How digital tools support the validation of outdoor modelling results

Abstract

Mathematical modelling addresses numerous demands of modern mathematics education: The learning of mathematics is directly linked to reality and hence to real objects. At the same time, these tasks are very challenging for students, especially when their own solution process needs to be validated and refined. Studies even show that some students do not validate their results at all. Recent research has shown that digital tools can enhance the support of modelling activities in different ways. In this paper, we take the modelling step of validation into a deeper account and explore the potential of MathCityMap, a digital tool for outdoor mathematics education. Hereby, its automatic solution validation by means of a predefined interval and assessment of the result’s quality are taken into consideration. The modelling activities of secondary school students are compared on a quantitative and qualitative level – half of the students working with the MathCityMap app and half of them solving the tasks without any digital support. Based on the quantitative results, we can see that the app functionalities for elaborative feedback are used to varying degrees: While student groups frequently access the hints, the sample solution is hardly accessed. Moreover, our analysis can show the value of corrective app feedback. Student groups that used the app solved a comparable number of problems, but failed significantly less often than student groups that worked on math trails without the app. The qualitative results show that in particular the solution validation forces the students to proceed with a second run in the modelling cycle if a result is valued as wrong in the app. In addition, it helps the students to assess their own result in terms of its correctness. Based on the combined results, we draw conclusions about the app usage in mathematical modelling tasks.