Finding formulas: Does active search facilitate appropriate generalization?

Cognitive Research: Principles and Implications

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

[1] Department of Psychology and Human Development, Vanderbilt University, 230 Appleton Place, Peabody #552, 37203-5721, Nashville, TN, USA;Department of Psychology, Florida State University, 1107 W. Call St., 32304, Tallahassee, FL, USA;Department of Psychology, Temple University, 1701 N. 13th Street, Weiss Hall, Room 318, 19122, Philadelphia, PA, USA;Microsoft, 1 Microsoft Way, 98052, Redmond, WA, USA;Stanford Graduate School of Education, 485 Lasuen Mall, 94305, Stanford, CA, USA;

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

DOI  :  10.1186/s41235-021-00316-y

来源: Springer

【 摘 要 】

BackgroundOne 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.ConclusionsSearching 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】

CC BY