Reciprocal and multiplicative relational reasoning with rational numbers

Abstract Developmental research has focused on the challenges that fractions pose to students in comparison to whole numbers. Usually the issues are blamed on children's failure to properly understand the magnitude of the fractional number because of its bipartite notation. However, recent research has shown that college-educated adults can capitalize on the structure of the fraction notation, performing more successfully with fractions than decimals in relational tasks, notably analogical reasoning. The present study examined whether this fraction advantage also holds in a more standard mathematical task, judging the veracity of multiplication problems. College students were asked to judge whether or not a multiplication problem involving either a fraction or decimal was correct. Some problems served as reciprocal primes for the problem that immediately followed it. Participants solved the fraction problems with higher accuracy than the decimals problems, and also showed significant relational priming with fractions. These findings indicate that adults can more easily identify relations between factors when rational numbers are expressed as fractions rather than decimals

Reciprocal and Multiplicative Relational Reasoning with Rational Numbers

Abstract Developmental research has focused on the challenges that fractions pose to students in comparison to whole numbers. Usually the issues are blamed on children's failure to properly understand the magnitude of the fractional number because of its bipartite notation. However, recent research has shown that college-educated adults can capitalize on the structure of the fraction notation, performing more successfully with fractions than decimals in relational tasks, notably analogical reasoning. The present study examined whether this fraction advantage also holds in a more standard mathematical task, judging the veracity of multiplication problems. College students were asked to judge whether or not a multiplication problem involving either a fraction or decimal was correct. Some problems served as reciprocal primes for the problem that immediately followed it. Participants solved the fraction problems with higher accuracy than the decimals problems, and also showed significant relational priming with fractions. These findings indicate that adults can more easily identify relations between factors when rational numbers are expressed as fractions rather than decimals