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Beurling numbers whose number of prime factors lies in a specified residue class Ghent University
We find asymptotics for SK,c(x), the number of positive integers below x whose number of prime factors is c mod K. We study this question in the context of Beurling integers.
Numerical magnitude understanding of natural and rational numbers in secondary-school students: a number line estimation study KU Leuven
Rational numbers, such as fractions and decimals, are harder to understand than natural numbers. Moreover, individuals struggle with fractions more than with decimals. The present study sought to disentangle the extent to which two potential sources of difficulty affect secondary-school students’ numerical magnitude understanding: number type (natural vs. rational) and structure of the notation system (place-value-based vs. ...
Focusing on numbers - An investigation of the role of children’s spontaneous focusing on Arabic number symbols in early mathematical development KU Leuven
Children start formal schooling with large individual differences in their mathematical competence. While some children can already perform simple calculations, others are still learning how to count small numerosities. This large variety in mathematical competence at the start of formal schooling can be explained by the early mathematical abilities children use in explicit mathematical situations, but to some extent also by their tendencies to ...
Judging the order of numbers relies on familiarity rather than activating the mental number line KU Leuven
A series of effects characterises the processing of symbolic numbers (i.e., distance effect, size effect, SNARC effect, size congruency effect). The combination of these effects supports the view that numbers are represented on a compressed and spatially oriented mental number line (MNL) as well as the presence of an interaction between numerical and other magnitude representations. However, when individuals process the order of digits, response ...
Can You Trust Your Number Sense: Distinct Processing of Numbers and Quantities in Elementary School Children KU Leuven
Theories of number development have traditionally argued that the acquisition and discrimination of symbolic numbers (i.e., number words and digits) are grounded in and are continuously supported by the Approximate Number System (ANS)—an evolutionarily ancient system for number. In the current study, we challenge this claim by investigating whether the ANS continues to support the symbolic number processing throughout development. To this end, ...
Abstract representations of number: what interactions with number form do not prove and priming effects do Ghent University
Natural number bias in arithmetic operations with missing numbers – A reaction time Study KU Leuven
When reasoning about numbers, students are susceptible to a natural number bias (NNB): When reasoning about non-natural numbers they use properties of natural numbers that do not apply. The present study examined the NNB when students are asked to evaluate the validity of algebraic equations involving multiplication and division, with an unknown, a given operand, and a given result; numbers were either small or large natural numbers, or decimal ...