representation of numerical magnitude (e.g., when children indicated that 150 is closer to 0 than to 1,000 on a 0-1,000 number line) to increasingly larger numerical magnitude contexts (0-10,000 or 0-100,000). In my second set of experiments, I examined how children estimated salaries denoted in fractional notation on a "money line"---an instance where possessing and employing an automatized linear representation of numeric magnitude led to costs in accuracy. In my final experiment, I investigated a potential experimental artifact common to many previous studies in the transfer literature that I believe helped to explain why researchers so often find that children have trouble with transfer. In sum, the conducted studies demonstrated that transfer is an automatic outcome of generalization, which depends on the similarity of how the training and transfer contexts are represented rather than the similarity of the training and transfer contexts themselves.