Is it possible to measure the intuitive acceptance of a mathematical statement?

The main purpose of the present research was to check the possibility of measuring the feeling of “intuitive acceptance”, experienced by a subject when he offers an intuitive solution to a problem. It was postulated that two dimensions have to be considered and combined: The level of confidence and the degree of obviousness. Almost all the questions asked referred to the notion of infinity. The subjects were pupils belonging to grades 8 and 9. Three main categories of problematic situations have been identified:

1. Problems which got high percentages of correct solutions and high levels of intuitive acceptance.
2. Problems which got two types of contradictory solutions, each of them being accepted with moderate intuitiveness.
3. Problems which got low frequencies of correct solutions and high frequencies of typical incorrect solutions, the second category presenting higher levels of intuitive acceptance than the first (counter-intuitive problematic situations).