Affordances of fractions and decimals for arithmetic.

Abstract

Rational numbers are represented by multiple notations: fractions, decimals, and percentages. Whereas previous studies have investigated affordances of these notations for representing different types of information (DeWolf et al., 2015; Tian et al., 2020), the present study investigated their affordances for solving different types of arithmetic problems. We hypothesized that decimals afford addition better than fractions do and that fractions afford multiplication better than decimals do. This hypothesis was tested in two experiments with university students (Ns = 77 and 80). When solving fraction and decimal arithmetic problems, participants converted addition problems from fraction to decimal form more than vice versa, and converted multiplication problems from decimal to fraction form more than vice versa, thus revealing preferences favoring decimals for addition and fractions for multiplication. Accuracies paralleled these revealed preferences: Addition accuracy was higher with decimals than fractions, whereas multiplication accuracy was higher with fractions than decimals. Variations in notation preferences as a function of the types of operands involved (e.g., equal vs. unequal denominator fractions) were more consistent with an explanation based on adaptive strategy choice (Siegler, 1996) than with one based on semantic interpretations associated with each notation.

A unified model of arithmetic with whole numbers, fractions, and decimals.

“…Of course, some arithmetic problems are conceptually more difficult than others. For example, division of fractions appears harder to conceptualize than other arithmetic operations with fractions (Ma, 1999), and multiplication of decimals is more difficult to understand than addition of decimals (Liu & Braithwaite, 2022). However, the present results suggest that such conceptual considerations are not necessary to explain many between-problem variations in error rates.…”

Basic mathematical skills and fraction understanding predict percentage understanding: Evidence from an intelligent tutoring system

“…Interestingly, over the last decade, a growing body of research focused on the learning of fractions-i.e., one format of rational numbers (Braithwaite et al, 2017(Braithwaite et al, , 2018(Braithwaite et al, , 2022Hansen et al, 2017;Jordan et al, 2013;Q. Liu & Braithwaite, 2022;Schneider & Siegler, 2010;Siegler et al, 2011;Tian et al, 2020;Tian & Siegler, 2017).…”