Journal of Numerical Cognition (JNC - PsychOpen)
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Math Predictors of Numeric Health and Non-Health Decision-Making Problems
No full textPeople frequently encounter numeric information in medical and health contexts. In this paper, we investigated the math factors that are associated with decision-making accuracy in health and non-health contexts. This is an important endeavor given that there is relatively little cross-talk between math cognition researchers and those studying health decision making. Ninety adults (M = 37 years; 86% White; 51% male) answered hypothetical health decision-making problems, and 93 adults (M = 36 years; 75% White; 42% males) answered a non-health decision-making problem. All participants were recruited from an online panel. Each participant completed a battery of tasks involving objective math skills (e.g., whole number and fraction estimation, comparison, arithmetic fluency, objective numeracy, etc.) and subjective ratings of their math attitudes, anxiety, and subjective numeracy. In separate regression models, we identified which objective and subjective math measures were associated with health and non-health decision-making accuracy. Magnitude comparison accuracy, multi-step arithmetic accuracy, and math anxiety accounted for significant variance in health decision-making accuracy, whereas attention to math, as illustrated in open-ended strategy reports, was the only significant predictor of non-health decision-making accuracy. Importantly, reliable and valid measures from the math cognition literature were more strongly related to health decision-making accuracy than were commonly used subjective and objective measures of numeracy. These results have a practical implication: Understanding the math factors that are associated with health decision-making performance could inform future interventions to enhance comprehension of numeric health information
Not Toeing the Number Line for Simple Arithmetic: Two Large-N Conceptual Replications of Mathieu et al. (Cognition, 2016, Experiment 1)
No full textWe conducted two conceptual replications of Experiment 1 in Mathieu, Gourjon, Couderc, Thevenot, and Prado (2016, https://doi.org/10.1016/j.cognition.2015.10.002). They tested a sample of 34 French adults on mixed-operation blocks of single-digit addition (4 + 3) and subtraction (4 – 3) with the three problem elements (O1, +/-, O2) presented sequentially. Addition was 34 ms faster if O2 appeared 300 ms after the operation sign and displaced 5° to the right of central fixation, whereas subtraction was 19 ms faster when O2 was displaced to the left. Replication Experiment 1 (n = 74 recruited at the University of Saskatchewan) used the same non-zero addition and subtraction problems and trial event sequence as Mathieu et al., but participants completed blocks of pure addition and pure subtraction followed by the mixed-operation condition used by Mathieu et al. Addition RT showed a 32 ms advantage with O2 shifted rightward relative to leftward but only in mixed-operation blocks. There was no effect of O2 position on subtraction RT. Experiment 2 (n = 74) was the same except mixed-operation blocks occurred before the pure-operation blocks. There was an overall 13 ms advantage with O2 shifted right relative to leftward but no interaction with operation or with mixture (i.e., pure vs mixed operations). Nonetheless, the rightward RT advantage was statistically significant for both addition and subtraction only in mixed-operation blocks. Taken together with the robust effects of mixture in Experiment 1, the results suggest that O2 position effects in this paradigm might reflect task specific demands associated with mixed operations
Language Effects in Early Development of Number Writing and Reading
No full textReading and writing multidigit numbers requires accurate switching between Arabic numbers and spoken number words. This is particularly challenging in languages with number-word inversion such as German (24 is pronounced as four-and-twenty), as reported by Zuber, Pixner, Moeller, and Nuerk (2009, https://doi.org/10.1016/j.jecp.2008.04.003). The current study aimed to replicate the qualitative error analysis by Zuber et al. and further extended their study: 1) A cross-linguistic (German, English) analysis enabled us to differentiate between language-dependent and more general transcoding challenges. 2) We investigated whether specific number structures influence accuracy rates. 3) To consider both transcoding directions (from Arabic numbers to number words and vice versa), we assessed performance for number reading in addition to number writing. 4) Our longitudinal design allowed us to investigate transcoding development between Grades 1 and 2. We assessed 170 German- and 264 English-speaking children. Children wrote and read the same set of 44 one-, two- and three-digit numbers, including the same number structures as Zuber et al. For German, we confirmed that a high amount of errors in number writing was inversion-related. For English, the percentage of inversion-related errors was very low. Accuracy rates were strongly related to number syntax. The impact of number structures was independent of transcoding direction or grade level and revealed cross-linguistic challenges of transcoding multidigit numbers. For instance, transcoding of three-digit numbers containing syntactic zeros (e.g., 109) was significantly more accurate than transcoding of items with lexical zeros (e.g., 190). Based on our findings, we suggest adaptations of current transcoding models
All Roads Lead to Rome: Semantic Priming Between Language and Arithmetic
No full textThis study evaluated the existence of universal principles of cognition, common to language and arithmetic. Specifically, we analysed cross-domain semantic priming between affirmative sentences and additions, and between negative sentences and subtractions. To this end, we developed and tested a new priming procedure composed of prime sentences and target arithmetic operations. On each trial, participants had to read an affirmative or negative sentence (e.g., “The circle is red”, “The square is not yellow”) and select, between two images, the one that matched the meaning of the sentence. Afterwards, participants had to solve a one-digit addition or subtraction (e.g., 7 + 4, 6 – 3), either by selecting the correct result between two possible alternatives (Experiment 1), or by verbalizing the result of the operation (Experiment 2). We manipulated the task difficulty of both the sentences and the operations by varying the similarity between the response options for the sentence (Experiment 1 and 2), and the numerical distance between the possible results for the operation (Experiment 1). We found semantic priming for subtractions, so that participants solved subtractions faster after negative versus affirmative sentences, and this effect was modulated by the difficulty of the operation. This is the first study reporting semantic priming effects between language and arithmetic. The outcomes of this work seem to suggest a shared semantic system between both cognitive domains
When Does the Story Matter? No Evidence for the Foregrounding Hypothesis in Math Story Problems
No full textMath story problems are difficult for many solvers because comprehension of mathematical and linguistic content must occur simultaneously. Across two studies, we attempted to conceptually replicate and extend findings reported by Mattarella-Micke and Beilock (2010, https://doi.org/10.3758/PBR.17.1.106) and Jarosz and Jaeger (2019, https://doi.org/10.1002/acp.3471). Mattarella-Micke and Beilock found that multiplication word problems in which an irrelevant number was associated with the protagonist of the problem (i.e., foregrounded in the text) were solved less accurately than problems in other conditions. Jarosz and Jaeger used similar materials but tested the more general inconsistent-operations hypothesis that association with the protagonist would interfere with multiplication whereas dissociation would interfere with division. They found partial support: When division problems were primed with dissociative scenarios, solvers made more errors, but they failed to replicate the associative findings for multiplication. In the present research, we conducted two studies (Ns = 205 and 359), in which we similarly manipulated whether irrelevant content was associated with or dissociated from the story protagonist. In these studies, we did not find support for either the foregrounding or inconsistent-operations hypotheses. Exploratory error analyses suggested that solvers’ errors were most often the result of calculation difficulties or inappropriate operation choices and were unrelated to the presence of associative or dissociative story elements. Our careful implementation of this manipulation and much greater power to detect effects suggests that the association manipulation in irrelevant text does not influence adults’ performance on simple math story problems
Not All Elementary School Teachers Are Scared of Math
No full textTeachers are strong role models for their pupils, especially at the beginning of education. This also holds true for math: If teachers feel anxious about math, the consequences on the mathematical education of their pupils is detrimental. Previous studies have shown that (future) elementary school teachers have higher levels of math anxiety than most people studying other subjects. Here, we set out to conceptually replicate these findings (e.g., meta-analysis by Hembree, 1990, https://doi.org/10.2307/749455) by comparing math anxiety levels of pre-service and in-service German and Belgian elementary school teachers to a reference group of German university students from various fields of study. Moreover, we questioned this finding by asking which elementary school teachers experience math anxiety, considering gender, specialization, and experience, and investigated how math anxiety relates to teaching attitudes towards math. We replicated the previous finding by showing that female elementary school teachers have a higher level of math anxiety as compared to other female students. Importantly, female elementary school teachers without math specialization indeed had higher levels of math anxiety than female students from other fields and almost a quarter of them experience critical math anxiety. In contrast, female elementary school teachers with math specialization did not show an increased level of math anxiety as compared to the reference sample. Considering that not only these but all teachers, regardless of specialization, teach math in elementary school in the investigated educational systems, the math anxiety of elementary school teachers is a potential problem for their pupils’ math attitudes and learning
Acquiring the Cardinal Knowledge of Number Words: A Conceptual Replication
No full textUnderstanding the way in which counting represent numerosities was shown to be a long-lasting process. As shown in the Give-a-number task, acquiring the meanings of verbal number words goes through successive developmental stages in which children first learn the cardinal meanings of small number words one at a time before generalizing the cardinal principle they have induced from the first three number words to all number words within their counting range. This acquisition would take about a year, and would be completed by the age of 3 ½ years. The aim of the present study was to provide a conceptual replication of the developmental sequence described in Wynn’s study nearly 30 years ago using the Give-a-number task. A first cross-sectional study was conducted on 213 Belgian children aged between 39 and 74 months using the Give-a-number task to examine the developmental pattern and the influence of age on this acquisition. The time span of acquisition was examined in a second study in which 34 children were tested five times every months between the age of 36 to 52 months. Results showed that acquiring the cardinal meanings of number words spread out over a protracted period, far more extended than assumed by Wynn. Furthermore, children do not generalize all-at-once to large number words, the cardinal knowledge they learned on small number words. Rather, number words were found to be learned one at a time in a really progressive manner. Results were discussed with regard to their implications for the existing theories and in relation with other tasks assessing the acquisition of verbal number symbols
Effects of Figural and Numerical Presentation Formats on Growing Pattern Performance
No full textPrior work exploring preschool-aged children’s reasoning with repeating patterns has shown that patterning ability is an important predictor of math achievement; however, there is limited research exploring older children’s growing pattern task performance. The current study tested whether presentation format impacts performance on growing pattern problems, and whether the effects of presentation format extend to transfer word problems for which no patterns are provided. Sixth grade students were randomly assigned to complete several growing pattern tasks in one of three presentation formats (figures, sequences of values, or tables of values), and later completed transfer story problems with no figures, sequences, or tables provided. Findings suggest that presenting growing patterns as figures can benefit performance, although these benefits may depend on both pattern type and task. No differences were observed in performance on transfer problems, likely because students rarely spontaneously generated figures. Additional exploratory analyses suggest that performance on growing pattern problems may be related to both standardized math ability and fraction task performance, whereas inhibitory control may only be related to performance for specific patterning tasks. These findings have implications for educators because describing/expressing patterns is critical to algebra and higher-level mathematics
