In engineering education, the students are often guided by their advisors to take courses related to their areas of expertise. In addition to the courses related to their areas of expertise, especially in the fields of applied engineering, taking math-based statistics or artificial intelligence courses improves students' analytical thinking skills significantly. For this reason, new perspectives for teaching in engineering education are required. In this study, the importance of teaching mathematically based statistical optimization techniques in engineering education has been discussed through an experimental case study. Within the study, the disposal of Drinking Water Treatment Sludge (DWTS) through its use in sandy soil improvement was studied experimentally and it was discussed whether the sludge usage improves the engineering properties of sandy soils. Besides, the experimental process of this research was supported by a Response Surface Methodology (RSM) analysis, thanks to the knowledge of a Ph.D. student.