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If students are very much familiar of basics of mathematics and the problem-solving skills, teachers must place emphasis on both the core contents and the numerical processes in the teaching and understanding of mathematics. This research presents the logical rationale and the key of study on deep to the understanding of mathematics. A survey was conducted on students of around 19 years of age and the findings indicated that students did employ the five phases of problem solving emphasized by Faculties. However, students fared better when they regulated their thinking process or employed study on deep skills in the process of solving numerical problems. This research also suggests the strength of a combined methodology in doing research by expanding an understanding from one methodology to another, and converging findings from different data sources.