The aim of the project was to develop, introduce to schools and evaluate a method of teaching the concept of "minus" in school mathematics (negative numbers and their opposites) on the basis of an educational game, implementing the constructivist approach to teaching with the use of activity-based methods and work with concrete materials - tokens, developed in the project. Our approach aimed to help students overcome common misconceptions such as "-x is less than zero". The approach has been designed to serve both as an introduction to negative numbers and algebraic expressions, and to help students who express difficulty in understanding concepts already introduced. It should be suitable for inclusive education for students with learning difficulties and for mathematically gifted young children.
Difficulties in understanding negative numbers and algebraic expressions involving operations on them are well known in the mathematics classroom practice and reported in research. The main motivation for this project is to find a way to overcome these difficulties. A common practice for introducing negative numbers in schools is to use models based on the number line, where the initial, basic assumption is that any negative number is less than zero. The consequence of learning negative numbers only on the basis of this model can be a very common misunderstanding that "-x" represents a negative number and is not interpreted in algebraic terms as an element opposite to x. This misinterpretation leads to profound difficulties in understanding and dealing with algebraic expressions. The results of the project provide the algebraic interpretation of the sign "minus" as "the opposite of", which is consistent with the interpretation of "minus" for "-x". Therefore, we claim that the introduction of our proposed model as an additional pedagogical model with the use of tokens in mathematics teaching should help to overcome the difficulties described above for a wide range of students, including those with special educational needs.