# The modulating role of sources of difficulty in interactive matchstick algebra

## TL;DR

This study examines how physical interaction affects problem-solving success in matchstick algebra, finding that it can sometimes hinder performance.

## Contribution

The paper introduces a nuanced view of how interactivity influences problem-solving based on specific difficulty sources.

## Key findings

- Interactive problem-solving did not lead to successful solutions in the experiments.
- Motor activity interfered with relaxing higher-level cognitive constraints.
- Physical interaction may hinder performance if it misaligns with cognitive demands.

## Abstract

Interactive problem solving has been proposed as an experimental manipulation that significantly increases the success of solving various matchstick algebra problems by allowing solvers to interact with physical representations of the problems. In contrast to this claim, we hypothesized that the influence of interactivity would vary based on the specific sources of difficulty inherent in the problems: perceptual chunks and cognitive constraints. We carried out a conceptual extended replication across three experimental series with conditions of varying degrees of interactivity, but failed to reproduce interactive solutions amongst our participants. A follow-up analysis of motor activity showed that the movements of the solvers did not contribute to chunk decomposition but significantly interfered with the relaxation of higher-level constraints. These findings suggest that motor activity can hinder performance when it does not align with the cognitive demands of the task. We therefore call for a more targeted and problem-specific understanding of how physical interaction contributes to restructuring in insight problem solving.