La introducción de la modelación matemática en el currículo de enseñanza media chileno, hace ya una decena de años, ha relevado la necesidad de estudios relativos a las prácticas de su enseñanza en la formación inicial de profesores en el país. Este trabajo presenta los resultados de una investigación que utiliza el marco conocimiento especializado del profesor de matemáticas (MTSK, por sus siglas en inglés) para analizar los conocimientos y la reflexión sobre modelación puestos en juego por estudiantes en formación inicial durante un ciclo de 14 sesiones de 90 minutos cada una. Los resultados muestran un progreso en el conocimiento matemático y en el conocimiento pedagógico del contenido. El trabajo discute posibles maneras de establecer modelos de enseñanza de la modelación y un momento propicio para hacer uso de una propuesta sobre la materia.

School is a space where learning mathematics should be accompanied by the student’s preferences; however, its valuation in the classroom is not necessarily the same. From a quantitative approach, we ask from the mathematical thinking styles (MTS) theory about the correlations between preferences of certain MTS and mathematical performance. For this, a valid test instrument and a sample of 275 16-year-old Chilean students were used to gain insight into their preferences, beliefs and emotions when solving mathematical tasks and when learning mathematics. The results show, among other things, a clear positive correlation between mathematical performance and analytical thinking style, and also evidence the correlation between self-efficacy, analytical thinking and grades. It is concluded that students who prefer the analytical style are more advantageous in school, since the evaluation processes have a higher valuation of analytic mathematical thinking.

This study shows the qualitative construction of a Referential Cognitive Graduate Profile (RCGP) for the Computer Engineering program of the University of Bernardo O'Higgins (UBO) in Chile, based on the theory of Mental Self-Governance and by using three data-gathering methods: document analysis, interviews, and questionnaires, reflecting the professional competencies expected by the end of the training, set forth by both the institution and program management. The proposed model allows to contrast the different thinking styles (TSs) found with the ones preferred by students in different levels of formation independently. With this purpose in mind, by using a quantitative methodology, 88% of male students in the program completed the questionnaires to determine these preferences, enabling us to perform a correspondence analysis through Fisher's exact test. The RCGP results show evident preference for the legislative, executive, hierarchical, and external styles of thinking and clear differences between the preferences of students and of the RCGP. Finally, we discuss about various ways to create new means to strengthen and upgrade both the program's graduate profile and the RCGP with the purpose of benefitting the formation of Computer Engineers and the future of the RCGP model.

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