# Insight elements of mathematical problem solving in generally gifted and mathematical experts: ERP amplitudes in PO electrodes

## TL;DR

This study explores how gifted students and math experts solve different types of math problems, using brain activity to understand insight and strategy-based problem solving.

## Contribution

The study links ERP amplitudes in PO electrodes to insight-based problem solving and relates them to general giftedness and mathematical expertise.

## Key findings

- Giftedness and mathematical expertise influence accuracy and reaction time in solving different math problems.
- ERP amplitudes in PO4/8 electrodes correlate with insight-based problem solving.
- Mathematical expertise is more important for strategic problem solving than general giftedness.

## Abstract

School mathematics mainly embraces algorithmic problem solving, pays less attention to strategic reasoning, and rarely contains insightful problem solving. Based on our previous research, we hypothesize that success in solving insight problems correlates strongly with general giftedness, while mathematical expertise is essential for strategy-based problem solving. Furthermore, we employ a phenomenon of greater ERP amplitudes in PO4/8 electrodes associated with insightful problem solving. In this study, 114 high school students (aged 16–18) with varying degrees of general giftedness and mathematical expertise were asked to solve mathematical problem of three distinct type: (1) function problems, whose solutions are memory-based; (2) area problems that necessitate strategic thinking; and (3) insight problems, that necessitate insight for their resolution. The problem solving process was accompanied by ERP recording. We demonstrate that variations in accuracy of solutions and reaction time for correct responses between tasks are influenced by students’ general giftedness and mathematical expertise. Our ERP analyses partly supported our hypotheses regarding the relationship between PO electrode activation, insight-based problem solving processes, and participants’ levels of giftedness and mathematical expertise.