The aim of this paper is to present a teaching proposal for the theoretical part relating to the first- and second-order linear difference equations with constant coefficients suitable for the first-year students at various types of universities. In contradistinction to the methods often applied (memorization of algorithms without a proper conceptual understanding), we provide an alternative methodological way-out for lecturers that is partially based on posing suitable questions and constructing the knowledge. Our approach is therefore characterized by the minimal input knowledge imposed on students. In fact, we assume that students are acquainted only with the summation of terms of geometric sequences and with solving linear and quadratic equations.