Shaping an Adaptive Path on Analytic Geometry with Automatic Formative Assessment and Interactive Feedback

This paper proposes a contribution to the practice of automatic formative assessment and adaptive education to highlight how it enhances the teaching and learning of Mathematics in secondary school. In this context we developed an adaptive learning path on Analytic Geometry, whose potential is discussed in the light of a theoretical framework, by describing and analyzing some activities. The activities allowed to introduce, address, explore the circle both as a geometric locus and its relationship with real situations through contextualized problems. The effectiveness of the path to reach the learning outcomes was tested through a quasi-experimental research design. The experimentation involved 98 third-year students from two upper secondary schools in Turin, Italy. Results were monitored through pre- and post-tests whose outcomes were compared with those of a control group; in addition, a final questionnaire was administered to the treated group. The results show the effectiveness o f the tested activities in improving mathematical understanding; they also suggest strategies to introduce automatic formative assessment for adaptive learning in an effective way into a learning path, but they also highlight the need of solid pedagogical foundations which require continuous training of teachers by experts.