Inconsistent operations: A weapon of math disruption

Abstract

SummaryWord problems embed a math equation within a short narrative. Due to their structure, both numerical and linguistic factors can contribute to problem difficulty. The present studies explored the role of irrelevant information in word problems, to determine whether its negative impact is due to numerical (foregrounding hypothesis) or linguistic (inconsistent‐operations hypothesis) interference. Across three experiments, participants solved multiplication and division word problems containing irrelevant numerical information, which was either associated or disassociated with the protagonist. Results demonstrated increased solution errors on division problems when irrelevant numbers were disassociated with the protagonist. When memory for numerical information was emphasized, disassociation was specifically impacted low‐working memory individuals. The effect of disassociation on division performance persisted even when irrelevant numbers, but not words, were removed from problems. These results suggest that, even in the presence of numerically interfering information, it is the language of word problems that often drive their difficulty.

When does the story matter? No evidence for the foregrounding hypothesis in math story problems

“…Analyses were conducted using repeated-measures ANOVAs. Error bars in figures are standard errors of the means, to be consistent with Mattarella-Micke and Beilock (2010) and Jarosz and Jaeger (2019). Furthermore, in addition to reporting frequentist statistics, Bayes factors were computed to evaluate the fit of the data under the null and alternative hypotheses.…”

“…The foregrounding hypothesis (Mattarella-Micke & Beilock, 2010) and the inconsistent-operations hypothesis (Jarosz & Jaeger, 2019) make the same prediction for multiplication problems: Solvers will make more errors on multiplication problems for associative than dissociative scenarios. In contrast, the inconsistent-operations hypothesis also predicts that solvers will make more errors on division problems for dissociative than for associative scenarios because dissocia tive scenarios contain subtraction language.…”

Testing the seductive details effect: Does the format or the amount of seductive details matter?

“…Therefore, the processing of seductive details serves to consume limited working memory resources during learning and thus compromise learning outcomes. The majority of prior research corroborates the cognitive overload hypothesis (Jarosz & Jaeger, 2018; Korbach, Brünken, & Park, 2016; Mayer et al, 2008; Mayer, Bove, Bryman, Mars, & Tapangco, 1996; Park, Moreno, Seufert, & Brünken, 2011), while there is also some evidence in support of the distraction hypothesis (Sanchez & Wiley, 2006; Strobel, Grund, & Lindner, 2019).…”

“…Other than merely confirming or interpreting the seductive details effect, investigating the boundary conditions of the effect has emerged as a fruitful research line as it can provide evidence on when and how teachers might be able to use these interesting antidotes. The existing empirical studies have revealed that the seductive details effect can be moderated by learners' individual characteristics such as their prior knowledge (Magner, Schwonke, Aleven, Popescu, & Renkl, 2014; Wang & Adesope, 2016a), working memory capacity (Jarosz & Jaeger, 2018; Sanchez & Wiley, 2006), attentional inhibitory control capacity (González, Saux, & Burin, 2019), and individual interest (Wang & Adesope, 2016b) as well as by contextual variables such as learning contexts (Park et al, 2011; Yue & Bjork, 2017) and instructional techniques (Eitel, Bender, & Renkl, 2019; McCrudden, 2019; Peshkam, Mensink, Putnam, & Rapp, 2011).…”

University students' misconceptions about rational numbers: Implications for developmental mathematics and instruction of younger students

“…We hypothesize the lack of error analyses within word‐problem solving featuring rational numbers is because most errors noted in the literature on word problems focus on the word‐problem process and not the calculations for word‐problem solution. For example, common researcher‐identified errors when solving word problems include understanding the language of the word problems (Daroczy et al, 2015; Sepeng & Sigola, 2013), identifying important information and ignoring irrelevant information (Jarosz & Jaeger, 2019; Wang et al, 2016), translation of word problem to pictorial representations or equations (Haryanti et al, 2018; Kingsdorf & Krawec, 2014; Tong & Loc, 2017), and performing calculations necessary for problem solution (Haghverdi et al, 2012; Sharpe et al, 2014) but no information about the types of errors related to calculation.…”