Is the mental number line a unique model of numerical cognition?

Abstract

Many theories of number propose that humans possess a ‘mental number line’ (MNL) representation. The MNL is commonly measured with a number-to-position (NP) task, and this task is often used to make inferences about the MNL representation. However, most research on MNL representations to date has made assumptions about the properties of the MNL without considering the role of ordinal relationships between numbers. The research reported in this thesis examined whether the MNL metaphor should be extended to include ordinal relationships, and to examine the nature of these relationships. A pilot study tested whether a linear MNL representation could be shifted with logarithmic training. Adults completed a series of logarithmic feedback sessions, and their NP task performance was assessed at the end of each training block. Findings revealed little to no systematic effect of logarithmic training on NP task performance, despite participants successfully learning the logarithmic function. They also revealed individual differences in the overall impact and learning of the logarithmic feedback. These findings suggested that relationships between numbers may change to allow accurate task performance, which may not be reflected in the NP task. Study 1 tested whether the linear response profile that describes NP performance is specific to number, or whether this pattern of responding is a feature of ordered lists more generally. Adults were given NP and alphabet-to-position tasks. Findings showed that numbers and letters both displayed similar linear trends. This suggested that the linear profiles attributed to number may reflect the way in which ordinal lists of symbols are learned. Studies 2a and 2b investigated whether leaning a list of novel symbols is mediated by the underlying spatial properties of the symbols (e.g., spatial complexity). Novel symbols were used to minimise the overlearned nature of Hindu-Arabic numerals. Study 2a aimed to determine the ideal novel symbol set to use in Study 2b, specifically, one which could be ordered by complexity. Participants made judgements on two novel symbol sets, and their relationship to a range of numerical stimuli. In Study 2b, a paired comparisons training method was used to teach participants the order of a list of novel symbols. Participants were allocated to either a spatial complexity or a random complexity condition, and made judgements regarding which of two symbols was numerically ‘larger’. When novel symbols were ordered by spatial complexity, learning was facilitated. These findings showed that the spatial complexity and relational information of symbols may mediate the construction of ordered representations. This suggests that a common cognitive representation underlies all ordinal lists. Overall, the findings of this research indicate that a more nuanced account of the MNL representation is required, particularly in terms of ordinal relationships between numbers. The findings also suggest that the NP task measures ordinal lists more generally. Arguably, the way in which ordered lists are learned, combined with the relative relationships between symbols, may account for performance on the NP task, and the MNL metaphor should be extended to account for these ordinal relationships.