Premium
How the Abstract Becomes Concrete: Irrational Numbers Are Understood Relative to Natural Numbers and Perfect Squares
Author(s) -
Patel Purav,
Varma Sashank
Publication year - 2018
Publication title -
cognitive science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.498
H-Index - 114
eISSN - 1551-6709
pISSN - 0364-0213
DOI - 10.1111/cogs.12619
Subject(s) - irrational number , task (project management) , natural number , natural (archaeology) , rational number , arithmetic , number line , computer science , numerical cognition , mathematics , real number , cognition , cognitive psychology , discrete mathematics , psychology , mathematics education , geometry , archaeology , management , neuroscience , economics , history
Mathematical cognition research has largely emphasized concepts that can be directly perceived or grounded in visuospatial referents. These include concrete number systems like natural numbers, integers, and rational numbers. Here, we investigate how a more abstract number system, the irrationals denoted by radical expressions like 2 , is understood across three tasks. Performance on a magnitude comparison task suggests that people interpret irrational numbers (specifically, the radicands of radical expressions) as natural numbers. Strategy self‐reports during a number line estimation task reveal that the spatial locations of irrationals are determined by referencing neighboring perfect squares. Finally, perfect squares facilitate the evaluation of arithmetic expressions. These converging results align with a constellation of related phenomena spanning tasks and number systems of varying complexity. Accordingly, we propose that the task‐specific recruitment of more concrete representations to make sense of more abstract concepts ( referential processing ) is an important mechanism for teaching and learning mathematics.