Inverse Modeling Problems and Task Enrichment: Analysis of Two Experiences with Spanish Prospective Teachers

Year 2019, Volume: 6 Issue: 4, 193 - 205, 26.12.2019

Victor Martinez-luaces José Antonio Fernández Plaza Luis Rico

Abstract

Problem solving and problem
posing are both important topics in mathematics education. Since in many
branches of science and technology, typical problems are posed in an inverse
form, we will focus on inverse problems that require modeling skills in order
to be solved, i.e., the so-called inverse modeling problems. In this article,
we will analyze them from the view point of their potential for task
enrichment. For this purpose, a research project was carried out, by using
inverse modeling problems to develop prospective teacher`s task enrichment
skills. The results of this experience, that took place in 2017, showed that
only few participants were very creative, whereas many others posed trivial
problems or simply imitated examples previously analyzed. After that, a new
research essay was implemented during the first months of 2019, with the aim of
avoiding – or at least attenuating – those difficulties observed in the
previous field work. The new results showed some few similarities and very
interesting differences, when compared with the other experience. In this
article, we comment our findings and some conclusions are reported.

Keywords

inverse problems, task enrichment, prospective teachers, mathematical modeling

Supporting Institution

Universidad de Granada, Spain

Project Number

PGC2018-095765-B-100

Thanks

The research was carried out with the support of the research project “Professional Competence of teachers in initial training and STEM Education” (PGC2018-095765-B-100)) of the National R + D + I Plan, and of the Research Group FQM-193: Didactics of Mathematics, Numerical Thought, of the Andalusian Plan for Research, Development and Innovation (PAIDI).

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