Intuitive errors in learners' fraction understanding: A dual-process perspective on the natural number bias.

Although a good rational number understanding is very important, many learners struggle to understand fractions. Recent research attributes many of these difficulties to the natural number bias - the tendency to apply natural number features in rational number tasks where this is inappropriate. Previous correlational dual process studies found evidence for the intuitive nature of the natural number bias in learners' response latencies. However, the reported correlations do not ascertain the causality that is assumed in this ascription. In the present study we therefore experimentally elicited intuitive responses in a fraction comparison task in educated adults by restricting reaction time. Results show that the natural number bias has an intuitive character. Findings also indicate that the detection of conflict between the natural number-based answer and the correct answer seems to work at an intuitive level.

Not realizing that you don't know: Fraction state anxiety is reduced by natural number bias.

BACKGROUND: Research has shown that mathematics anxiety negatively correlates with primary school mathematics performance, including fraction knowledge. However, recently no significant correlation was found between fraction arithmetic performance and state anxiety measured after the fraction task. One possible explanation is the natural number bias (NNB), a tendency to apply natural number reasoning in fraction tasks, even when this is inappropriate. Students with the NNB may not realize they are answering incorrectly. AIMS: The aim is to examine whether a misconception, namely the NNB, can influence students' fraction state anxiety. SAMPLE: The participants were 119 fifth- and sixth-grade students categorized as belonging to an NNB group (n = 60) or a No-NNB group (n = 59), according to their NNB-related answering profile on a fraction arithmetic task. METHODS: Group differences were examined for state anxiety and performance on a fraction and a whole number arithmetic task and self-reported trait mathematics anxiety. RESULTS: The NNB group reported lower fraction state anxiety than the No-NNB group, but there was no significant difference in trait mathematics anxiety. Furthermore, the NNB group reported lower fraction state anxiety than whole number state anxiety, while the opposite was true for the No-NNB group. CONCLUSION: The present study suggests that students' perceptions of their own performance influence their state anxiety responses, and students with a NNB may not be aware of their misconception and poor performance. Not taking into account qualitative differences in low performance, such as misconceptions, may lead to misinterpretations in state anxiety-performance relations.

Numeracy and COVID-19: examining interrelationships between numeracy, health numeracy and behaviour.

During the COVID-19 pandemic, people across the globe have been exposed to large amounts of statistical data. Previous studies have shown that individuals' mathematical understanding of health-related information affects their attitudes and behaviours. Here, we investigate the relation between (i) basic numeracy, (ii) COVID-19 health numeracy, and (iii) COVID-19 health-related attitudes and behaviours. An online survey measuring these three variables was distributed in Canada, the United States (US) and the United Kingdom (UK) (n = 2032). In line with predictions, basic numeracy was positively related to COVID-19 health numeracy. However, predictions, neither basic numeracy nor COVID-19 health numeracy was related to COVID-19 health-related attitudes and behaviours (e.g. follow experts' recommendations on social distancing, wearing masks etc.). Multi-group analysis was used to investigate mean differences and differences in the strength of the correlation across countries. Results indicate there were no between-country differences in the correlations between the main constructs but there were between-country differences in latent means. Overall, results suggest that while basic numeracy is related to one's understanding of data about COVID-19, better numeracy alone is not enough to influence a population's health-related attitudes about disease severity and to increase the likelihood of following public health advice.

Unique contribution of Ecuadorian kindergartners' spontaneous focusing on numerosity to their early numerical abilities.

Recent evidence indicates that young children's spontaneous focusing on numerosity (SFON) uniquely contributes to their early numerical abilities. This study complements previous findings by validating the relation between young children's SFON and their early numerical abilities in a developing country, namely Ecuador. We analysed 355 Ecuadorian 5- to 6-year-olds' SFON in relation to their early numerical abilities at the start of kindergarten, controlling for children's socio-demographic (socio-economic status, age) and general cognitive (working memory, intelligence) characteristics. Our results evidence the unique contribution of Ecuadorian kindergartners' SFON to their early numerical abilities, controlling for children's working memory, intelligence, socio-economic status, and age. Our findings support the validity of previous findings on the unique contribution of SFON to young children's early numerical abilities in developed countries for developing countries. Additionally, they raise timely questions for further theoretical and methodological studies on young children's numerical development worldwide, in developing and developed countries. Statement of contribution What is already known? SFON uniquely contributes to early numerical abilities. However, this is only documented in Finnish samples. Previously only limited control for domain-general cognitive and socio-demographic characteristics. What does the study add? SFON uniquely contributes to early numerical abilities in Ecuadorian 5- to 6-year-olds. This unique contribution remains after controlling for WM, IQ, SES, and age. Evidence for the universal nature of the association between SFON and early numerical ability.

Number sense in the transition from natural to rational numbers.

BACKGROUND: Rational numbers are of critical importance both in mathematics and in other fields of science. However, they form a stumbling block for learners. One widely known source of the difficulty learners have with rational numbers is the natural number bias, that is the tendency to (inappropriately) apply natural number properties in rational number tasks. Still, it has been shown that a good understanding of natural numbers is highly predictive for mathematics achievement in general, and for performance on rational number tasks in particular. AIMS: In this study, we further investigated the relation between learners' natural and rational number knowledge, specifically in cases where a natural number bias may lead to errors. SAMPLE: Participants were 140 sixth graders from six different primary schools. METHOD: Participants completed a symbolic and a non-symbolic natural number comparison task, a number line estimation task, and a rational number sense test. RESULTS: Learners' natural number knowledge was found to be a good predictor of their rational number knowledge. However, after first controlling for learners' general mathematics achievement, their natural number knowledge only predicted the subaspect of operations with rational numbers. CONCLUSION: The results of this study suggest that the relation between learners' natural and rational number knowledge can largely be explained by their relation with learners' general mathematics achievement.

The natural number bias and its role in rational number understanding in children with dyscalculia. Delay or deficit?

BACKGROUND: Previous research indicated that in several cases learners' errors on rational number tasks can be attributed to learners' tendency to (wrongly) apply natural number properties. There exists a large body of literature both on learners' struggle with understanding the rational number system and on the role of the natural number bias in this struggle. However, little is known about this phenomenon in learners with dyscalculia. AIMS: We investigated the rational number understanding of learners with dyscalculia and compared it with the rational number understanding of learners without dyscalculia. METHOD: Three groups of learners were included: sixth graders with dyscalculia, a chronological age match group, and an ability match group. RESULTS: The results showed that the rational number understanding of learners with dyscalculia is significantly lower than that of typically developing peers, but not significantly different from younger learners, even after statistically controlling for mathematics achievement. CONCLUSION: Next to a delay in their mathematics achievement, learners with dyscalculia seem to have an extra delay in their rational number understanding, compared with peers. This is especially the case in those rational number tasks where one has to inhibit natural number knowledge to come to the right answer.