A STUDY ABOUT THE COMPREHENSION OF GEOMETRIES: THE CASE OF THE BARYCENTER

Appears in: EDULEARN14 Proceedings

Publication year: 2014

Pages: 2505-2512

ISBN: 978-84-617-0557-3

ISSN: 2340-1117

Publication year: 2014

Pages: 2505-2512

ISBN: 978-84-617-0557-3

ISSN: 2340-1117

Conference name: 6th International Conference on Education and New Learning Technologies

Dates: 7-9 July, 2014

Location: Barcelona, Spain

Dates: 7-9 July, 2014

Location: Barcelona, Spain

The pedagogical innovations concern mostly the so called problem-based learning which has been enhanced with the original didactic materials providing visualization and geometric interpretations of abstract mathematical objects.

We will present results from a qualitative study carried out at the end of a mathematics course where there has been analyzed the comprehension of Analytic Geometry (AG) by various groups of university students. In order to evaluate students learning, the authors, based on the assumption that students could achieve meaningful learning if some topics from the Euclidean Geometry (EG) are taken into consideration previously, proposed the problem that is very useful in applications: “Given the coordinates of a system of three particles, find the Center of Masses (barycenter) of the system”. The objective was to study how students take into consideration some elements from the Euclidean geometry to obtain the barycenter “G” in the context of AG as well as to explain the operational use of usual formulas.

Theoretical elements from the Ontosemiotic Approach, OSA, [1], [2], have been employed to describe the mathematical activity carried out by the students. In OSA, mathematical activity plays a central role and is modeled in terms of systems of operative and discursive practices. From these practices, the different types of related mathematical objects emerge, building cognitive (personal perspective) or epistemic (institutional perspective) configurations among them. In this context, problems promote and contextualize the activity; languages (symbols, notations, graphics, etc.) represent the other entities and serve as tools for action; arguments justify the procedures and propositions that relate the concepts.

For the qualitative study we rely on technical analysis of OSA, [3], [4], for describing systematic cognitive configurations (problem-situation, representations, concepts, properties, methods and arguments) of students to solve the task given and perform a comparison with an epistemic reference configuration.

The results of evaluations reveal that most students, who have no previous knowledge of EG, solve the given task operatively (and some are unable to resolve it) and no proper meaning was attributed to certain elements of the AG. However, students who have prior knowledge of EG show a better performance.

Similar results have been obtained on the evaluation of some topics of the courses on Probability and Statistics, depending on the implementation of didactic material providing some technology of visualization.

References:

[1] Godino, J. D., Batanero, C., & Font, V. (2007). The International Journal on Mathematics Education, 39(1-2), pp. 127–135.

[2] Font, V., Planas, N. y Godino, J. D. (2010). Modelo para el análisis didáctico en educación matemática. Infancia y Aprendizaje, 33(1), pp. 89-105.

[3] Malaspina, U. (2007). Revista Latinoamericana de Investigación en Matemática Educativa, 10(3), pp. 365-399.

[4] Malaspina, U., & Font, V. (2010). Educational Studies in Mathematics, 75(1), pp.107-130.

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