Syntactical and semantic aspects in solving equations: a study with 14 year old pupils

The capacity to write and to solve equations is a crucial point in the construction of algebraic thinking, since it involves both the mastery of the formal rules of algebraic language and calculation, as well as the correct interpretation of the meaning of the symbols used. Our research study is mainly concentrated on examining the possibility of improving the capacity of students to solve first grade equations during their first year of high school, by establishing a dialectical relationship between the application of properties and their semantic control. In this report we would like to present certain observations concerned with the problem exposed in relation to equations without solutions or with an infinite number of solution