Abstract:

In this article we present a computer-based learning environment for individualized development of mathematical learning and self-regulated learning competencies.

The learning environment can be used in the secondary school as an introductory module on mathematical modelling. It contains a generalized scheme or a simplified plan for solving typical modelling exercises and demonstrates the execution of this plan applied to a realistic optimization example.

In the present study, the learning software was tested in a number of the eighth grade classes. Correspondingly, the teaching materials were constructed so as to fit the curriculum. In particular, the technical topic of proportions is assumed to be well-known to the learners. Numerous exercises on proportions have to be solved by the learner along the way, while working on the modelling exercise. This allows to refresh this important topic with its broad variety of used representations and changes among them. In this way, the module sets an example of integrating competence development into curricular learning.

Several kinds of scaffolds constitute the heart of the learning environment. On the metacognitive level, the software provides support for planning, monitoring, reflexion and modification processes, both for mastering the small exercises on proportions and the larger modelling exercise. On the cognitive level, the software delivers progressive hints in form of analogous solved examples, as interaction feedback or on the learner’s request. The learning environment is designed in a number of variants, differing with respect to the amount and form of provided scaffolds.

The practical usage of the learning environment in several school classes allowed to compare its variants with respect to the usage preferences and learning effects. For the latter, empirical data were obtained a week before and a week after the learning episode with the software. Tests and questionnaires were employed to observe the learners’ beliefs about mathematics and its applicability to the real-world problems, personal metacognitive problem solving and learning strategies, as well as proficiency in dealing with proportions. Additionally, log files were analysed to obtain a realistic picture of the learner-system interactions and the usage of scaffolds and feedback.

This article reports on the results of the practical employment of the learning environment. The factors effecting learning determined in this study are described and analysed in comparison to those known from the literature. In this way, theoretical foundations and principles of high-quality learning software design are re-examined and critically evaluated. Conclusions are drawn concerning the design of such learning software and the choice of scaffolds and feedback strategies.