Early Mathematics Learners’ Numerical Errors: Consequence of Poor Learners’ Comprehension and Teachers’ Instructions

While the coronavirus disease 2019 (COVID-19) is still considered as a pandemic in recent human history, evidence from World Health Organization (2021) so far has recorded a total of 116,521,281 confirmed cases of COVID-19 with 2,589,548 as a total of deaths from over 215 countries or territories worldwide. Recognizing that COVID-19 is not only pandemic since March 11, 2020, but spreading worldwide at unprecedented rate, number of sectors including schools and universities as a measure to minimize person-to-person transmission closed their services. Such an uncertain closure warranted restructuring of services provided by schools and universities. The challenges therefore have necessitated the current research to investigate and alleviate challenges brought about by the COVID-19. In essence, the present research’s aim was to report on early mathematics learners (foundation phase) numerical errors, which is as a consequence of poor learners’ comprehension and teachers’ instructions. Based on the aim, the study was positioned within a cognitive theory in order to examine processing of numerical competence among early mathematics learners. A case study via 80 grade 3 learners with ages 8 and 9 was sampled. A textual analysis was used in unpacking and de-contextualizing processing of numerical competence by early mathematics learners. The evidence revealed learners’ mathematical mistakes were caused from limited reading skills and ill-presented problems via teachers. Due to the need to teach children at home (home school) due to the COVID-19, it is hoped that the findings thus assist audience, including non-academic and parents, who grapple with poor instructions coupled with poor learners’ comprehension.

Understanding of Numerical Information during the COVID-19 Pandemic

Media news during the Coronavirus Disease 2019 (COVID-19) pandemic often entail complex numerical concepts such as exponential increase or reproduction number. This study investigated whether people have difficulties in understanding such information and whether these difficulties are related to numerical competence, reflective thinking, and risk proneness. One hundred sixty-three participants provided answers to a numeracy scale focusing on complex numerical concepts relevant to COVID-19 (COV Numeracy Scale). They also provided responses to well-established objective and subjective scales, questions about affective states, and questions about the COVID-19 pandemic. Higher scores on the COV Numeracy Scale correlated with higher scores on the Health Numeracy Scale, in the Cognitive Reflection Test (CRT), and in self-assessments of verbal comprehension, mathematical intelligence, and subjective numeracy. Interestingly, scores on the COV Numeracy Scale also positively correlated with the number of consulted information sources about COVID-19. Accuracy in the CRT emerged as a significant predictor, explaining ca. 14% of variance on the COV Numeracy Scale. The results suggest that people with lower reflective thinking skills and lower subjective and objective numerical competence can be more at disadvantage when confronted with COVID-related numerical information in everyday life. These findings advise caution in the communication of relevant public health information that entails complex numerical concepts.

Enculturation and the historical origins of number words and concepts

In the literature on enculturation—the thesis according to which higher cognitive capacities result from transformations in the brain driven by culture—numerical cognition is often cited as an example. A consequence of the enculturation account for numerical cognition is that individuals cannot acquire numerical competence if a symbolic system for numbers is not available in their cultural environment. This poses a problem for the explanation of the historical origins of numerical concepts and symbols. When a numeral system had not been created yet, people did not have the opportunity to acquire number concepts. But, if people did not have number concepts, how could they ever create a symbolic system for numbers? Here I propose an account of the invention of symbolic systems for numbers by anumeric people in the remote past that is compatible with the enculturation thesis. I suggest that symbols for numbers and number concepts may have emerged at the same time through the re-semantification of words whose meanings were originally non-numerical.

Neuroethology of number sense across the animal kingdom

ABSTRACT Many species from diverse and often distantly related animal groups (e.g. monkeys, crows, fish and bees) have a sense of number. This means that they can assess the number of items in a set – its ‘numerosity’. The brains of these phylogenetically distant species are markedly diverse. This Review examines the fundamentally different types of brains and neural mechanisms that give rise to numerical competence across the animal tree of life. Neural correlates of the number sense so far exist only for specific vertebrate species: the richest data concerning explicit and abstract number representations have been collected from the cerebral cortex of mammals, most notably human and nonhuman primates, but also from the pallium of corvid songbirds, which evolved independently of the mammalian cortex. In contrast, the neural data relating to implicit and reflexive numerical representations in amphibians and fish is limited. The neural basis of a number sense has not been explored in any protostome so far. However, promising candidate regions in the brains of insects, spiders and cephalopods – all of which are known to have number skills – are identified in this Review. A comparative neuroscientific approach will be indispensable for identifying evolutionarily stable neuronal circuits and deciphering codes that give rise to a sense of number across phylogeny.

Perspective taking as a mechanism for children’s developing preferences for equitable distributions

How do young children develop a concept of equity? Infants prefer dividing resources equally and expect others to make such distributions. Between the ages of 3–8, children begin to exhibit preferences to avoid inequitable outcomes in their distributions, dividing resources unequally if the result of that distribution is a more equitable outcome. Four studies investigated children’s developing preferences for generating equitable distributions, focusing on the mechanisms for this development. Children were presented with two characters with different amount of resources, and then a third character who will distribute more resources to them. Three- to 8-year-olds were asked whether the third character should give an equal number of resources to the recipients, preserving the inequity, or an unequal number to them, creating an equitable outcome. Starting at age 7, children showed a preference for equitable distributions (Study 1, N = 144). Studies 2a (N = 72) and 2b (N = 48) suggest that this development is independent of children’s numerical competence. When asked to take the perspective of the recipient with fewer resources, 3- to 6-year-olds were more likely to make an equitable distribution (Study 3, N = 122). These data suggest that social perspective taking underlies children’s prosocial actions, and supports the hypothesis that their spontaneous capacity to take others’ perspectives develops during the early elementary-school years.

Characterising ontogeny of numerosity discrimination in zebrafish reveals use of multiple, numerical and non- numerical mechanisms

Non-symbolic number cognition based on an approximate sense of magnitude has been documented in adult zebrafish. Here we investigated the ontogeny of this ability using a group size preference task in juvenile zebrafish. Fish showed group size preference from 26 days post fertilization (dpf) and from 27 dpf fish reliably chose the larger group when presented with discrimination ratios from 1:8 to 2:3. When the ratio between the number of conspecifics in each group was maintained at 1:2, fish could discriminate between 1 vs. 2 individuals and 3 vs. 6, but not when given a choice between 2 vs. 4 individuals. These findings suggest that the systems involved in numerosity representation in fish do not operate separately from other cognitive mechanisms. Rather they suggest numerosity processing is the result of an interplay between attentional, cognitive and memory-related mechanisms that orchestrate numerical competence both in humans and animals. Our results emphasise the potential of the use of zebrafish to explore the genetic and neural processes underlying the ontogeny of number cognition.