The structure of the notation system in adults' number line estimation: An eye-tracking study

Area of Science:

• Cognitive Psychology
• Mathematics Education
• Numerical Cognition

Background:

• Adults exhibit greater difficulty comprehending the numerical magnitude of rational numbers compared to natural numbers.
• Within rational numbers, fractions present a more significant challenge to magnitude understanding than decimals.

Purpose of the Study:

• To investigate how number type (natural vs. rational) and notation system structure (place-value-based vs. non-place-value-based) impact adults' numerical magnitude understanding.
• To analyze performance using a number line estimation (NLE) task across four conditions: natural numbers, decimals, fractions, and separated fractions.

Main Methods:

• A within-subjects design was employed, presenting participants with four distinct numerical notation conditions.
• Data collection included percentage absolute error (PAE), response times, and eye-tracking metrics.
• Analysis focused on comparing estimation accuracy, response speed, and visual attention patterns.

Main Results:

• Natural numbers and place-value-based notations were estimated more accurately than rational and non-place-value-based notations, respectively.
• Fractions elicited slower response times and increased encoding/revisiting durations compared to other notations.
• Non-place-value-based notations generally required more time for number line positioning than place-value-based notations.

Conclusions:

• Numerical magnitude understanding is significantly impaired when a notation combines rational properties with a non-place-value system (e.g., fractions).
• The presence of a single difficulty source (either rational or non-place-value) results in better understanding than when both are present.
• The strongest numerical magnitude understanding is observed in notations that are both natural and place-value-based (e.g., standard natural numbers).