Transitions in learning: Evidence for simultaneously activated strategies.

Abstract

Children in transition with respect to a concept, when asked to explain that concept, often convey one strategy in speech and a different one in gesture. Are both strategies activated when that child solves problems instantiating the concept? While solving a math task, discordant children (who produced different strategies in gesture and speech on a pretest) and concordant children (who produced a single strategy) were given a word recall task. All of the children solved the math task incorrectly. However, if discordant children are activating two strategies to arrive at these incorrect solutions, they should expend more effort on this task than concordant children, and consequently have less capacity left over for word-recall and perform less well on it. This prediction was confirmed, suggesting that the transitional state is characterized by dual representations, both of which are activated when attempting to explain or solve a problem.

You'll see what you mean: Students encode equations based on their knowledge of arithmetic

“…The freed-resources account predicts that encoding performance should decrease as strategy variability increases. Individuals expend resources in managing multiple, competing strategies and in selecting one to execute (Goldin-Meadow, Alibali, & Church, 1993;Goldin-Meadow, Nusbaum, Garber, & Church, 1993;Siegler, 1989), so as the number of strategies in their repertoires increases, they have fewer resources available for encoding. Conversely, the action-primacy account predicts that encoding performance should increase as strategy variability increases.…”

Gesture offers insight into problem-solving in adults and children

“…2 The cognitive load study described earlier (Goldin-Meadow et al, 1993b) suggests that the explanations problem-solvers produce when asked to describe how they solved a problem are a good index of how they actually go about solving problems of that type. We, therefore, assumed that the explanations produced in this study reflected the steps that the participants took when solving Tower of Hanoi problems-either the steps they had taken when actually solving the problem (including their planning steps) or, more likely, the steps they took when re-solving the problem on-line during the explanation.…”

“…Gesture-speech mismatch, thus, reflects the activation of two strategies on a single problem. We have gathered indirect evidence for this hypothesis using a cognitive load paradigm (Goldin-Meadow, Nusbaum, Garber, & Church, 1993b). We observed 9-10-year-old children, all of whom solved a mathematical equivalence problem incorrectly.…”

When Gesture Is and Is Not Language

“…These children were then asked to remember a list of words while at the same time solving the math problem. All of the children solved the problem incorrectly, but children known to be mismatchers worked harder to arrive at their incorrect answers than children known to be matchers: they remembered fewer words when solving the problems, suggesting that they were indeed activating more than one strategy (Goldin-Meadow, Nusbaum, Garber, and Church 1993). Producing mismatches appears to reflect the activation of two ideas at the same time (see also Thurnham and Pine 2006).…”