To prevent difficulties in learning mathematics, effective and innovative teaching methodologies should be used. The present study presents the results of a relational and comparative study between the application of the open number-based algorithm (ABN) and the closed number-based algorithm (CNB) method. The research was of a descriptive cross-sectional quantitative type. Descriptive and comparative, quasi-experimental cross-sectional design study. The sample was 320 students of the first cycle of the National University of Education (UNAE). A multiple choice questionnaire with geometry exercises and a Likert type scale was applied for the data collection. The results were analyzed through an analysis of variance (ANOVA). We worked with two variables, the informal geometric reasoning variable and the formal geometric reasoning variable. We applied a correction of the degrees of freedom with Welch's robust test. The results indicated that the ABN-oriented group (n=151) achieved better results than the CNB-oriented group (n=92). The results were relevant, because the skills demonstrated in the results, show that the ABN method reinforces the capacity to give solution to the exercises, contributing to the development of the numerical sense. Concluding that it can be described as a flexible or innovative model in the field of mathematics teaching.