This paper shows an alternative to the traditional teaching approach, focusing on the application of a STE(A)M-based learning methodology. In particular, we present an engineering technology problem-solving approach to encourage and motivate the mathematics learning of high school students by promoting positive beliefs about this subject. We report on qualitative data from a group of seven students and two teachers, who developed high-tech engineering projects during a two-year period, applying mathematical concepts and procedures. This data is part of a quasi-experimental study carried out with more than one hundred Spanish students. The findings revealed that solving problems in an engineering technology context helps to develop a practical sense of the applicability of mathematics, generating students' positive beliefs about this discipline.