The research results published so far have shown that success in mathematics positively affects the retention rate at technical and economic universities. Various studies have explored different forms, methods, and tools in mathematics teaching to improve student success, but an effective teaching model is yet to be identified. Based on previous experience and published results, a model of effective teaching was proposed with an emphasis on developing selected cross-sectional competencies to increase student retention. A recent study aimed to verify the effectiveness of this model in the pilot subject Mathematics I. The study included 211 first-year students of 7 bachelor's technical-economic study programs. Results showed significant improvement in the group of students who struggled with mathematics. The study confirmed that an appropriately chosen intervention in mathematics can increase the success rate of completing technical and economic study programs, and this approach can also be applied at other universities.