A domain/field of research can often benefit from a consensus. Agreement regarding terminology and tasks used to measure specific constructs may be particularly beneficial. Our group authored such a consensus paper on measuring the Approximate Number System in young children (Krajcsi et al., 2024). In preparing that paper, we followed the procedure described here. In the presented paper, we describe a method for preparing multi-author consensus papers along with our reflections on implementing and streamlining this procedure. We hope it is useful to authors interested in initiating such collaborative projects.

Studying numerical interferences has become a widely used method for investigating the representations that underlie numerical cognition. Here, we contrast the classic Approximate Number System (ANS) framework and a more recently proposed hybrid ANS-Discrete Semantic System (DSS) framework with respect to their distinctive predictions for the symbolic and nonsymbolic SNARC effects (the most extensively studied interference between numbers and space). We compare the symbolic (Indo-Arabic numbers) to the nonsymbolic (arrays of dots) version of a SNARC paradigm (n=77). In contrast to previous studies, in the present experiment, (1) the magnitude is irrelevant for solving the task (a colorjudgment task) for the nonsymbolic task, too, and (2) the nonsymbolic stimuli contain arrays of dots outside the subitizing range, which would not activate the ANS. We found clear evidence for the SNARC effect in the symbolic color task. However, we found no indication of the SNARC effect in the nonsymbolic color task. This pattern of results supports the hybrid ANS-DSS framework, assuming that the SNARC interference is a symbolic effect while refuting the pure ANS view of the SNARC effect, which necessitates the presence of the SNARC interference using nonsymbolic notation, too.

The approximate number system (ANS) is a hypothesized mechanism responsible for the representation and processing of numerical information in an imprecise fashion. According to the predominant theory, the ANS is essential in solving simple numerical tasks such as comparing which of two quantities is numerically larger, and some research has indicated that individual differences in its acuity influence higher-level mathematical performance. Because of this far-reaching role of the ANS, it is essential to assess its acuity with measures that are reliable, and valid. The present work reviews and synthesizes many of the methodological problems that are relevant for measuring ANS acuity in young children. We discuss issues related to task comprehension , the role of non-numerical perceptual properties of the stimuli, the role of inhibition, and the appropriateness and reliability of the ANS acuity indices. Recommendations and open questions are summarized.

The approximate number system (ANS) is a hypothesized mechanism responsible for the representation and processing of numerical information in an imprecise fashion. According to the predominant theory, the ANS is essential in solving simple numerical tasks such as comparing which of two quantities is numerically larger, and some research has indicated that individual differences in its acuity influence higher-level mathematical performance. Because of this far-reaching role of the ANS, it is essential to assess its acuity with measures that are reliable, and valid. The present work reviews and synthesizes many of the methodological problems that are relevant for measuring ANS acuity in young children. We discuss issues related to task comprehension, the role of non-numerical perceptual properties of the stimuli, the role of inhibition, and the appropriateness and reliability of the ANS acuity indices. Recommendations and open questions are summarized.

Initial acquisition of the first symbolic numbers is measured with the Give a Number (GaN) task. According to the classic method, it is assumed that children who know only 1, 2, 3, or 4 in the GaN task, (termed separately one‐, two‐, three‐, and four‐knowers, or collectively subset‐knowers) have only a limited conceptual understanding of numbers. On the other hand, it is assumed that children who know larger numbers understand the fundamental properties of numbers (termed cardinality‐principle‐knowers), even if they do not know all the numbers as measured with the GaN task, that are in their counting list (e.g., five‐ or six‐knowers). We argue that this practice may not be well‐established. To validate this categorization method, here, the performances of groups with different GaN performances were measured separately in a symbolic comparison task. It was found that similar to one to four‐knowers, five‐, six‐, and so forth, knowers can compare only the numbers that they know in the GaN task. We conclude that five‐, six‐, and so forth, knowers are subset‐knowers because their conceptual understanding of numbers is fundamentally limited. We argue that knowledge of the cardinality principle should be identified with stricter criteria compared to the current practice in the literature. RESEARCH HIGHLIGHTS Children who know numbers larger than 4 in the Give a Number (GaN) task are usually assumed to have a fundamental conceptual understanding of numbers. We tested children who know numbers larger than 4 but who do not know all the numbers in their counting list to see whether they compare numbers more similar to children who know only small numbers in the GaN task or to children who have more firm number knowledge. Five‐, six‐, and so forth, knowers can compare only the numbers they know in the GaN task, similar to the performance of the one, two, three, and four‐knowers. We argue that these children have a limited conceptual understanding of numbers and that previous works may have miscategorized them.