A TEACHING
MODEL: A QUALITATIVE-TYPE ANALYSIS IN
PROBLEM SOLVING
Escuela Normal Superior de México
Centro de Investigación y de Estudios vanzados
del IPN, Mexico
dfiguera@mailer.main.conacyt.mx
In the research being carried out with undergraduate mathematics
students at the Escuela Normal Superior
de México, aspects linked to a qualitative analysis in the solving of
non-numerical and school problems related to ratio, proportion, and
proportional variation are being examined.
The theoretical framework is described in López & Figueras (1999),
and a report is also there on the findings of the first two stages. For the third stage of this study, a
methodology is employed that combines a clinical-type inquiry, and
experimentation through a simulation of didactic sequences. The latter requires the construction of a
teaching model, which is put to the test by means of individual
interviews. The model’s didactic
sequences are structured in the form of interview protocols which are organized
as a double-entry matrix. Three main axes
are considered in its design: a) the findings from the analysis of the teaching
models underlying the textbooks used at the aforementioned educational
institution; b) the construction of networks of non-numerical and school
problems dealing with mixtures, mobile objects, proportional sharing,
work/time, water pumps, etc.; and c) the various representations used by
students to solve these kinds of problems, such as qualitative and numerical
variation tables, drawings and schemes.
The direction of the lines in the matrix is based on a series of
problems pertaining to the same class; the first of these is a non-numerical
one, and the last one is a school problem.
The direction of the columns in the matrix defines routes to link
various contexts, and also to graduate the complexity of the different classes
which integrate the matrix to the didactic sequence.
References
López, G., & Figueras, O (1999).
Qualitative reasoning in problem solving related to ratio, proportion, and
proportional variation concepts. In: F.
Hitt, & M. Santos (Eds). Proceedings
of the twenty first meeting of the North American Chapter of the International
Group for Psychology of matehematics Education. Vol. 2 (pp. 599-605).
México: Cinvestav. Columbus, Ohio:
ERIC.