A review of the research in teaching and learning the negative numbers: an “action research” concerning the application of the geometrical model of the number line

The notion of negative numbers is one of the most fundamental in mathematics. For many years, they have caused confusion and they have been an object of controversy among great researchers, until the development of symbolic algebra led to their acceptance in the form they have today. When students are first introduced to the concept of negative numbers and the operations between them, various difficulties occur and misconceptions arise, as expected. Their comprehension is one of the most challenging tasks of teaching mathematics due to their complexity and abstract nature. For this purpose, various models have been devised and employed. In the present study we expose some of the epistemological obstacles commonly observed in understanding negative numbers and then exhibit and compare two different models frequently used for introducing the four basic operations between them.