Finding Formulas: Does Active Search Facilitate Appropriate Generalization?

Autor/inn/en	Hallinen, Nicole R.; Sprague, Lauren N.; Blair, Kristen P.; Adler, Rebecca M.; Newcombe, Nora S.
Titel	Finding Formulas: Does Active Search Facilitate Appropriate Generalization?
Quelle	In: Cognitive Research: Principles and Implications, 6 (2021), Artikel 50 (18 Seiten) PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Hallinen, Nicole R.) Weitere Informationen
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2365-7464
DOI	10.1186/s41235-021-00316-y
Schlagwörter	Mathematics Education; Algebra; Generalization; Mathematics Skills; Equations (Mathematics); Freehand Drawing; Error Patterns; Visual Aids; Mathematical Formulas; Logical Thinking + Suchen Sie Ihr Suchwort? Mathematische Bildung; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Equations; Mathematics; Gleichungslehre; Drawing; Zeichnen; Fehlertyp; Anschauungsmaterial; Mathematische Formel
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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01