Abstract Three rational number notations -- fractions, decimals, and percentages -- have existed in their modern forms for over 300 years, suggesting that each notation serves a distinct function. However, it is unclear what these functions are and how people choose which notation to use in a given situation. In the present article, we propose quantification process theory to account for people’s preferences among fractions, decimals, and percentages. According to this theory, the preferred notation for representing a ratio corresponding to a given situation depends on the processes used to quantify the ratio or its components. Quantification process theory predicts that if exact enumeration is used to generate a ratio, fractions will be preferred to decimals and percentages; in contrast, if estimation is used to generate the ratio, decimals and percentages will be preferred to fractions. Moreover, percentages will be preferred over decimals for representing ratios when approximation to the nearest percent is sufficiently precise, due to the lesser processing demands of using percentages. Experiments 1, 2, and 3 yielded empirical evidence regarding preferences that were consistent with quantification process theory. Experiment 4 indicated that the accuracy with which participants identified the numerical values of ratios when they used different notations generally paralleled their preferences. Educational implications of the findings are discussed.

PsychoPy is an application for the creation of experiments in behavioral science (psychology, neuroscience, linguistics, etc.) with precise spatial control and timing of stimuli. It now provides a choice of interface; users can write scripts in Python if they choose, while those who prefer to construct experiments graphically can use the new Builder interface. Here we describe the features that have been added over the last 10 years of its development. The most notable addition has been that Bui...

Many children and adults have difficulty gaining a comprehensive understanding of rational numbers. Although fractions are taught before decimals and percentages in many countries, including the USA, a number of researchers have argued that decimals are easier to learn than fractions and therefore teaching them first might mitigate children’s difficulty with rational numbers in general. We evaluate this proposal by discussing evidence regarding whether decimals are in fact easier to understand t...

#1Maureen E. Gray(UCLA: University of California, Los Angeles)H-Index: 2

#2Melissa DeWolf(UCLA: University of California, Los Angeles)H-Index: 11

Last. Keith J. Holyoak(UCLA: University of California, Los Angeles)H-Index: 86

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ABSTRACTThe present study examined whether a dissociation among formats for rational numbers (fractions, decimals, and percentages) can be obtained in tasks that require comparing a number to a non-symbolic quantity (discrete or else continuous). In Experiment 1, college students saw a discrete or else continuous image followed by a rational number, and had to decide which was numerically larger. In Experiment 2, participants saw the same displays but had to make a judgment about the type of rat...

#1Yulia Tyumeneva(HSE: National Research University – Higher School of Economics)H-Index: 4

#2Galina Larina(HSE: National Research University – Higher School of Economics)H-Index: 2

Last. Keith J. Holyoak(UCLA: University of California, Los Angeles)H-Index: 86

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ABSTRACTSolutions to word problems are moderated by the semantic alignment of real-world relations with mathematical operations. Categorical relations between entities (tulips, roses) are aligned with addition, whereas certain functional relations between entities (tulips, vases) are aligned with division. Similarly, discreteness vs. continuity of quantities (marbles, water) is aligned with different formats for rational numbers (fractions and decimals, respectively). These alignments have been ...

#1Patrick Plummer(UCLA: University of California, Los Angeles)H-Index: 4

#2Melissa DeWolf(UCLA: University of California, Los Angeles)H-Index: 11

Last. Keith J. Holyoak(UCLA: University of California, Los Angeles)H-Index: 86

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Recent research has begun to investigate the impact of different formats for rational numbers on the processes by which people make relational judgments about quantitative relations. DeWolf, Bassok, and Holyoak (Journal of Experimental Psychology: General, 144(1), 127–150, 2015) found that accuracy on a relation identification task was highest when fractions were presented with countable sets, whereas accuracy was relatively low for all conditions where decimals were presented. However, it is un...

This paper describes the survey of Skills, Technology, and Management Practices (STAMP), which emphasizes the use of behaviourally specific questions in order to improve the quality of job measures. Such measures yield better understanding of the absolute levels of job demands compared to items or scales with arbitrary units that lack definite meaning outside the framework of a particular survey. STAMP measures reveal most workers use relatively simple levels of math on their jobs, but there is ...

#2Melissa DeWolf(UCLA: University of California, Los Angeles)H-Index: 11

Last. Keith J. Holyoak(UCLA: University of California, Los Angeles)H-Index: 86

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Previous work has shown that adults in the United States process fractions and decimals in distinctly different ways, both in tasks requiring magnitude judgments and in tasks requiring mathematical reasoning. In particular, fractions and decimals are preferentially used to model discrete and continuous entities, respectively. The current study tested whether similar alignments between the format of rational numbers and quantitative ontology hold for Korean college students, who differ from Ameri...

Last. Robert S. Siegler(CMU: Carnegie Mellon University)H-Index: 100

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Abstract Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about fraction and decimal arithmetic and to stimulate greater amounts of research in the area, we devoted this review to analyzing why learning fract...

The approximate number system (ANS) subserves estimation of the number of items in a set. Typically, ANS function is assessed by requiring participants to compare the number of dots in two arrays. Accuracy is determined by the numerical ratio of the sets being compared, and each participant’s Weber fraction (w) provides a quantitative index of ANS acuity. When making numerical comparisons, however, performance is also influenced by non-numerical features of the stimuli, such as the size and spac...

#2Jake McMullen(UTU: University of Turku)H-Index: 13

Last. Michelle Hurst(U of C: University of Chicago)H-Index: 5

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Understanding fractions and decimals requires not only understanding each notation separately, or within-notation knowledge, but also understanding relations between notations, or cross-notation knowledge. Multiple notations pose a challenge for learners but could also present an opportunity, in that cross-notation knowledge could help learners to achieve a better understanding of rational numbers than could easily be achieved from within-notation knowledge alone. This hypothesis was tested by r...