Sensorimotor Underpinnings of Mathematical Imagination: Qualitative Analysis

Area of Science:

• Cognitive Science
• Neuroscience
• Mathematics Education

Background:

• Mathematicians often possess rich internal mental imagery.
• The sensorimotor underpinnings of mathematical imagination are not well understood.

Purpose of the Study:

• To investigate the sensorimotor foundations of mathematical mental imagery.
• To explore how altering body position affects mathematical visualizations.

Main Methods:

• Participants (mathematicians) were asked to engage in mental imagery tasks.
• Their body positions, including head and vestibular system orientation relative to gravity, were manipulated.
• Qualitative descriptions of mental imagery were collected and analyzed.

Main Results:

• No two mathematicians reported identical imagery.
• Eight of 11 participants habitually visualized, one used sensorimotor imagery, and two did not.
• Imagery exhibited intentionality and partial autonomy, with visualizations adapting to body position and spatial relationships.
• Imagery interacted dynamically with the body, forming a dyad where imagery and body movements complemented each other.

Conclusions:

• Mathematical mental imagery has sensorimotor foundations, influenced by bodily orientation.
• The interaction between imagery habits and autonomy can be a source of mathematical creativity.
• Individual differences in imagery are significant, highlighting the diverse nature of mathematical cognition.