Relational Priming Based on a Multiplicative Schema for Whole Numbers and Fractions

Abstract

Why might it be (at least sometimes) beneficial for adults to process fractions componentially? Recent research has shown that college-educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study examined patterns of relational priming for problems with fractions in a task that required arithmetic computations. College students were asked to judge whether or not multiplication equations involving fractions were correct. Some equations served as structurally inverse primes for the equation that immediately followed it (e.g., 4 × 3/4 = 3 followed by 3 × 8/6 = 4). Students with relatively high math ability showed relational priming (speeded solution times to the second of two successive relationally related fraction equations) both with and without high perceptual similarity (Experiment 2). Students with relatively low math ability also showed priming, but only when the structurally inverse equation pairs were supported by high perceptual similarity between numbers (e.g., 4 × 3/4 = 3 followed by 3 × 4/3 = 4). Several additional experiments established boundary conditions on relational priming with fractions. These findings are interpreted in terms of componential processing of fractions in a relational multiplication context that takes advantage of their inherent connections to a multiplicative schema for whole numbers.

The relational luring effect: Retrieval of relational information during associative recognition.

“…Indeed, previous research has shown that when it is known that the relevant relations in the base and the target have been encoded correctly, participants are more likely to retrieve the base analogue (Catrambone & Holyoak, 1989; Gentner, Loewenstein, & Thompson, 2003; Gick & Holyoak, 1983). Recent research also shows that there are individual differences in how well relations are encoded and represented (DeWolf et al, 2017). For example, relational priming during mathematical problem solving occurs without the assistance of superficial similarity between the exemplars only for students that have high math ability (DeWolf et al, 2017).…”

“…Recent research also shows that there are individual differences in how well relations are encoded and represented (DeWolf et al, 2017). For example, relational priming during mathematical problem solving occurs without the assistance of superficial similarity between the exemplars only for students that have high math ability (DeWolf et al, 2017). In summary, in order to claim that a genuine “retrieval gap” exists, researchers should demonstrate that the relational structure that they want participants to retrieve has actually been encoded in the first place.…”

“…One major line of evidence that has been used to address these questions concerns relational priming. Relational priming occurs when the processing of one relational instance (e.g., the word pair planet-core ) influences the processing of a subsequent different, but relationally similar, instance (e.g., fruit-pit ; Bassok, Pedigo, & Oskarsson, 2008; DeWolf, Son, Bassok, & Holyoak, 2017; Estes & Jones, 2006; Gagné, 2001; Hristova, 2009; Popov & Hristova, 2015; Raffray, Pickering, & Branigan, 2007; Spellman et al, 2001; Wisniewski & Love, 1998). Early efforts to find unintentional priming of relations between pairs of words were unsuccessful (Spellman et al, 2001).…”

The role of visual representations in college students’ understanding of mathematical notation.

“…Because previous work has found relational understanding of fractions to be related to algebra understanding (DeWolf et al, 2015b), a measure of algebra understanding was added in Experiment 2. A 27-question paper-and-pencil assessment provided a baseline measure of participants’ algebra understanding (DeWolf, Son, Bassok, & Holyoak, 2015; adapted from DeWolf et al, 2015b). This assessment included algebra problems that were either taken from the California State Standards for Grade 8 or adapted from Booth, Newton, and Twiss-Garrity (2014).…”

Relational Reasoning: A Foundation for Higher Cognition Based on Abstraction

“…For example, much of K‐12 mathematics is arguably based on understanding relational concepts—for example, equivalence as the underpinning of most arithmetic equations, greater than or less than, the relationship between the side of a square and its area, or what happens to x in relation to y. It has been suggested that fractions, a topic that children and adults consistently struggle with, may be difficult specifically because of their inherently relational nature (DeWolf, Bassok, & Holyoak, 2015a, 2015b, 2016; Dewolf, Son, Bassok, & Holyoak, 2017; DeWolf & Vosniadou, 2015; Kalra, Hubbard, & Matthews, 2020). For instance, when relating the numerator to the denominator, half of a pizza is the same relation as half of an hour, but no perceptual features or entity identities contribute to identifying the relation.…”