Abstract The objective of this investigation was to determine the styles of reasoning according to the taxonomy structured of observed learning objectives of John Biggs in the students of geometry of the specialty of mathematics of the “Universidad Pedagógica Experimental Libertador”, Venezuela. The stated problem is that teachers of mathematics must know the problems of teaching mathematics; besides, they should know how their students learn, since according to the reasoning styles of John Biggs, one can determine how and with what depth a person learns. The methodology is quantitative, not experimental, and descriptive at the field level, where specialized literature was reviewed, and the results obtained from the application of the test with the super-item, as a data collection instrument, were analyzed by objectives based on the construction of the database in statistical package for the social sciences, the statistical analysis and the detailed interpretation of the procedure performed for each item, which allowed the analysis and interpretation of the results. These results reach the uni-structural level catalogued by Biggs as inferior or superficial. Therefore, recommendations are offered to improve the learning level of the students in question.