Filling vessels An exciting way to investigate functional dependencies

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Laura Sergi
Stefan Götz


When discussing and analyzing functional dependencies, schoolbooks, and teachers often use different filling curves—asking students to match various vessels with their corresponding graphs. After presenting the three basic ideas of functional thinking, the authors demonstrate ways of determining functional equations from analyses of filling data and discuss the use of dynamic applets with students.

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Author Biographies

Laura Sergi, Studyly LLC, Vienna Austria

Laura Sergi,, obtained a master’s degree in teacher education for Mathematics and English at the University of Vienna. In her master’s thesis, she focused on creating GeoGebra applets and their educational value. Laura is now working for Studyly, a digital learning environment that supports pupils in understanding mathematical concepts by providing adaptive and interactive exercises and explanations.

Stefan Götz, Faculty of Mathematics and Centre for Teacher Education, University of Vienna

Stefan Gotz,, is an Associate Professor of Mathematics Education at the University of Vienna, Austria. Stefan’s research interests are didactics of stochastics, didactics of analysis and the interrelation of content knowledge and pedagogical content knowledge in the education of pre-service mathematics teachers.