Journal of Numerical Cognition (JNC - PsychOpen)
Not a member yet
230 research outputs found
Sort by
Individual Differences in Numerical Comparison Is Independent of Numerical Precision
No full textNumeracy, as measured by performance on the non-symbolic numerical comparison task, is a key construct in numerical and mathematical cognition. The current study examines individual variation in performance on the numerical comparison task. We contrast the hypothesis that performance on the numerical comparison task is primarily due to more accurate representations of numbers with the hypothesis that performance dependent on decision-making factors. We present data from two behavioral experiments and a mathematical model. In both behavioral experiments we measure the precision of participant’s numerical value representation using a free response estimation task. Taken together, results suggest that individual variation in numerical comparison performance is not predicted by variation in the precision of participants’ numerical value representation
Reducing Interference Improves the Memorization of Multiplication Facts in Case of Hypersensitivity to Interference
No full textHypersensitivity to interference (HYSTI) is a situation in which a person has a severe difficulty in memorizing verbal items that are similar to each other. This may result in induced dyscalculia: HYSTI was shown to correlate with a difficulty in learning the multiplication table, presumably because the multiplication table, which is memorized verbally, has much similarity between the items ("six times seven equals forty two", "six times eight equals forty eight", etc.). Here, we show causal evidence that HYSTI disrupts the memorization of multiplication facts. We report DL, a woman with HYSTI who had extremely poor knowledge of the multiplication table. To examine whether her multiplication difficulty resulted from HYSTI, we tested whether she could learn multiplication facts when interference was reduced. In a series of merely 12 short sessions over a period of 4 weeks, DL rehearsed 16 multiplication facts – four facts per week. When the 4 facts in a given week were similar to each other, DL’s learning was poor. Conversely, when the 4 facts in a given week were dissimilar from each other, DL learned them quickly and easily. The effect of similarity was observed during the training period and persisted at least two months after the end of training. These results provide the first causal evidence that HYSTI impairs the learning or retrieval of arithmetic facts. From a pedagogical perspective, our findings may call for re-considering how multiplication facts should be taught in elementary school
When “One” Can Be “Two”: Cross-Linguistic Differences Affect Children’s Interpretation of the Numeral One
No full textIn English, a lexical distinction is drawn between the indefinite determiner “a” and the numeral “one”. English-speaking children also interpret the two terms differently, with an exact, upper bounded interpretation of the numeral “one”, but no upper bounded interpretation of the indefinite determiner “a”. Unlike English, however, German does not draw a distinction between the indefinite determiner and the numeral one but instead uses the same term “ein/e” to express both functions. To find out whether this cross-linguistic difference affects children’s upper bounded interpretation of “ein/e”, we tested German-speaking children and adults in a truth-value-judgment task and compared their performance to English-speaking children. Our results revealed that German-speaking children differed from both English children and German adults. Whereas the majority of German adults interpreted “ein/e” in an upper bounded way (i.e. as exactly one, not two), the majority of German-speaking children favored a non-upper bounded interpretation (thus accepting two as a valid response to “ein/e”). German-speaking children’s proportion of upper bounded responses to “ein/e” was also significantly lower than English children’s upper bounded responses to “one”. However, German children’s rate of upper bounded responses increased once a number-biasing context was provided. These findings suggest that German-speaking children can interpret “ein/e” in an upper bounded way but that they need additional cues in order to do so. When no such cues are present, German-speaking children differ from both German-speaking adults and from their English-speaking peers, demonstrating that cross-linguistic differences can affect the way speakers interpret numbers
The Conception of Substitution of the Equals Sign Plays a Unique Role in Students' Algebra Performance
No full textStudents’ conceptions of the equals sign are related to algebraic success. Research has identified two common conceptions held by children: operational and relational. The latter has been widely operationalised in terms of the sameness of the values on each side of the equals sign, but it has been recently argued that the substitution component of relational equivalence should also be operationalised (Jones, Inglis, Gilmore, & Dowens, 2012, https://doi.org/10.1016/j.jecp.2012.05.003). In this study, we investigated whether students’ endorsement of the substitution definition of the equals sign is a unique predictor of their algebra performance independent of the other two definitions (operational and sameness). Secondary school students were asked to rate the ‘cleverness’ of operational, sameness, and substitution definitions of the equals sign and completed an algebra test. Our findings demonstrate that endorsement of substitution plays a unique role in explaining secondary school students’ algebra performance above and beyond school year and the other definitions. These findings contribute new insights into how students’ algebra learning relates to their conceptions of the equals sign
The Association Between Number Magnitude and Space Is Dependent on Notation: Evidence From an Adaptive Perceptual Orientation Task
No full textResearch on adults' numerical abilities suggests that number representations are spatially oriented. This association of numbers with spatial response is referred to as the SNARC (i.e., spatial–numerical association of response codes) effect. The notation-independence hypothesis of numeric processing predicts that the SNARC effect will not vary with notation (e.g., Arabic vs. number word). To test such assumption, the current study introduced an adaptive experimental procedure based on a simple perceptual orientation task that can automatically smooth out the mean reaction time difference between Arabic digits and traditional Chinese number. We found that the SNARC effect interacted with notation, showing a SNARC effect for Arabic digits, but not for verbal number words. The results of this study challenged the commonly held view that notation does not affect numerical processes associated with spatial representations. We introduced a parallel model to explain the notation-dependent SNARC effect in the perceptual orientation judgment task
Relation of State- and Trait-Math Anxiety to Intelligence, Math Achievement and Learning Motivation
No full textThis study investigates math anxiety (MA) by comparing trait-components of MA with real-time assessments of situational anxiety responses (state-components) in children. The research to date on MA in children is somewhat disparate in regard to methodology, and firm conclusions regarding the relation of MA to intelligence, math achievement and learning motivation are not readily drawn. Typically, the measures used in the MA research have differed by operationalizing either trait-MA and/or state- (or statelike)-MA, but have failed to compare the implications of their respective assumptions and the significance of their findings. Trait-MA and state-MA, self-ratings of math skills, attitudes towards mathematics, math achievement, the social anxiety, test anxiety, learning motivation and intelligence of 1,179 students (48.1% girls) from grades 4 and 5, were assessed. The findings yield evidence of a pronounced state-trait discrepancy. A negative correlation between state-MA and math achievement was observed for all intelligence levels, even when controlling for test- and social-anxiety traits, while there was no negative relation between trait-MA and achievement. State-MA was associated with lower intelligence, lower self-ratings, more negative attitudes, higher performance avoidance and work avoidance goals. In contrast, trait-MA was slightly related to higher mastery approach goals. The failure to adequately differentiate between state- and trait-based research into MA appears to be one reason for key inconsistencies between research findings and warrants further investigations
Cognitive Heterogeneity of Math Difficulties: A Bottom-up Classification Approach
No full textMath learning difficulties (MD) correspond to math achievement below the 25th percentile and are cognitively heterogeneous. It is not known precisely how cognitive mechanisms underlie distinct subtypes of MD. A bottom-up, cluster-analytic strategy, based on visuoconstructional, visuospatial and phonological working memory, and non-symbolic and symbolic magnitude processing accuracy, was used to form subgroups of children from 3rd to 5th grades according to their math achievement. All children had nonverbal intelligence above the 20th percentile and presented a broad spectrum of variation in math ability. External validity of subgroups was examined considering intelligence and math achievement. Groups did not differ in age. Two groups with a high incidence of MD were associated, respectively, with low visuospatial/visuoconstructional and low magnitude processing accuracy. One group with average cognitive performance also presented above average intelligence and a small incidence of MD. A fourth group with high cognitive performance presented high math performance and high intelligence. Phonological working memory was associated with high but not with low math achievement. MD may be related to complex patterns of associations and dissociations between intelligence and specific cognitive abilities in distinct subgroups. Consistency and stability of these subgroups must be further characterized. However, a bottom-up classification strategy contributes to reducing the cognitive complexity of MD
Impairment of Non-Symbolic Number Processing in Children With Mathematical Learning Disability
No full textThe functional origin of Mathematical Learning Disability (MLD), an impairment affecting mathematics learning, remains controversial. We aimed to study the number sense deficit hypothesis in children with MLD. We explored the processing of non-symbolic numbers in Quebec French-speaking 8‒9-year-old children with three non-symbolic tasks (number comparison, number matching and dot set selection task). Results showed that children with MLD were as successful as typically developing children in a comparison task, but less successful in a matching task. Their performance in numerical re-production was also similar to that of typically developing children for large (10-99) numerosities, while they were less successful in transcoding small (1-4) and medium (5-9) numerosities. Children with MLD also presented with general cognitive and reading difficulties. Results suggest a deficit in processing small and medium numerosities in children with MLD that could be largely attributed to their poorer cognitive skills
The Effects of Depression on Number Perception and its Implications for Theories of Numerical Cognition
No full textMost theories of numerical cognition assume that the perception of a quantity is independent of that which the quantity describes (termed an abstract quantity representation). Beck’s cognitive theory of depression, in contrast, assumes that depressed individuals maintain negative perceptual biases and that depressed individuals’ perception of quantity will be dependent on that which the quantity describes. Here, we explore the nature of quantity representations by assessing whether level of depression and valence of events influences individuals’ perceptions of numerical quantities. In a number bisection task, we presented participants with three quantities: one associated with the time until a positive event, one associated with the time until a negative event, and a target number. The participant was asked to judge whether the quantity denoted by the target number was closer to the time until the positive or negative event. Results indicated that event valence influenced the perception of quantity and this perceptual bias interacted with the level of depression. Thus, these findings indicate that quantity representations are malleable and are represented non-abstractly in the brain