Reasoning strategies with rational numbers revealed by eye tracking

Area of Science:

• Cognitive psychology
• Mathematical cognition
• Human-computer interaction

Background:

• Relational judgments about quantitative relations are influenced by rational number formats.
• Previous research shows fractions with countable sets yield higher accuracy than decimals.
• Underlying processing strategies for these accuracy disparities remain unclear.

Purpose of the Study:

• To investigate how different rational number formats (fractions vs. decimals) and quantity types (discrete vs. continuous images) affect cognitive processing strategies.
• To use eye-tracking to externalize and analyze these processing strategies during relational judgment tasks.
• To understand the joint influence of number format and image properties on strategy selection and task accuracy.

Main Methods:

• An experiment employing eye-tracking to record participants' eye movements during a relational judgment task.
• Manipulation of rational number formats (fractions, decimals) and image types (discrete, continuous quantities).
• Analysis of eye-movement behavior to infer underlying cognitive strategies (e.g., counting, magnitude estimation).

Main Results:

• Eye-movement behavior was jointly determined by image type and number format.
• Discrete images prompted counting strategies for both fractions and decimals, but accuracy improved only for fractions.
• Continuous images led to magnitude estimation/comparison strategies, decreasing accuracy for both number formats.

Conclusions:

• Rational number format and image properties interact to shape cognitive strategies in relational judgment tasks.
• Eye-tracking provides valuable insights into the strategic choices underlying performance, complementing accuracy data.
• Understanding these interactions is crucial for designing effective quantitative representations and educational tools.