We present a study carried out in Uruguay, with secondary school students and tertiary level mathematics students, concerning the zero-product property. In our research we observed that when early secondary and late secondary school students have to solve equations of the form (ax + b)(cx + d) = 0, they do not always apply the property, even when it is the only available tool and have received specific instruction on its application to the resolution of equations of this type. We also detected an error that students make when they have to verify the solutions of this type of equations. The error consists of the assignment of two different values to the unknown simultaneously. Our study also revealed that late secondary and tertiary level students show a certain tendency to generalize the zero-product property to other algebraic structures where it is not always valid.
Ochoviet, Cristina and Oktaç, Asuman
"IF A.B = 0 THEN A = 0 or B = 0?,"
The Mathematics Enthusiast: Vol. 6
, Article 12.
Available at: http://scholarworks.umt.edu/tme/vol6/iss1/12