Finding formulas: Does active search facilitate appropriate generalization?

Cognitive Research

Rebecca M. Adler¹  Lauren N. Sprague²  Nora S. Newcombe³  Nicole R. Hallinen⁴  Kristen P. Blair⁵ 

[1] Department of Psychology and Human Development, Vanderbilt University;Department of Psychology, Florida State University;Department of Psychology, Temple University;Microsoft;Stanford Graduate School of Education;

关键词: Induction;    Transfer;    Mathematics learning;    Sketching;    Algebra;   

DOI  :  10.1186/s41235-021-00316-y

来源: DOAJ

【 摘 要 】

Abstract Background One criterion of adaptive learning is appropriate generalization to new instances based on the original learning context and avoiding overgeneralization. Appropriate generalization requires understanding what features of a solution are applicable in a new context and whether the new context requires modifications or a new approach. In a series of three experiments, we investigate whether searching for an algebraic formalism before receiving direct instruction facilitates appropriate generalization. Results (1) Searching buffers against negative transfer: participants who first searched for an equation were less likely to overgeneralize compared to participants who completed a tell-and-practice activity. (2) Likelihood of creating a correct new adaptation varied by performance on the searching task. (3) Asking people to sketch alleviated some of the negative effects of tell-and-practice, but sketching did not augment the effect of searching. (4) When participants received more elaborate tell-and-practice instruction, the advantages of searching were less notable. Conclusions Searching for an algebraic formula prior to direct instruction may be a productive way to help learners connect a formula to its referent and avoid overgeneralization. Tell-and-practice instruction that only described the mathematical procedures led to the greatest levels of overgeneralization errors and worst performance. Tell-and-practice instruction that highlighted connections between the mathematical structure of the formula and the visual referent performed at similar or marginally worse levels than the search-first conditions.

【 授权许可】

Unknown