Why introductory experiments on functional relationships should be qualitative to foster covariation
Résumé
The covariation aspect of functional thinking (FT) is difficult for students but at the same time central for the development of a concept of function. Looking at high school mathematics, covariation is not in focus. Prevalent approaches put the well accessible correspondence aspect in foreground and support this imbalance with numeric processing. Although student experiments have proven to be a beneficial introduction to functional relationships, the measurements collection could contribute to this problem. In our pre-post-test intervention study, we contrast a numerical and a qualitative introductory learning environment to functional relationships with a combination of hands-on and digital experiments. Results (N = 332) show significant increases in functional thinking in both settings, but significantly higher gains in the qualitative setting. Effects of the constraints cooperation level and school form indicate possibly relevant influential factors on this lead in line with theory.
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