The paper presents an experiment carried out with 354 eleven to twelve year old pupils from schools in Ústí nad Labem and Prague regions. It answers a fundamental question: “What solving strategies do these pupils tend to use?” We focused on heuristic solving strategies: Analogy, Graphical representation, Guess – Check – Revise and Auxiliary Elements, and their spontaneous use by pupils in solving “nonschool” problems.
The presented research suggests that for eleven to twelve year old pupils it is most convenient to develop Graphical representation and Auxiliary element strategies.