Modeling the process of problem-solving by associative networks capable of improving the performance

Area of Science:

• Cognitive Science
• Computational Neuroscience
• Artificial Intelligence

Background:

• Arithmetic problem-solving involves complex cognitive processes.
• Existing models often lack detailed memory representations for procedural and semantic knowledge.
• Understanding the neural basis of mathematical cognition is crucial.

Purpose of the Study:

• To describe a neural network model for arithmetic problem-solving.
• To incorporate procedural, semantic, and working memory within an associative processor framework.
• To simulate and analyze the model's performance in addition tasks.

Main Methods:

• Constructed memory models (procedural, semantic, working) within the HASP associative processor framework.
• Simulated the neural network model on a digital computer.
• Memorized primitive addition knowledge and procedural control strategies.

Main Results:

• The model successfully performed multi-digit addition by utilizing memorized semantic and procedural knowledge.
• Performance improved by approximately 20% due to serial associations (priming) and step merging.
• The model generated four types of addition bugs observed in children when trained with incorrect procedures.

Conclusions:

• The proposed neural network model effectively simulates arithmetic problem-solving, particularly addition.
• Procedural priming and merging significantly enhance computational efficiency.
• The model's ability to generate common errors provides insights into children's mathematical learning and misconceptions.