Brain mechanisms underlying mathematics and its acquisition

Introduction

Mathematics is a fundamental tool by which we understand the universe, yet its cognitive and brain mechanisms are vastly understudied. I propose a systematic study of the human representation of mathematical concepts and their growth with education. The project will test the “language of thought” theory according to which humans share core concepts with other animals (numbers, objects, shapes, spatial maps) but the growth of math relies on a human symbolic composition system that recursively recombines those concepts into arbitrarily more complex expressions.

Work Package 1: Mapping Mathematical Concepts

Work package (WP) 1 will generate maps of mathematical concepts in adults varying in education, using high-resolution single-subject 7T fMRI and MEG.

Education Impact

The impact of education will be studied by:

1. Testing concepts ranging from elementary to advanced.
2. Comparing adults whose education varies from high school to professional math.
3. Including blind and high-functioning autism subjects in the study.

Work Package 2: Central Mathematical Concepts

WP2 will focus on 5 concepts of central importance in math:

• Geometrical shape
• Pattern
• Set
• Number line
• Graph

Developmental Change

For each concept, we will map developmental change by acquiring behavioral and fMRI data in adults and children. The model predicts that concept acquisition can be modeled as a construction of increasingly complex mental expressions whose complexity is predicted by minimal description length (MDL).

Work Package 3: Brain Changes During Concept Acquisition

WP3 will map the brain changes during the acquisition of a math concept.

Experimental Focus

Experiments will test the role of:

• Feedback
• Repetition
• Retrieval practice
• Sleep
• Conceptual diversity
• Age

These factors will be examined in facilitating behavioral and brain measures of conceptual change.

Work Package 4: Artificial Neural Networks

Finally, WP4 will examine whether artificial neural networks can capture the above results and investigate how these networks can be enhanced to achieve human-like performance.

Conclusion

Overall, the results will shed light on how mathematical education changes the human brain and how conceptual change occurs, thus paving the way to real-life educational applications in schools.