Electronic Thesis and Dissertation Repository

Thesis Format

Alternative Format

Degree

Master of Science

Program

Neuroscience

Supervisor

Daniel, A

Abstract

The ability to process the quantities of sets in the world around us, referred to as ‘non-symbolic numerical processing,’ relies on two primary systems: the Approximate Number System (ANS) for processing large sets, and the Object-file system for the rapid and accurate processing of small sets (1-4 items). In numerical cognition research, sets of 1-9 are frequently used, inadvertently blending the use of these two systems. The primary objective of this study was to investigate whether the inclusion of subitizable trials within the 1-9 non-symbolic comparison task affects its validity as a pure measure of the true ratio effect of the ANS. Specifically, we sought to determine if the ANS operates independently across different numerical ranges or if subitizing introduces confounding effects. Our findings revealed that the 1-9 range is processed differently compared to other ranges, both in symbolic and non-symbolic contexts. This suggests that the 1-9 range may not reliably measure the true ratio effect of the ANS. The implications of this study recommend against using the 1-9 range for assessing ANS acuity or for cross-format numerical comparisons.

Summary for Lay Audience

Humans and many animals share a basic ability called "number sense," which helps us quickly judge quantities, like figuring out which checkout line is shorter. This ability involves comparing groups of objects (non-symbolic quantities), such as apples, using two processes. The first is "subitizing," which is our quick recognition of small groups of items, typically within the range of 1-4 items. The second process is estimation, which is used for larger groups and relies on what’s known as the Approximate Number System (ANS).

Researchers often study this number sense by presenting people with two groups of dots and asking them to decide which group is larger. Many studies focus on comparing quantities within the range of 1 to 9 items. However, there is some debate about whether this range truly measures the ANS, since it includes both small, easily recognizable groups (1-4 items) and larger groups that require estimation.

My research aimed to understand whether the 1-9 range is a good measure of the ANS by exploring two key questions: First, does our ability to quickly recognize small groups (subitizing) affect how we compare larger groups beyond 4? Second, are comparisons within the 1-9 range more like how we process symbolic numbers (like 1, 2, 3) than to how we estimate larger groups (like 5 to 45 items)?

The findings showed that comparisons within the 1-9 range are processed differently from those within the 5-45 range, particularly for smaller quantities. Specifically, when people compared small groups of items within the 1-4 range, they processed them faster than when comparing larger groups (5-20). Additionally, comparisons within the 1-9 range were more like how we process symbolic numbers and were better at predicting math skills than comparisons involving larger groups. This suggests that the 1-9 range does not purely measure the ANS.

In summary, the findings suggest that using the 1-9 range may not be the best way to understand how we estimate non-symbolic quantities because it mixes two different processes: subitizing and the ANS. This could influence the accuracy of research findings on numerical estimation and its connection to broader math abilities.

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